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CN116432338A - Design method and structure for repairing internal damaged cylindrical pressure-resistant shell by adopting composite material - Google Patents

Design method and structure for repairing internal damaged cylindrical pressure-resistant shell by adopting composite material Download PDF

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CN116432338A
CN116432338A CN202310229041.7A CN202310229041A CN116432338A CN 116432338 A CN116432338 A CN 116432338A CN 202310229041 A CN202310229041 A CN 202310229041A CN 116432338 A CN116432338 A CN 116432338A
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滕赟
张建
展铭
王明禄
狄陈阳
萨克迪拉特-凯文鲁恩
李政
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Jiangsu University of Science and Technology
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Abstract

本发明公开了一种采用复合材料修复内部损伤柱形耐压壳的设计方法及结构，方法包括以下步骤：第一步：判断长短壳；第二步：确定完美柱壳设计压力；第三步：确定缺陷柱壳断裂应力；第四步：确定缺陷柱壳设计压力；第五步：设计复合材料修复层；第六步：有限元验证。本发明中以柱形耐压壳初始与修复后的承载能力相同为基准，会根据管道内部损伤程度不同，计算出具体的修复方案，给出修复层数和修复长度。利用该设计方法修复的内部损伤柱形耐压壳，可最大化的节约修复成本，保证恢复初始承载能力的同时，阻断后续海洋环境对该区域柱壳表面二次腐蚀。

Figure 202310229041

The invention discloses a design method and structure for using composite materials to repair internally damaged cylindrical pressure-resistant shells. The method includes the following steps: the first step: judging the length of the shell; the second step: determining the design pressure of the perfect cylindrical shell; the third step : Determine the fracture stress of the defective cylindrical shell; the fourth step: determine the design pressure of the defective cylindrical shell; the fifth step: design the composite repair layer; the sixth step: finite element verification. In the present invention, the initial and repaired bearing capacity of the cylindrical pressure shell is the same as the benchmark, and the specific repair plan is calculated according to the degree of internal damage of the pipeline, and the number of repair layers and repair length are given. The internally damaged cylindrical pressure hull repaired by this design method can save the repair cost to the greatest extent, ensure the restoration of the initial bearing capacity, and block the secondary corrosion of the surface of the cylindrical shell in the subsequent marine environment.

Figure 202310229041

Description

采用复合材料修复内部损伤柱形耐压壳的设计方法及结构Design method and structure of cylindrical pressure hull repaired with composite materials

技术领域Technical Field

本发明涉及深海工程维修技术领域，尤其是涉及采用复合材料修复内部损伤柱形耐压壳的设计方法及结构。The invention relates to the technical field of deep sea engineering maintenance, and in particular to a design method and structure for repairing an internally damaged cylindrical pressure hull using composite materials.

背景技术Background Art

目前，为了探索海洋领域、开发海洋资源，海洋工程装备已成为大洋勘查和深海研究的重要组成部分。人类构建深海空间站、深海管道体系以及制造核动力潜艇等不同种类的潜水器进行探测海底世界，而随着下潜深度增加，设备承受的静水压力会越大，圆柱形耐压壳作为大部分海洋工程装备的主体结构，因其加工难度低，承载能力强，成熟的加工工艺，良好的强度、稳定性，壳体空间利用率，被广泛应用于油气运输、深海潜器等工程领域。At present, in order to explore the ocean and develop marine resources, marine engineering equipment has become an important part of ocean exploration and deep-sea research. Humans build deep-sea space stations, deep-sea pipeline systems, and manufacture different types of submersibles such as nuclear-powered submarines to explore the underwater world. As the diving depth increases, the hydrostatic pressure on the equipment will increase. The cylindrical pressure hull is the main structure of most marine engineering equipment. It is widely used in engineering fields such as oil and gas transportation and deep-sea submersibles because of its low processing difficulty, strong bearing capacity, mature processing technology, good strength, stability, and hull space utilization.

然而，为了满足相应的工艺制造要求、存储腐蚀性液体或油气运输，长时间使用会造成局部腐蚀、内壁减薄，形成局部失稳，以致寿命降低。现有的维修技术则是通过钢套加固、更换设备或者利用焊接技术进行维修，而在实际操作过程中，由于处于深海环境下使得维修难度增加，成本升高，以及在维修后也无法避免海水对于壳体表面的二次腐蚀。However, in order to meet the corresponding process manufacturing requirements, store corrosive liquids or transport oil and gas, long-term use will cause local corrosion, thinning of the inner wall, local instability, and reduced life. The existing maintenance technology is to reinforce the steel sleeve, replace the equipment or use welding technology for maintenance. In actual operation, due to the deep sea environment, the maintenance difficulty increases, the cost increases, and after the maintenance, it is impossible to avoid secondary corrosion of the shell surface by seawater.

如今，复合材料，如纤维增强聚合物复合材料被广泛使用在各个领域，如压力容器的设计、飞机的机翼、汽车的车身等。纤维增强聚合物复合材料凭借其防腐蚀、强度高的优点，应用于柱形耐压壳的维修具有可行性，而如何将纤维增强聚合物复合材料作为金属管道的修复材料，基于现有维修技术存在的弊端，在修复过程中实现原位精确快速修复、高安全性以及高经济性，则是亟待解决的问题。Nowadays, composite materials, such as fiber-reinforced polymer composites, are widely used in various fields, such as pressure vessel design, aircraft wings, and automobile bodies. With its advantages of corrosion resistance and high strength, fiber-reinforced polymer composites are feasible for the repair of cylindrical pressure hulls. However, how to use fiber-reinforced polymer composites as repair materials for metal pipes, based on the drawbacks of existing repair technologies, to achieve in-situ precise and rapid repair, high safety, and high economy during the repair process is an urgent problem to be solved.

发明内容Summary of the invention

发明目的：针对上述问题，本发明的目的是提供一种采用复合材料修复内部损伤柱形耐压壳的设计方法，提出具体修复方案解决现有问题，增强安全性，降低成本。并提出了其修复结构。Purpose of the invention: In view of the above problems, the purpose of the present invention is to provide a design method for repairing internally damaged cylindrical pressure hulls using composite materials, propose a specific repair solution to solve existing problems, enhance safety, and reduce costs. And propose its repair structure.

技术方案：一种采用复合材料修复内部损伤柱形耐压壳的设计方法，包括以下步骤：Technical solution: A design method for repairing internally damaged cylindrical pressure hulls using composite materials, comprising the following steps:

第一步：判断长短壳；Step 1: Determine the length of the shell;

根据耐压壳的外径D和壁厚t计算临界长度Lcr,对于耐压壳进行判断分类，其中：The critical length L cr is calculated based on the outer diameter D and wall thickness t of the pressure hull, and the pressure hull is judged and classified, where:

Figure BDA0004119529210000021
Figure BDA0004119529210000021

当耐压壳计算长度≥临界长度时，为长柱壳；当耐压壳计算长度<临界长度，为短柱壳；When the calculated length of the pressure shell is ≥ the critical length, it is a long cylindrical shell; when the calculated length of the pressure shell is < the critical length, it is a short cylindrical shell.

第二步：确定完美柱壳设计压力；Step 2: Determine the perfect column shell design pressure;

对于钢制柱形耐压壳，当处于深海中，外部压力均匀的作用在柱壳表面，按照耐压壳的分类按以下公式进行壳体临界压力的计算：For a steel cylindrical pressure hull, when it is in the deep sea, the external pressure acts evenly on the surface of the cylindrical hull. According to the classification of the pressure hull, the critical pressure of the hull is calculated according to the following formula:

长柱壳：

Figure BDA0004119529210000022
Long cylindrical shell:
Figure BDA0004119529210000022

短柱壳：

Figure BDA0004119529210000023
Short cylindrical shell:
Figure BDA0004119529210000023

其中，L为柱壳长度，E为柱壳的弹性模量，Pcr为临界压力；Where, L is the length of the cylindrical shell, E is the elastic modulus of the cylindrical shell, and P cr is the critical pressure;

考虑耐压壳成型过程中多种因素对临界压力造成的不良影响，引入安全系数m，则满足临界压力为设计压力为：Considering the adverse effects of various factors on the critical pressure during the pressure hull forming process, the safety factor m is introduced, and the critical pressure is satisfied as the design pressure:

Figure BDA0004119529210000024
Figure BDA0004119529210000024

第三步：确定缺陷柱壳断裂应力；Step 3: Determine the fracture stress of the defective cylindrical shell;

S1：确定缺陷区域的具体形态，引入缺陷当量长度z,求出缺陷在轴向穿壁平面的投影面积S：S1: Determine the specific shape of the defect area, introduce the defect equivalent length z, and calculate the projection area S of the defect on the axial through-wall plane:

Figure BDA0004119529210000025
Figure BDA0004119529210000025

其中，l为损失最大轴向长度，d为损失的最大深度，davg为损失平均厚度；Among them, l is the maximum axial length of the loss, d is the maximum depth of the loss, and d avg is the average thickness of the loss;

S2：根据缺陷程度，γ＝d/t，确定材料的流变应力Sflow：S2: According to the degree of defect, γ = d/t, determine the flow stress S flow of the material:

Figure BDA0004119529210000026
Figure BDA0004119529210000026

其中，SMYS为最小屈服强度；Among them, SMYS is the minimum yield strength;

S3：计算内部损失柱壳环向断裂应力：S3: Calculate the annular fracture stress of the internal loss cylindrical shell:

以Dugdale塑性尺寸模型、受外压耐压壳的轴向缺陷的Folias分析和经验的缺陷深度与柱壳厚度关系为基础，得到环向断裂应力为：Based on the Dugdale plastic size model, the Folias analysis of the axial defect of the pressure shell under external pressure and the empirical relationship between the defect depth and the thickness of the cylindrical shell, the circumferential fracture stress is obtained as:

Figure BDA0004119529210000027
Figure BDA0004119529210000027

其中，SF为环向断裂应力，S0为缺陷处原始管壁的横截面积，S0＝lt，Mt为Flias系数，代入投影面积S，则：Where, SF is the circumferential fracture stress, S0 is the cross-sectional area of the original pipe wall at the defect, S0 = lt, Mt is the Flias coefficient, and substituting it into the projected area S, we get:

Figure BDA0004119529210000031
Figure BDA0004119529210000031

第四步：确定缺陷柱壳设计压力；Step 4: Determine the design pressure of the defective column shell;

柱形耐压壳失效压力PF：Failure pressure PF of cylindrical pressure hull:

PF＝SF2t/D； PF = SF 2t/D;

柱形耐压壳设计压力PS：Design pressure PS of cylindrical pressure hull:

PS＝PF/SF； PS = PF / SF;

其中，SF为常数，SF＝1.2～1.6；Wherein, SF is a constant, SF = 1.2 ~ 1.6;

第五步：设计复合材料修复层；Step 5: Design the composite repair layer;

修复厚度：Repair thickness:

Figure BDA0004119529210000032
Figure BDA0004119529210000032

其中，Ep为柱壳的拉伸模量，Ea为纤维增强聚合物轴向的拉伸模量，Pd为设计压力；Where, Ep is the tensile modulus of the cylindrical shell, Ea is the axial tensile modulus of the fiber-reinforced polymer, and Pd is the design pressure;

修复长度：Repair Length:

F＝2πrtσy；F = 2πrtσ y ;

Figure BDA0004119529210000033
Figure BDA0004119529210000033

其中，F为柱形耐压壳轴向屈服载荷；l0为修复长度；σy柱形耐压壳的屈服强度，τ为粘合剂的剪切强度，r为柱形耐压壳外部半径。Where, F is the axial yield load of the cylindrical pressure hull; l 0 is the repair length; σ y is the yield strength of the cylindrical pressure hull, τ is the shear strength of the adhesive, and r is the outer radius of the cylindrical pressure hull.

进一步的，在第二步中，耐压壳成型过程中考虑的因素包括因加工操作、制造造成的误差及材料性能在加工过程中存在硬化现象，安全系数m的取值范围为1.2～1.5。Furthermore, in the second step, factors to be considered during the pressure hull forming process include errors caused by processing operations and manufacturing, and hardening of material properties during processing, and the safety factor m ranges from 1.2 to 1.5.

进一步的，在第三步的步骤S1中，缺陷当量长度z为：Furthermore, in step S1 of the third step, the defect equivalent length z is:

Figure BDA0004119529210000034
Figure BDA0004119529210000034

当z≤20时；When z≤20;

Figure BDA0004119529210000035
Figure BDA0004119529210000035

当z＞20时；When z＞20;

沿着轴向等间距h测量缺陷深度分别为d0、d1、d2...dn、dn+1，共测量n+1次构成n个梯形：The defect depths are measured at equal intervals h along the axial direction, and are d 0 , d 1 , d 2 ... d n , d n+1 , respectively. A total of n+1 measurements are made to form n trapezoids:

Figure BDA0004119529210000041
Figure BDA0004119529210000041

其中，d0、dn为两端的深度，在理想情况下可视为0，则有：Among them, d 0 and d n are the depths of the two ends, which can be regarded as 0 in an ideal situation, so:

Figure BDA0004119529210000045
Figure BDA0004119529210000045

进一步的，在第三步的步骤S3中，Mt由l、Di、t确定：Furthermore, in step S3 of the third step, M t is determined by l, D i , and t:

Figure BDA0004119529210000042
Figure BDA0004119529210000042

Figure BDA0004119529210000043
Figure BDA0004119529210000043

其中，Di为耐压壳内径；Where, D i is the inner diameter of the pressure shell;

将Mt进行修正，其表达式可分为：After M t is corrected, its expression can be divided into:

Figure BDA0004119529210000044
Figure BDA0004119529210000044

其中，λ为缺陷柱壳系数。Among them, λ is the imperfect cylindrical shell coefficient.

最佳额，本发明还包括第六步，有限元验证：分别建立初始、缺陷和修复的几何模型与有限元模型，确定模型各部分的截面参数，对复合材料赋予相应的铺层角度；采用非线性屈曲分析，定义有限元模型边界条件，在给予微小缺陷模拟真实耐压壳极限屈曲载荷，比较三者的屈曲载荷，验证理论计算的修复条件满足内部损伤柱形耐压壳修复状态。Optimally, the present invention also includes a sixth step, finite element verification: respectively establishing the initial, defective and repaired geometric models and finite element models, determining the cross-sectional parameters of each part of the model, and assigning corresponding ply angles to the composite material; using nonlinear buckling analysis, defining the boundary conditions of the finite element model, simulating the real pressure hull limit buckling load by giving tiny defects, comparing the buckling loads of the three, and verifying that the repair conditions calculated theoretically meet the repair state of the internally damaged cylindrical pressure hull.

一种上述的采用复合材料修复内部损伤柱形耐压壳设计方法得到的修复结构，包括柱形耐压壳、复合材料修复层，柱形耐压壳上厚板的内壁上具有损伤缺口，复合材料修复层在损伤缺口的位置处固定于厚板的外壁上，复合材料修复层覆盖损伤缺口，且其沿柱形耐压壳轴向的长度大于损伤缺口沿柱形耐压壳轴向的长度。A repair structure obtained by the above-mentioned design method of using composite materials to repair internally damaged cylindrical pressure hulls includes a cylindrical pressure hull and a composite material repair layer. The inner wall of the thick plate on the cylindrical pressure hull has a damaged notch. The composite material repair layer is fixed to the outer wall of the thick plate at the position of the damaged notch. The composite material repair layer covers the damaged notch, and its length along the axial direction of the cylindrical pressure hull is greater than the length of the damaged notch along the axial direction of the cylindrical pressure hull.

最佳的，复合材料修复层的材料为纤维增强聚合物复合材料。Preferably, the material of the composite repair layer is a fiber reinforced polymer composite.

有益效果：与现有技术相比，本发明的优点是：Beneficial effects: Compared with the prior art, the advantages of the present invention are:

1、本发明以柱形耐压壳初始与修复后的承载能力相同为基准，会根据管道内部损伤程度不同，计算出具体的修复方案，给出修复层数和修复长度。利用该设计方法修复的内部损伤柱形耐压壳，可最大化的节约修复成本，保证恢复初始承载能力的同时，阻断后续海洋环境对该区域柱壳表面二次腐蚀。1. The present invention takes the same bearing capacity of the cylindrical pressure hull at the beginning and after repair as the benchmark, and will calculate the specific repair plan according to the different degrees of internal damage of the pipeline, and provide the number of repair layers and repair length. The internally damaged cylindrical pressure hull repaired by this design method can save the repair cost to the maximum extent, ensure the restoration of the initial bearing capacity, and block the subsequent marine environment from secondary corrosion to the surface of the cylindrical hull in this area.

2、本发明设计符合计算纤维增强聚合物复合材料修复层的最小数值，利用共节点的方式进行有限元验证，考虑了采用非线性屈曲计算验证理论设计的修复参数的正确性，保证了评估方法的有效性。2. The design of the present invention complies with the calculation of the minimum value of the fiber reinforced polymer composite material repair layer, uses the common node method to perform finite element verification, takes into account the correctness of the repair parameters designed by nonlinear buckling calculation verification theory, and ensures the effectiveness of the evaluation method.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

图1为本发明方法流程图；Fig. 1 is a flow chart of the method of the present invention;

图2为修复后的柱形耐压壳结构示意图；FIG2 is a schematic diagram of the repaired cylindrical pressure hull structure;

图3为z≤20时柱形耐压壳缺陷区域投影面积S设计说明图；FIG3 is a design diagram illustrating the projection area S of the defect region of the cylindrical pressure hull when z≤20;

图4为z＞20时柱形耐压壳缺陷区域投影面积S设计说明图；FIG4 is a design diagram illustrating the projection area S of the defect region of the cylindrical pressure hull when z＞20;

图5为实施例1修复区域示意图；FIG5 is a schematic diagram of the repair area of Implementation Example 1;

图6为实施例2修复区域示意图；FIG6 is a schematic diagram of the repair area in Example 2;

图7为实施例3修复区域示意图；FIG7 is a schematic diagram of the repair area of Example 3;

图8为实施例4修复区域示意图；FIG8 is a schematic diagram of the repair area of Implementation Example 4;

图9为实施例5修复区域示意图；FIG9 is a schematic diagram of the repair area of Implementation Example 5;

图10为实施例6修复区域示意图；FIG10 is a schematic diagram of the repair area of Implementation Example 6;

图11为实施例修复效果图。FIG. 11 is a diagram showing the repair effect of the embodiment.

具体实施方式DETAILED DESCRIPTION

下面结合附图和具体实施例，进一步阐明本发明，应理解这些实施例仅用于说明本发明而不用于限制本发明的范围。The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

一种采用复合材料修复内部损伤柱形耐压壳的设计方法，参见图1，包括以下步骤：A design method for repairing an internally damaged cylindrical pressure hull using composite materials, as shown in FIG1 , comprises the following steps:

第一步：判断长短壳；Step 1: Determine the length of the shell;

根据耐压壳的直径(D)和壁厚(t)计算临界长度(Lcr),对于耐压壳进行判断分类The critical length (L cr ) is calculated based on the diameter (D) and wall thickness (t) of the pressure hull, and the pressure hull is classified.

Figure BDA0004119529210000051
Figure BDA0004119529210000051

判断标准：当耐压壳计算长度≥临界长度时，为长柱壳；当耐压壳计算长度<临界长度，为短柱壳。Judgment criteria: When the calculated length of the pressure shell is ≥ the critical length, it is a long cylindrical shell; when the calculated length of the pressure shell is < the critical length, it is a short cylindrical shell.

第二步：确定完美柱壳设计压力；Step 2: Determine the perfect column shell design pressure;

对于钢制柱形耐压壳，当处于深海中，外部压力均匀的作用在柱壳表面，按照耐压壳的分类按以下公式进行壳体临界压力的计算(弹性范围内)：For a steel cylindrical pressure hull, when it is in the deep sea, the external pressure acts evenly on the surface of the cylindrical hull. According to the classification of the pressure hull, the critical pressure of the hull is calculated according to the following formula (within the elastic range):

长柱壳：

Figure BDA0004119529210000061
短柱壳：
Figure BDA0004119529210000062
Long cylindrical shell:
Figure BDA0004119529210000061
Short cylindrical shell:
Figure BDA0004119529210000062

其中，L为柱壳长度，E为柱壳的弹性模量，Pcr为临界压力，由于柱壳在成型过程中，因加工操作、制造造成的误差及材料性能在其过程中存在硬化现象等因素会对耐压壳的临界压力造成不良影响，在计算时需要考虑安全系数m＝1.2～1.5。Wherein, L is the length of the column shell, E is the elastic modulus of the column shell, and P cr is the critical pressure. During the forming process of the column shell, errors caused by processing operations and manufacturing, as well as hardening of material properties during the process, will have an adverse effect on the critical pressure of the pressure shell. Therefore, a safety factor of m = 1.2 to 1.5 needs to be considered in the calculation.

设计压力：

Figure BDA0004119529210000063
Design Pressure:
Figure BDA0004119529210000063

第三步：确定缺陷柱壳断裂应力；Step 3: Determine the fracture stress of the defective cylindrical shell;

S1：确定缺陷区域的具体形态，引入缺陷当量长度z：

Figure BDA0004119529210000064
其中，l为损失最大轴向长度，求出缺陷在轴向穿壁平面的投影面积S：S1: Determine the specific shape of the defect area and introduce the defect equivalent length z:
Figure BDA0004119529210000064
Where l is the maximum axial length of the loss, and the projection area S of the defect on the axial through-wall plane is calculated as:

如图3所示，当z≤20时：

Figure BDA0004119529210000065
其中，d为损失的最大深度；As shown in Figure 3, when z≤20:
Figure BDA0004119529210000065
Where d is the maximum depth of loss;

如图4所示当z＞20时，沿着轴向等间距h测量缺陷深度分别为d0、d1、d2…dn、dn+1共测量n+1次构成n个梯形As shown in FIG4 , when z>20, the defect depths are measured along the axial direction at equal intervals h, and are d 0 , d 1 , d 2 ... d n , d n+1 respectively. A total of n+1 measurements are made to form n trapezoids.

Figure BDA0004119529210000066
Figure BDA0004119529210000066

d0、dn为两端的深度，在理想情况下可视为0，则有：d 0 and d n are the depths of the two ends, which can be regarded as 0 in an ideal situation, then:

Figure BDA0004119529210000067
Figure BDA0004119529210000067

综上可得缺陷在轴向穿壁平面的投影面积S：In summary, the projection area S of the defect on the axial through-wall plane is:

Figure BDA0004119529210000068
其中，davg为损失平均厚度。
Figure BDA0004119529210000068
Where d avg is the average thickness of the loss.

S2：根据缺陷程度，γ＝d/t，确定材料的流变应力Sflow：S2: According to the degree of defect, γ = d/t, determine the flow stress S flow of the material:

Figure BDA0004119529210000069
Figure BDA0004119529210000069

其中，SMYS为最小屈服强度。Where SMYS is the minimum yield strength.

S3：计算内部损失柱壳环向断裂应力：S3: Calculate the annular fracture stress of the internal loss cylindrical shell:

该公式以Dugdale塑性尺寸模型、受外压耐压壳的轴向缺陷的“Folias”分析和经验的缺陷深度与柱壳厚度关系为基础，其表达式为：The formula is based on the Dugdale plastic size model, the "Folias" analysis of axial defects in pressure hulls subjected to external pressure, and the empirical relationship between defect depth and cylindrical shell thickness. Its expression is:

Figure BDA0004119529210000071
Figure BDA0004119529210000071

其中SF：环向断裂应力；S0：缺陷处原始管壁的横截面积，S0＝lt；Mt:Flias系数，它由l、Di、t确定，由下式确定：Where S F : circumferential fracture stress; S 0 : cross-sectional area of the original pipe wall at the defect, S 0 = lt; M t : Flias coefficient, which is determined by l, Di , and t, and is determined by the following formula:

Figure BDA0004119529210000072
Figure BDA0004119529210000072

将Mt进行修正，其表达式可分为：After M t is corrected, its expression can be divided into:

Figure BDA0004119529210000073
Figure BDA0004119529210000073

其中，λ为缺陷柱壳系数，此处z的范围是依据柱壳整体结构确定。Among them, λ is the defective cylindrical shell coefficient, and the range of z here is determined according to the overall structure of the cylindrical shell.

根据修正后的断裂应力SF：

Figure BDA0004119529210000074
According to the corrected fracture stress SF :
Figure BDA0004119529210000074

第四步：确定缺陷柱壳设计压力；Step 4: Determine the design pressure of the defective column shell;

柱形耐压壳失效压力PF：PF＝SF2t/D (15)；Failure pressure of cylindrical pressure hull P F : P F = S F 2t/D (15);

柱形耐压壳设计压力PS：PS＝PF/SF(SF＝1.2～1.6) (16)；Design pressure of cylindrical pressure hull PS : PS = PF / SF (SF = 1.2 ~ 1.6) (16);

第五步：设计复合材料修复层；Step 5: Design the composite repair layer;

修复厚度：Repair thickness:

Figure BDA0004119529210000075
Figure BDA0004119529210000075

其中，Ep为柱壳的拉伸模量，Ea为纤维增强聚合物轴向的拉伸模量，Pd为设计压力。修复长度:Where, Ep is the tensile modulus of the column shell, Ea is the axial tensile modulus of the fiber-reinforced polymer, and Pd is the design pressure. Repair length:

F＝2πrtσy (18)；F = 2πrtσ y (18);

Figure BDA0004119529210000076
Figure BDA0004119529210000076

其中，F为柱形耐压壳轴向屈服载荷；l0为修复长度；σy柱形耐压壳的屈服强度，τ为粘合剂的剪切强度。Where, F is the axial yield load of the cylindrical pressure hull; l 0 is the repair length; σ y is the yield strength of the cylindrical pressure hull, and τ is the shear strength of the adhesive.

第六步：有限元验证；Step 6: Finite element verification;

根据船级社标准，利用相关软件，分别建立初始、缺陷和修复的几何模型与有限元模型，确定模型各部分的截面参数，对复合材料赋予相应的铺层角度；采用非线性屈曲分析，定义有限元模型边界条件，在给予微小缺陷模拟真实耐压壳极限屈曲载荷，比较三者的屈曲载荷，验证理论计算的修复条件满足内部损伤柱形耐压壳修复状态。According to the classification society standards, relevant software was used to establish the initial, defective and repaired geometric models and finite element models, determine the cross-sectional parameters of each part of the model, and assign corresponding layup angles to the composite materials. Nonlinear buckling analysis was used to define the boundary conditions of the finite element model, and the real pressure hull ultimate buckling load was simulated by giving tiny defects. The buckling loads of the three were compared to verify that the theoretically calculated repair conditions met the repair status of the internally damaged cylindrical pressure hull.

如图2所示，修复结构包括柱形耐压壳1、复合材料修复层3，柱形耐压壳1上厚板1的内壁上具有损伤缺口，复合材料修复层3在损伤缺口的位置处固定于厚板1的外壁上，复合材料修复层3覆盖损伤缺口，复合材料修复层3的材料为纤维增强聚合物复合材料。下面通过多个代入具体数据的实施例进一步验证本发明。As shown in FIG2 , the repair structure includes a cylindrical pressure hull 1 and a composite material repair layer 3. The inner wall of the thick plate 1 on the cylindrical pressure hull 1 has a damage notch. The composite material repair layer 3 is fixed to the outer wall of the thick plate 1 at the location of the damage notch. The composite material repair layer 3 covers the damage notch. The material of the composite material repair layer 3 is a fiber-reinforced polymer composite material. The present invention is further verified by multiple examples in which specific data are substituted.

实施例1：Embodiment 1:

提供一种采用复合材料修复内部损伤柱形耐压壳的设计方法如图5所示，具体包括如下步骤：A design method for repairing an internally damaged cylindrical pressure hull using composite materials is provided as shown in FIG5 , and specifically comprises the following steps:

表1初始柱形耐压壳尺寸参数Table 1 Dimensional parameters of initial cylindrical pressure shell

Figure BDA0004119529210000081
Figure BDA0004119529210000081

(一)根据柱形耐压壳的尺寸计算临界长度，当耐压壳设计长度≥临界长度时，为长柱壳；当耐压壳设计长度<临界长度，为短柱壳，代入公式(1)，此实施例1的临界长度为：(I) The critical length is calculated according to the size of the cylindrical pressure hull. When the design length of the pressure hull is ≥ the critical length, it is a long cylindrical hull; when the design length of the pressure hull is < the critical length, it is a short cylindrical hull. Substituting into formula (1), the critical length of this embodiment 1 is:

Figure BDA0004119529210000082
Figure BDA0004119529210000082

由此可得出该柱形耐压壳为短柱壳；It can be concluded that the cylindrical pressure shell is a short cylindrical shell;

(二)对于钢制柱形耐压壳，当处于深海中，外部压力均匀的作用在柱壳表面，按照耐压壳的分类进行壳体临界压力的计算(弹性范围内)，具体地，E为弹性模量，如图表2所示，该实施例为短轴柱形耐压壳，代入公式(3)，计算得出：(II) For a steel cylindrical pressure hull, when it is in the deep sea, the external pressure acts evenly on the surface of the cylindrical hull. The critical pressure of the hull is calculated (within the elastic range) according to the classification of the pressure hull. Specifically, E is the elastic modulus, as shown in Figure 2. This embodiment is a short-axis cylindrical pressure hull. Substituting it into formula (3), it is calculated:

Figure BDA0004119529210000083
Figure BDA0004119529210000083

由于柱壳在成型过程中，因加工操作、制造造成的误差及材料性能在其过程中存在硬化现象等因素会对耐压壳的临界压力造成不良影响，在计算时需要考虑安全系数m,即满足临界压力为设计压力的m倍，代入公式(4)，可得：

Figure BDA0004119529210000084
(三)选取如图5所示柱形耐压壳内部受损状态，引入缺陷当量长度z，代入公式(5)可得：
Figure BDA0004119529210000091
根据缺陷当量的长度范围，代入公式(9)，计算缺陷在轴向穿壁平面的投影面积S:During the forming process of the cylindrical shell, the errors caused by processing operations and manufacturing, as well as the hardening of material properties during the process, will have an adverse effect on the critical pressure of the pressure shell. Therefore, the safety factor m needs to be considered in the calculation, that is, the critical pressure is m times the design pressure. Substituting it into formula (4), we can get:
Figure BDA0004119529210000084
(III) Select the damaged state of the cylindrical pressure hull as shown in Figure 5, introduce the defect equivalent length z, and substitute it into formula (5) to obtain:
Figure BDA0004119529210000091
According to the length range of the defect equivalent, substitute it into formula (9) to calculate the projection area S of the defect on the axial through-wall plane:

Figure BDA0004119529210000092
Figure BDA0004119529210000092

对于缺陷区域原始管壁横街面积S0，可定义为：S0＝lt＝20×2＝40(mm2)；The original pipe wall cross-sectional area S 0 of the defective region can be defined as: S 0 = lt = 20 × 2 = 40 (mm 2 );

(四)计算柱形耐压壳缺陷程度，d/t＝50％，确定材料流变应力Sflow，代入公式(10),计算可得：Sflow＝1.1×304＝334.4(MPa)；(iv) Calculate the defect degree of the cylindrical pressure hull, d/t = 50%, determine the material flow stress S flow , substitute it into formula (10), and calculate: S flow = 1.1 × 304 = 334.4 (MPa);

(五)根据上述获得的S、S0、Sflow，以Dugdale塑性尺寸模型、受外压耐压壳的轴向缺陷的“Folias”分析和经验的缺陷深度与柱壳厚度关系为基础，计算环向断裂应力SF，代入公式(14)；其中，Mt为Folias系数，由柱形耐压壳内径、缺陷长度、柱壳壁厚确定，代入公式(13)计算可得：(V) Based on the above-obtained S, S0 , and Sflow , the circumferential fracture stress S F is calculated based on the Dugdale plastic size model, the "Folias" analysis of the axial defect of the pressure hull under external pressure, and the empirical relationship between the defect depth and the thickness of the cylindrical shell, and substituted into formula (14); where Mt is the Folias coefficient, which is determined by the inner diameter of the cylindrical pressure hull, the defect length, and the thickness of the cylindrical shell. Substituting it into formula (13) yields:

Figure BDA0004119529210000093
Figure BDA0004119529210000093

Figure BDA0004119529210000094
Figure BDA0004119529210000094

(六)根据内部损伤柱形耐压壳的环向断裂应力，确定缺陷柱壳设计压力PS为，代入公式(15)、(16)，计算可得：

Figure BDA0004119529210000095
(VI) According to the circumferential fracture stress of the internally damaged cylindrical pressure shell, the design pressure PS of the defective cylindrical shell is determined as follows: Substituting into formulas (15) and (16), the following is obtained:
Figure BDA0004119529210000095

(七)设计复合材料修复层，计算缠绕复合材料的最小厚度tmin、长度l0，代入公式(17)(19)中，最小厚度tmin、长度分别为l0：(VII) Design the composite material repair layer, calculate the minimum thickness t min and length l 0 of the wrapped composite material, and substitute them into formulas (17) and (19). The minimum thickness t min and length l 0 are:

Figure BDA0004119529210000096
Figure BDA0004119529210000096

Figure BDA0004119529210000097
Figure BDA0004119529210000097

(八)通过理论计算求出的修复厚度和修复长度，在符合实际情况条件下，最终选取tmin＝1.6(mm)、l0＝32(mm)，作为修复参数，进行有限元验证:(VIII) The repair thickness and repair length obtained through theoretical calculations were finally selected as t min = 1.6 (mm) and l 0 = 32 (mm) as repair parameters under the actual conditions for finite element verification:

8.1、在Hypermesh软件中，选择Geom中的nodes,在笛卡尔坐标系下建立两个节点分别为(0，0，105)和(0，0，-105),作为参考点；选择Geom中的surface,选中Cylinder Full,给出相应的半径r＝35mm和高度h＝210mm，以两节点作为地面中心和法向处置方向，点击创建，柱壳外表创建完成；点击菜单栏中2D中的automesh,根据真实模型，输入合适的网格尺寸，采用四边形的网格单元划分方式，点击创建，表面网格创建完成；创建柱壳两端网格，选择2D中的spline，以节点路径的方式(node path),按照一定的方向选择两端所有节点创建网格；选中网格类型(element type),将四边形网格类型调整为S4R，框选所有创建网格，点击更新；调整两端面网格的法向方向，选择Tool中normals,选中网格，点击“display”,统一法向堆栈方向由里往外；返回Geom,选择temp nodes，删除所有创建的节点，完成几何模型及其网格建立。8.1. In Hypermesh software, select nodes in Geom, and create two nodes (0, 0, 105) and (0, 0, -105) in the Cartesian coordinate system as reference points; select surface in Geom, select Cylinder Full, give the corresponding radius r = 35mm and height h = 210mm, use the two nodes as the ground center and normal direction, click Create, and the surface of the cylindrical shell is created; click Automesh in 2D in the menu bar, enter the appropriate mesh size according to the real model, use the quadrilateral mesh unit division method, click Create, and the surface mesh is created; create the mesh at both ends of the cylindrical shell, select spline in 2D, and select all nodes at both ends in a certain direction to create meshes in the node path method; select the mesh type (element type), adjust the quadrilateral mesh type to S4R, select all created meshes, and click Update; adjust the normal direction of the mesh at both ends, select normals in Tool, select the mesh, click "display", and unify the normal stack direction from inside to outside; return to Geom, select temp nodes, delete all created nodes, and complete the geometric model and its mesh establishment.

8.2、建立有限元模型计算模型，柱形耐压壳及碳纤维复合材料如表2所示：8.2. Establish the finite element model calculation model. The cylindrical pressure hull and carbon fiber composite material are shown in Table 2:

表2材料参数Table 2 Material parameters

Figure BDA0004119529210000101
Figure BDA0004119529210000101

选择Tool中的set,创建set集，将其柱壳模型分为端盖、完美、减薄以及修复区域，前三个区域建立连续均匀的壳单元截面属性，端盖厚度t0＝20mm，完美区域t1＝2mm,减薄区域t2＝1mm，厚度方向选取5个积分点，完美、减薄区域从顶面赋厚，端盖区域从底面赋厚；隐藏柱壳模型，仅显示修复区域的网格，进入Mesh模块，将修复区域的网格进行实体化，选择网格(mesh)中的编辑(edit),种类选择网格，方法选择创建实体层，从顶面由里往外进行偏置，其厚度为t3＝1.6mm，两个不同材料的接触面以共节点的方式进行连接。创建从顶面和底面新的单元，相应的网格类型需改成连续壳单元SC8R，再重新回到Property模块,定义修复区域网格的截面属性，创建复合材料铺层，给出铺层的数目8层，其网格单元类型与在mesh模块中保持一致，铺层方向以离散的方式进行定义，法向轴方向与初始轴方向分别选择方向3和1，其面和边则是选择网格面和以柱壳轴向的网格的一条边，堆栈方是向外进行铺层，输入每一层的材料都为复合材料、相对厚度为0.2mm以及选取角度为90°，每层选取三个积分点，完成创建。Select set in Tool to create a set. Divide the cylindrical shell model into end cap, perfect, thinning and repair areas. Establish continuous and uniform shell unit section properties for the first three areas. The thickness of the end cap is t 0 = 20 mm, the perfect area is t 1 = 2 mm, and the thinning area is t 2 = 1 mm. Select 5 integration points in the thickness direction. The perfect and thinning areas are thickened from the top surface, and the end cap area is thickened from the bottom surface. Hide the cylindrical shell model and only display the mesh of the repair area. Enter the Mesh module to solidify the mesh of the repair area. Select Edit in Mesh, select Mesh as the type, and select Create a solid layer as the method. Offset from the top surface from the inside to the outside. The thickness is t 3 = 1.6 mm. The contact surfaces of two different materials are connected in the form of common nodes. Create new units from the top and bottom surfaces, and the corresponding mesh type needs to be changed to continuous shell unit SC8R. Then go back to the Property module, define the cross-sectional properties of the repair area mesh, create composite material plies, and give the number of plies to 8. The mesh unit type is consistent with that in the mesh module. The ply direction is defined in a discrete manner. The normal axis direction and the initial axis direction are selected as directions 3 and 1 respectively. The face and edge are the mesh face and an edge of the mesh in the axial direction of the cylindrical shell. The stacking direction is to lay the layers outward. The material of each layer is input as composite material, the relative thickness is 0.2mm, and the angle is selected as 90°. Three integration points are selected for each layer to complete the creation.

8.3、采用Riks弧长分析步，考虑几何非线性选项，允许根据计算效率来自动选择弧长增量，考虑到分析不安全，其分析步中最大增量步数至少200步，在比例载荷——位移空间中沿静态平衡路径的初始弧长值一般设置为0.01，最大载荷增量设为0.1，最小载荷增量设为10-5；采用三点定位的方式限制模型的自由度，对于柱壳模型的两端面，选择其圆心处，固定其平面自由度，释放其法向自由度，对于柱壳表面，选择柱壳表面中心处一点，固定垂直于该点法向平面的自由度，释放其余自由度，并对整个模型的外表面施加均匀外压。8.3. Use the Riks arc length analysis step, consider the geometric nonlinearity option, and allow the arc length increment to be automatically selected based on the calculation efficiency. Considering the unsafe analysis, the maximum number of incremental steps in the analysis step is at least 200 steps. The initial arc length value along the static equilibrium path in the proportional load-displacement space is generally set to 0.01, the maximum load increment is set to 0.1, and the minimum load increment is set to 10-5; use three-point positioning to limit the degree of freedom of the model. For the two end faces of the cylindrical shell model, select the center of the circle, fix its plane degree of freedom, and release its normal degree of freedom. For the cylindrical shell surface, select a point at the center of the cylindrical shell surface, fix the degree of freedom perpendicular to the normal plane of the point, release the remaining degrees of freedom, and apply uniform external pressure to the outer surface of the entire model.

8.4、重复上述过程，只改变定义分析步方式，选择线性屈曲分(为非线性分析引入缺陷做准备)，采用子空间迭代法，分析六个特征值下的变形情况，特征向量选择12，最大的迭代次数选择3000。创建分析任务，导出文件，在非线性屈曲文件中加入缺陷扰动，调用线性屈曲分析文件，其扰动量一般是0.01t(t为壁厚)，进行求解；打开结果文件，查看后屈曲状态，得出随弧长增量变化的非线性屈曲载荷，提取最大临界载荷值，比较其理论设计的修复条件是否满足修复强度。8.4. Repeat the above process, only changing the definition of the analysis step mode, select linear buckling points (to prepare for the introduction of defects in nonlinear analysis), use the subspace iteration method, analyze the deformation under six eigenvalues, select 12 eigenvectors, and select 3000 for the maximum number of iterations. Create an analysis task, export the file, add defect perturbations to the nonlinear buckling file, call the linear buckling analysis file, and the perturbation amount is generally 0.01t (t is the wall thickness) for solution; open the result file, check the post-buckling state, obtain the nonlinear buckling load that changes with the arc length increment, extract the maximum critical load value, and compare whether the repair conditions of the theoretical design meet the repair strength.

实施例2：Embodiment 2:

提供一种采用复合材料修复内部损伤柱形耐压壳的设计方法如图6所示，具体包括如下步骤：A design method for repairing an internally damaged cylindrical pressure hull using composite materials is provided as shown in FIG6 , and specifically comprises the following steps:

表3初始柱形耐压壳尺寸参数Table 3 Dimensional parameters of initial cylindrical pressure shell

(一)根据柱形耐压壳的尺寸计算临界长度，当耐压壳设计长度≥临界长度时，为长柱壳；当耐压壳设计长度<临界长度，为短柱壳，代入公式(1)，此实施例2的临界长度为：(I) The critical length is calculated according to the size of the cylindrical pressure hull. When the design length of the pressure hull is ≥ the critical length, it is a long cylindrical hull; when the design length of the pressure hull is < the critical length, it is a short cylindrical hull. Substituting into formula (1), the critical length of this embodiment 2 is:

Figure BDA0004119529210000112
Figure BDA0004119529210000112

由此可得出该柱形耐压壳为短柱壳；It can be concluded that the cylindrical pressure shell is a short cylindrical shell;

(二)对于钢制柱形耐压壳，当处于深海中，外部压力均匀的作用在柱壳表面，按照耐压壳的分类进行壳体临界压力的计算(弹性范围内)，具体地，E为弹性模量，如图表2所示，该实施例为短轴柱形耐压壳，代入公式(3)，计算得出：(II) For a steel cylindrical pressure hull, when it is in the deep sea, the external pressure acts evenly on the surface of the cylindrical hull. The critical pressure of the hull is calculated (within the elastic range) according to the classification of the pressure hull. Specifically, E is the elastic modulus, as shown in Figure 2. This embodiment is a short-axis cylindrical pressure hull. Substituting it into formula (3), it is calculated:

Figure BDA0004119529210000113
Figure BDA0004119529210000113

由于柱壳在成型过程中，因加工操作、制造造成的误差及材料性能在其过程中存在硬化现象等因素会对耐压壳的临界压力造成不良影响，在计算时需要考虑安全系数m,即满足临界压力为设计压力的m倍，代入公式(4)，可得：

Figure BDA0004119529210000114
(三)选取如图6所示柱形耐压壳内部受损状态，引入缺陷当量长度z，代入公式(5)可得：
Figure BDA0004119529210000115
During the forming process of the cylindrical shell, the errors caused by processing operations and manufacturing, as well as the hardening of material properties during the process, will have an adverse effect on the critical pressure of the pressure shell. Therefore, the safety factor m needs to be considered in the calculation, that is, the critical pressure is m times the design pressure. Substituting it into formula (4), we can get:
Figure BDA0004119529210000114
(III) Select the damaged state of the cylindrical pressure hull as shown in Figure 6, introduce the defect equivalent length z, and substitute it into formula (5) to obtain:
Figure BDA0004119529210000115

根据缺陷当量的长度范围，代入公式(9)，计算缺陷在轴向穿壁平面的投影面积S:According to the length range of the defect equivalent, substitute it into formula (9) to calculate the projection area S of the defect on the axial through-wall plane:

Figure BDA0004119529210000121
Figure BDA0004119529210000121

对于缺陷区域原始管壁横街面积S0，可定义为：S0＝lt＝20×2×40(mm2)；The original pipe wall cross-sectional area S 0 of the defective region can be defined as: S 0 = lt = 20 × 2 × 40 (mm 2 );

(四)计算柱形耐压壳缺陷程度，d/t＝60％，确定材料流变应力Sflow，代入公式(10),计算可得：Sflow＝304×1.1＝334.4(MPa)；(iv) Calculate the defect degree of the cylindrical pressure hull, d/t = 60%, determine the material flow stress S flow , substitute it into formula (10), and calculate: S flow = 304 × 1.1 = 334.4 (MPa);

(五)根据上述获得的S、S0、Sflow，以Dugdale塑性尺寸模型、受外压耐压壳的轴向缺陷的“Folias”分析和经验的缺陷深度与柱壳厚度关系为基础，计算环向断裂应力SF，代入公式(14)；其中，Mt为Folias系数，由柱形耐压壳内径、缺陷长度、柱壳壁厚确定，代入公式(13)计算可得：(V) Based on the above-obtained S, S0 , and Sflow , the circumferential fracture stress S F is calculated based on the Dugdale plastic size model, the "Folias" analysis of the axial defect of the pressure hull under external pressure, and the empirical relationship between the defect depth and the thickness of the cylindrical shell, and substituted into formula (14); where Mt is the Folias coefficient, which is determined by the inner diameter of the cylindrical pressure hull, the defect length, and the thickness of the cylindrical shell. Substituting it into formula (13) yields:

Figure BDA0004119529210000122
Figure BDA0004119529210000122

Figure BDA0004119529210000123
Figure BDA0004119529210000123

(六)根据内部损伤柱形耐压壳的环向断裂应力，确定缺陷柱壳设计压力PS为，代入公式(15)、(16)，计算可得：(VI) According to the circumferential fracture stress of the internally damaged cylindrical pressure shell, the design pressure PS of the defective cylindrical shell is determined as follows: Substituting into formulas (15) and (16), the following is obtained:

Figure BDA0004119529210000124
Figure BDA0004119529210000124

(七)设计复合材料修复层，计算缠绕复合材料的最小厚度tmin、长度l0，代入公式(17)(19)中，最小厚度tmin、长度分别为l0：(VII) Design the composite material repair layer, calculate the minimum thickness t min and length l 0 of the wrapped composite material, and substitute them into formulas (17) and (19). The minimum thickness t min and length l 0 are:

Figure BDA0004119529210000125
Figure BDA0004119529210000125

(八)通过理论计算求出的修复厚度和修复长度，在符合实际情况条件下，最终选取tmin＝1.8(mm)、l0＝32(mm)，作为修复参数，进行有限元验证:(VIII) The repair thickness and repair length obtained through theoretical calculations were finally selected as t min = 1.8 (mm) and l 0 = 32 (mm) as repair parameters under the actual conditions for finite element verification:

8.1、在Hypermesh软件中，选择Geom中的nodes,在笛卡尔坐标系下建立两个节点分别为(0，0，105)和(0，0，-105),作为参考点；选择Geom中的surface,选中Cylinder Full,给出相应的半径r＝35mm和高度h＝210mm，以两节点作为地面中心和法向处置方向，点击创建，柱壳外表创建完成；点击菜单栏中2D中的automesh,根据真实模型，输入合适的网格尺寸，采用四边形的网格单元划分方式，点击创建，表面网格创建完成；创建柱壳两端网格，选择2D中的spline，以节点路径的方式(node path),按照一定的方向选择两端所有节点创建网格；选中网格类型(element type),将四边形网格类型调整为S4R，框选所有创建网格，点击更新；调整两端面网格的法向方向，选择Tool中normals,选中网格，点击“display”,统一法向堆栈方向由里往外；返回Geom,选择temp nodes，删除所有创建的节点，完成几何模型及其网格建立。8.1. In Hypermesh software, select nodes in Geom, and create two nodes (0, 0, 105) and (0, 0, -105) in the Cartesian coordinate system as reference points; select surface in Geom, select Cylinder Full, give the corresponding radius r = 35mm and height h = 210mm, use the two nodes as the ground center and normal direction, click Create, and the surface of the cylindrical shell is created; click Automesh in 2D in the menu bar, enter the appropriate mesh size according to the real model, use the quadrilateral mesh unit division method, click Create, and the surface mesh is created; create the mesh at both ends of the cylindrical shell, select spline in 2D, and select all nodes at both ends in a certain direction to create meshes in the node path method; select the mesh type (element type), adjust the quadrilateral mesh type to S4R, select all created meshes, and click Update; adjust the normal direction of the mesh at both ends, select normals in Tool, select the mesh, click "display", and unify the normal stack direction from inside to outside; return to Geom, select temp nodes, delete all created nodes, and complete the geometric model and its mesh establishment.

8.2、建立有限元模型计算模型，柱形耐压壳及碳纤维复合材料如表4所示：8.2. Establish the finite element model calculation model. The cylindrical pressure hull and carbon fiber composite material are shown in Table 4:

表4材料参数Table 4 Material parameters

Figure BDA0004119529210000131
Figure BDA0004119529210000131

选择Tool中的set,创建set集，将其柱壳模型分为端盖、完美、减薄以及修复区域，前三个区域建立连续均匀的壳单元截面属性，端盖厚度t0＝20mm，完美区域t1＝2mm,减薄区域t2＝1.2mm，厚度方向选取5个积分点，完美、减薄区域从顶面赋厚，端盖区域从底面赋厚；隐藏柱壳模型，仅显示修复区域的网格，进入Mesh模块，将修复区域的网格进行实体化，选择网格(mesh)中的编辑(edit),种类选择网格，方法选择创建实体层，从顶面由里往外进行偏置，其厚度为t3＝1.8mm，两个不同材料的接触面以共节点的方式进行连接。创建从顶面和底面新的单元，相应的网格类型需改成连续壳单元SC8R，再重新回到Property模块,定义修复区域网格的截面属性，创建复合材料铺层，给出铺层的数目9层，其网格单元类型与在mesh模块中保持一致，铺层方向以离散的方式进行定义，法向轴方向与初始轴方向分别选择方向3和1，其面和边则是选择网格面和以柱壳轴向的网格的一条边，堆栈方是向外进行铺层，输入每一层的材料都为复合材料、相对厚度为0.2mm以及选取角度为90°，每层选取三个积分点，完成创建。Select set in Tool to create a set. Divide the cylindrical shell model into end cap, perfect, thinning and repair areas. Establish continuous and uniform shell unit section properties for the first three areas. The thickness of the end cap is t 0 = 20 mm, the perfect area is t 1 = 2 mm, and the thinning area is t 2 = 1.2 mm. Select 5 integration points in the thickness direction. The perfect and thinning areas are thickened from the top surface, and the end cap area is thickened from the bottom surface. Hide the cylindrical shell model and only display the mesh of the repair area. Enter the Mesh module, solidify the mesh of the repair area, select Edit in Mesh, select Mesh as the type, and select Create a solid layer as the method. Offset from the top surface from the inside to the outside, and its thickness is t 3 = 1.8 mm. The contact surfaces of two different materials are connected in the form of common nodes. Create new units from the top and bottom surfaces, and the corresponding mesh type needs to be changed to continuous shell unit SC8R. Then go back to the Property module, define the cross-sectional properties of the repair area mesh, create composite material plies, and give the number of plies to 9. The mesh unit type is consistent with that in the mesh module. The ply direction is defined in a discrete manner. The normal axis direction and the initial axis direction are selected as directions 3 and 1 respectively. The face and edge are the mesh face and an edge of the mesh in the axial direction of the cylindrical shell. The stacking direction is to lay the layers outward. The material of each layer is composite material, the relative thickness is 0.2mm, and the angle is 90°. Three integration points are selected for each layer to complete the creation.

8.3、采用Riks弧长分析步，考虑几何非线性选项，允许根据计算效率来自动选择弧长增量，考虑到分析不安全，其分析步中最大增量步数至少200步，在比例载荷——位移空间中沿静态平衡路径的初始弧长值一般设置为0.01，最大载荷增量设为0.1，最小载荷增量设为10-5；采用三点定位的方式限制模型的自由度，对于柱壳模型的两端面，选择其圆心处，固定其平面自由度，释放其法向自由度，对于柱壳表面，选择柱壳表面中心处一点，固定垂直于该点法向平面的自由度，释放其余自由度，并对整个模型的外表面施加均匀外压。8.3. Use the Riks arc length analysis step, consider the geometric nonlinearity option, and allow the arc length increment to be automatically selected based on the calculation efficiency. Considering the unsafe analysis, the maximum number of incremental steps in the analysis step is at least 200 steps. The initial arc length value along the static equilibrium path in the proportional load-displacement space is generally set to 0.01, the maximum load increment is set to 0.1, and the minimum load increment is set to 10-5; use three-point positioning to limit the degree of freedom of the model. For the two end faces of the cylindrical shell model, select the center of the circle, fix its plane degree of freedom, and release its normal degree of freedom. For the cylindrical shell surface, select a point at the center of the cylindrical shell surface, fix the degree of freedom perpendicular to the normal plane of the point, release the remaining degrees of freedom, and apply uniform external pressure to the outer surface of the entire model.

8.4、重复上述过程，只改变定义分析步方式，选择线性屈曲分(为非线性分析引入缺陷做准备)，采用子空间迭代法，分析六个特征值下的变形情况，特征向量选择12，最大的迭代次数选择3000。创建分析任务，导出文件，在非线性屈曲文件中加入缺陷扰动，调用线性屈曲分析文件，其扰动量一般是0.01t(t为壁厚)，进行求解；打开结果文件，查看后屈曲状态，得出随弧长增量变化的非线性屈曲载荷，提取最大临界载荷值，比较其理论设计的修复条件是否满足修复强度。8.4. Repeat the above process, only changing the definition of the analysis step mode, select linear buckling points (to prepare for the introduction of defects in nonlinear analysis), use the subspace iteration method, analyze the deformation under six eigenvalues, select 12 eigenvectors, and select 3000 for the maximum number of iterations. Create an analysis task, export the file, add defect perturbations to the nonlinear buckling file, call the linear buckling analysis file, and the perturbation amount is generally 0.01t (t is the wall thickness) for solution; open the result file, check the post-buckling state, obtain the nonlinear buckling load that changes with the arc length increment, extract the maximum critical load value, and compare whether the repair conditions of the theoretical design meet the repair strength.

实施例3：Embodiment 3:

提供一种采用复合材料修复内部损伤柱形耐压壳的设计方法如图7所示，具体包括如下步骤：A design method for repairing an internally damaged cylindrical pressure hull using composite materials is provided as shown in FIG7 , and specifically comprises the following steps:

表5初始柱形耐压壳尺寸参数Table 5 Dimensional parameters of initial cylindrical pressure shell

Figure BDA0004119529210000141
Figure BDA0004119529210000141

(一)根据柱形耐压壳的尺寸计算临界长度，当耐压壳设计长度≥临界长度时，为长柱壳；当耐压壳设计长度<临界长度，为短柱壳，代入公式(1)，此实施例3的临界长度为：(I) The critical length is calculated according to the size of the cylindrical pressure hull. When the design length of the pressure hull is ≥ the critical length, it is a long cylindrical hull; when the design length of the pressure hull is < the critical length, it is a short cylindrical hull. Substituting into formula (1), the critical length of this embodiment 3 is:

Figure BDA0004119529210000142
Figure BDA0004119529210000142

由此可得出该柱形耐压壳为短柱壳；It can be concluded that the cylindrical pressure shell is a short cylindrical shell;

(二)对于钢制柱形耐压壳，当处于深海中，外部压力均匀的作用在柱壳表面，按照耐压壳的分类进行壳体临界压力的计算(弹性范围内)，具体地，E为弹性模量，如图表2所示，该实施例为短轴柱形耐压壳，代入公式(3)，计算得出：(II) For a steel cylindrical pressure hull, when it is in the deep sea, the external pressure acts evenly on the surface of the cylindrical hull. The critical pressure of the hull is calculated (within the elastic range) according to the classification of the pressure hull. Specifically, E is the elastic modulus, as shown in Figure 2. This embodiment is a short-axis cylindrical pressure hull. Substituting it into formula (3), it is calculated:

Figure BDA0004119529210000143
Figure BDA0004119529210000143

由于柱壳在成型过程中，因加工操作、制造造成的误差及材料性能在其过程中存在硬化现象等因素会对耐压壳的临界压力造成不良影响，在计算时需要考虑安全系数m,即满足临界压力为设计压力的m倍，代入公式(4)，可得：During the forming process of the cylindrical shell, the errors caused by processing operations and manufacturing, as well as the hardening of material properties during the process, will have an adverse effect on the critical pressure of the pressure shell. Therefore, the safety factor m needs to be considered in the calculation, that is, the critical pressure is m times the design pressure. Substituting it into formula (4), we can get:

Figure BDA0004119529210000144
Figure BDA0004119529210000144

(三)选取如图7所示柱形耐压壳内部受损状态，引入缺陷当量长度z，代入公式(5)可得：(III) Select the damaged state of the cylindrical pressure hull as shown in Figure 7, introduce the defect equivalent length z, and substitute it into formula (5) to obtain:

Figure BDA0004119529210000145
Figure BDA0004119529210000145

根据缺陷当量的长度范围，代入公式(9)，计算缺陷在轴向穿壁平面的投影面积S:According to the length range of the defect equivalent, substitute it into formula (9) to calculate the projection area S of the defect on the axial through-wall plane:

Figure BDA0004119529210000146
Figure BDA0004119529210000146

对于缺陷区域原始管壁横街面积S0，可定义为：S0＝lt＝20×2＝40(mm2)；The original pipe wall cross-sectional area S 0 of the defective region can be defined as: S 0 = lt = 20 × 2 = 40 (mm 2 );

(四)计算柱形耐压壳缺陷程度，d/t＝40％，确定材料流变应力Sflow，代入公式(10),计算可得：(IV) Calculate the defect degree of the cylindrical pressure hull, d/t = 40%, determine the material flow stress S flow , and substitute it into formula (10) to obtain:

Sflow＝304+69＝373(MPa)；S flow =304+69=373(MPa);

(五)根据上述获得的S、S0、Sflow，以Dugdale塑性尺寸模型、受外压耐压壳的轴向缺陷的“Folias”分析和经验的缺陷深度与柱壳厚度关系为基础，计算环向断裂应力SF，代入公式(14)；其中，Mt为Folias系数，由柱形耐压壳内径、缺陷长度、柱壳壁厚确定，代入公式(13)计算可得：(V) Based on the above-obtained S, S0 , and Sflow , the circumferential fracture stress SF is calculated based on the Dugdale plastic size model, the "Folias" analysis of the axial defect of the pressure hull under external pressure, and the empirical relationship between the defect depth and the thickness of the cylindrical shell, and substituted into formula (14); where Mt is the Folias coefficient, which is determined by the inner diameter of the cylindrical pressure hull, the defect length, and the thickness of the cylindrical shell. Substituting it into formula (13) yields:

Figure BDA0004119529210000151
Figure BDA0004119529210000151

Figure BDA0004119529210000152
Figure BDA0004119529210000152

(六)根据内部损伤柱形耐压壳的环向断裂应力，确定缺陷柱壳设计压力PS为，代入公式(15)、(16)，计算可得：(VI) According to the circumferential fracture stress of the internally damaged cylindrical pressure shell, the design pressure PS of the defective cylindrical shell is determined as follows: Substituting into formulas (15) and (16), the following is obtained:

Figure BDA0004119529210000153
Figure BDA0004119529210000153

(七)设计复合材料修复层，计算缠绕复合材料的最小厚度tmin、长度l0，代入公式(17)(19)中，最小厚度tmin、长度分别为l0：(VII) Design the composite material repair layer, calculate the minimum thickness t min and length l 0 of the wrapped composite material, and substitute them into formulas (17) and (19). The minimum thickness t min and length l 0 are:

Figure BDA0004119529210000154
Figure BDA0004119529210000154

(八)通过理论计算求出的修复厚度和修复长度，在符合实际情况条件下，最终选取tmin＝1.4(mm)、l0＝32(mm)，作为修复参数，进行有限元验证:(VIII) The repair thickness and repair length obtained through theoretical calculations were finally selected as t min = 1.4 (mm) and l 0 = 32 (mm) as repair parameters under the actual conditions for finite element verification:

8.1、在Hypermesh软件中，选择Geom中的nodes,在笛卡尔坐标系下建立两个节点分别为(0，0，105)和(0，0，-105),作为参考点；选择Geom中的surface,选中Cylinder Full,给出相应的半径r＝35mm和高度h＝210mm，以两节点作为地面中心和法向处置方向，点击创建，柱壳外表创建完成；点击菜单栏中2D中的automesh,根据真实模型，输入合适的网格尺寸，采用四边形的网格单元划分方式，点击创建，表面网格创建完成；创建柱壳两端网格，选择2D中的spline，以节点路径的方式(node path),按照一定的方向选择两端所有节点创建网格；选中网格类型(element type),将四边形网格类型调整为S4R，框选所有创建网格，点击更新；调整两端面网格的法向方向，选择Tool中normals,选中网格，点击“display”,统一法向堆栈方向由里往外；返回Geom,选择temp nodes，删除所有创建的节点，完成几何模型及其网格创建。8.1. In Hypermesh software, select nodes in Geom, and create two nodes (0, 0, 105) and (0, 0, -105) in the Cartesian coordinate system as reference points; select surface in Geom, select Cylinder Full, give the corresponding radius r = 35mm and height h = 210mm, use the two nodes as the ground center and normal direction, click Create, and the surface of the cylindrical shell is created; click Automesh in 2D in the menu bar, enter the appropriate mesh size according to the real model, use the quadrilateral mesh unit division method, click Create, and the surface mesh is created; create the mesh at both ends of the cylindrical shell, select spline in 2D, and select all nodes at both ends in a certain direction to create meshes in the node path method; select the mesh type (element type), adjust the quadrilateral mesh type to S4R, select all created meshes, and click Update; adjust the normal direction of the mesh at both ends, select normals in Tool, select the mesh, click "display", and unify the normal stack direction from inside to outside; return to Geom, select temp nodes, delete all created nodes, and complete the creation of the geometric model and its mesh.

8.2、建立有限元模型计算模型，柱形耐压壳及碳纤维复合材料如表6所示：8.2. Establish the finite element model calculation model. The cylindrical pressure hull and carbon fiber composite material are shown in Table 6:

表6材料参数Table 6 Material parameters

Figure BDA0004119529210000161
Figure BDA0004119529210000161

选择Tool中的set,创建set集，将其柱壳模型分为端盖、完美、减薄以及修复区域，前三个区域建立连续均匀的壳单元截面属性，端盖厚度t0＝20mm，完美区域t1＝2mm,减薄区域t2＝0.8mm，厚度方向选取5个积分点，完美、减薄区域从顶面赋厚，端盖区域从底面赋厚；隐藏柱壳模型，仅显示修复区域的网格，进入Mesh模块，将修复区域的网格进行实体化，选择网格(mesh)中的编辑(edit),种类选择网格，方法选择创建实体层，从顶面由里往外进行偏置，其厚度为t3＝1.4mm，两个不同材料的接触面以共节点的方式进行连接。创建从顶面和底面新的单元，相应的网格类型需改成连续壳单元SC8R，再重新回到Property模块,定义修复区域网格的截面属性，创建复合材料铺层，给出铺层的数目7层，其网格单元类型与在mesh模块中保持一致，铺层方向以离散的方式进行定义，法向轴方向与初始轴方向分别选择方向3和1，其面和边则是选择网格面和以柱壳轴向的网格的一条边，堆栈方是向外进行铺层，输入每一层的材料都为复合材料、相对厚度为0.02mm以及选取角度为90°，每层选取三个积分点，完成创建。Select set in Tool to create a set. Divide the cylindrical shell model into end cap, perfect, thinning and repair areas. Establish continuous and uniform shell unit section properties for the first three areas. The thickness of the end cap is t 0 = 20 mm, the perfect area is t 1 = 2 mm, and the thinning area is t 2 = 0.8 mm. Select 5 integration points in the thickness direction. The perfect and thinning areas are thickened from the top surface, and the end cap area is thickened from the bottom surface. Hide the cylindrical shell model and only display the mesh of the repair area. Enter the Mesh module, solidify the mesh of the repair area, select Edit in Mesh, select Mesh as the type, and select Create a solid layer as the method. Offset from the top surface from the inside to the outside, and its thickness is t 3 = 1.4 mm. The contact surfaces of two different materials are connected in the form of common nodes. Create new units from the top and bottom surfaces, and the corresponding mesh type needs to be changed to continuous shell unit SC8R. Then go back to the Property module, define the cross-sectional properties of the repair area mesh, create composite material plies, and give the number of plies to 7. The mesh unit type is consistent with that in the mesh module. The ply direction is defined in a discrete manner. The normal axis direction and the initial axis direction are selected as directions 3 and 1 respectively. The face and edge are the mesh face and an edge of the mesh in the axial direction of the cylindrical shell. The stacking direction is to lay the layers outward. The material of each layer is composite material, the relative thickness is 0.02mm, and the angle is 90°. Select three integration points for each layer to complete the creation.

8.3、采用Riks弧长分析步，考虑几何非线性选项，允许根据计算效率来自动选择弧长增量，考虑到分析不安全，其分析步中最大增量步数至少200步，在比例载荷——位移空间中沿静态平衡路径的初始弧长值一般设置为0.01，最大载荷增量设为0.1，最小载荷增量设为10-5；采用三点定位的方式限制模型的自由度，对于柱壳模型的两端面，选择其圆心处，固定其平面自由度，释放其法向自由度，对于柱壳表面，选择柱壳表面中心处一点，固定垂直于该点法向平面的自由度，释放其余自由度，并对整个模型的外表面施加均匀外压。8.3. Use the Riks arc length analysis step, consider the geometric nonlinearity option, and allow the arc length increment to be automatically selected based on the calculation efficiency. Considering the unsafe analysis, the maximum number of incremental steps in the analysis step is at least 200 steps. The initial arc length value along the static equilibrium path in the proportional load-displacement space is generally set to 0.01, the maximum load increment is set to 0.1, and the minimum load increment is set to 10-5; use three-point positioning to limit the degree of freedom of the model. For the two end faces of the cylindrical shell model, select the center of the circle, fix its plane degree of freedom, and release its normal degree of freedom. For the cylindrical shell surface, select a point at the center of the cylindrical shell surface, fix the degree of freedom perpendicular to the normal plane of the point, release the remaining degrees of freedom, and apply uniform external pressure to the outer surface of the entire model.

8.4、重复上述过程，只改变定义分析步方式，选择线性屈曲分(为非线性分析引入缺陷做准备)，采用子空间迭代法，分析六个特征值下的变形情况，特征向量选择12，最大的迭代次数选择3000。创建分析任务，导出文件，在非线性屈曲文件中加入缺陷扰动，调用线性屈曲分析文件，其扰动量一般是0.01t(t为壁厚)，进行求解；打开结果文件，查看后屈曲状态，得出随弧长增量变化的非线性屈曲载荷，提取最大临界载荷值，比较其理论设计的修复条件是否满足修复强度。8.4. Repeat the above process, only changing the definition of the analysis step mode, select linear buckling points (to prepare for the introduction of defects in nonlinear analysis), use the subspace iteration method, analyze the deformation under six eigenvalues, select 12 eigenvectors, and select 3000 for the maximum number of iterations. Create an analysis task, export the file, add defect perturbations to the nonlinear buckling file, call the linear buckling analysis file, and the perturbation amount is generally 0.01t (t is the wall thickness) for solution; open the result file, check the post-buckling state, obtain the nonlinear buckling load that changes with the arc length increment, extract the maximum critical load value, and compare whether the repair conditions of the theoretical design meet the repair strength.

实施例4：Embodiment 4:

提供一种采用复合材料修复内部损伤柱形耐压壳的设计方法如图8所示，具体包括如下步骤：A design method for repairing an internally damaged cylindrical pressure hull using composite materials is provided as shown in FIG8 , and specifically comprises the following steps:

表7初始柱形耐压壳尺寸参数Table 7 Dimensional parameters of initial cylindrical pressure shell

Figure BDA0004119529210000171
Figure BDA0004119529210000171

(一)根据柱形耐压壳的尺寸计算临界长度，当耐压壳设计长度≥临界长度时，为长柱壳；当耐压壳设计长度<临界长度，为短柱壳，代入公式(1)，此实施例4的临界长度为：(I) The critical length is calculated according to the size of the cylindrical pressure hull. When the design length of the pressure hull is ≥ the critical length, it is a long cylindrical hull; when the design length of the pressure hull is < the critical length, it is a short cylindrical hull. Substituting into formula (1), the critical length of this embodiment 4 is:

Figure BDA0004119529210000172
Figure BDA0004119529210000172

由此可得出该柱形耐压壳为短柱壳；It can be concluded that the cylindrical pressure shell is a short cylindrical shell;

(二)对于钢制柱形耐压壳，当处于深海中，外部压力均匀的作用在柱壳表面，按照耐压壳的分类进行壳体临界压力的计算(弹性范围内)，具体地，E为弹性模量，如图表2所示，该实施例为短轴柱形耐压壳，代入公式(3)，计算得出：(II) For a steel cylindrical pressure hull, when it is in the deep sea, the external pressure acts evenly on the surface of the cylindrical hull. The critical pressure of the hull is calculated (within the elastic range) according to the classification of the pressure hull. Specifically, E is the elastic modulus, as shown in Figure 2. This embodiment is a short-axis cylindrical pressure hull. Substituting it into formula (3), it is calculated:

Figure BDA0004119529210000173
Figure BDA0004119529210000173

由于柱壳在成型过程中，因加工操作、制造造成的误差及材料性能在其过程中存在硬化现象等因素会对耐压壳的临界压力造成不良影响，在计算时需要考虑安全系数m,即满足临界压力为设计压力的m倍，代入公式(4)，可得：During the forming process of the cylindrical shell, the errors caused by processing operations and manufacturing, as well as the hardening of material properties during the process, will have an adverse effect on the critical pressure of the pressure shell. Therefore, the safety factor m needs to be considered in the calculation, that is, the critical pressure is m times the design pressure. Substituting it into formula (4), we can get:

Figure BDA0004119529210000174
Figure BDA0004119529210000174

(三)选取如图8所示柱形耐压壳内部受损状态，引入缺陷当量长度z，代入公式(5)可得：(III) Select the damaged state of the cylindrical pressure hull as shown in Figure 8, introduce the defect equivalent length z, and substitute it into formula (5) to obtain:

Figure BDA0004119529210000175
Figure BDA0004119529210000175

根据缺陷当量的长度范围，代入公式(9)，计算缺陷在轴向穿壁平面的投影面积S:According to the length range of the defect equivalent, substitute it into formula (9) to calculate the projection area S of the defect on the axial through-wall plane:

Figure BDA0004119529210000181
Figure BDA0004119529210000181

对于缺陷区域原始管壁横街面积S0，可定义为：S0＝lt＝20×2＝40(mm2)；The original pipe wall cross-sectional area S 0 of the defective region can be defined as: S 0 = lt = 20 × 2 = 40 (mm 2 );

(四)计算柱形耐压壳缺陷程度，d/t＝30％，确定材料流变应力Sflow，代入公式(10),计算可得：(IV) Calculate the defect degree of the cylindrical pressure hull, d/t = 30%, determine the material flow stress S flow , and substitute it into formula (10) to obtain:

Sflow＝304×69＝373(MPa)；S flow =304×69=373(MPa);

(五)根据上述获得的S、S0、Sflow，以Dugdale塑性尺寸模型、受外压耐压壳的轴向缺陷的“Folias”分析和经验的缺陷深度与柱壳厚度关系为基础，计算环向断裂应力SF，代入公式(14)；其中，Mt为Folias系数，由柱形耐压壳内径、缺陷长度、柱壳壁厚确定，代入公式(13)计算可得：(V) Based on the above-obtained S, S0 , and Sflow , the circumferential fracture stress S F is calculated based on the Dugdale plastic size model, the "Folias" analysis of the axial defect of the pressure hull under external pressure, and the empirical relationship between the defect depth and the thickness of the cylindrical shell, and substituted into formula (14); where Mt is the Folias coefficient, which is determined by the inner diameter of the cylindrical pressure hull, the defect length, and the thickness of the cylindrical shell. Substituting it into formula (13) yields:

Figure BDA0004119529210000182
Figure BDA0004119529210000182

Figure BDA0004119529210000183
Figure BDA0004119529210000183

(六)根据内部损伤柱形耐压壳的环向断裂应力，确定缺陷柱壳设计压力PS为，代入公式(15)、(16)，计算可得：(VI) According to the circumferential fracture stress of the internally damaged cylindrical pressure shell, the design pressure PS of the defective cylindrical shell is determined as: Substituting into formulas (15) and (16), the following is obtained:

Figure BDA0004119529210000184
Figure BDA0004119529210000184

(七)设计复合材料修复层，计算缠绕复合材料的最小厚度tmin、长度l0，代入公式(17)(19)中，最小厚度tmin、长度分别为l0：(VII) Design the composite material repair layer, calculate the minimum thickness t min and length l 0 of the wrapped composite material, and substitute them into formulas (17) and (19). The minimum thickness t min and length l 0 are:

Figure BDA0004119529210000185
Figure BDA0004119529210000185

(八)通过理论计算求出的修复厚度和修复长度，在符合实际情况条件下，最终选取tmin＝0.8(mm)、l0(32(mm)，作为修复参数，进行有限元验证:(VIII) The repair thickness and repair length obtained through theoretical calculations were finally selected as t min = 0.8 (mm) and l 0 (32 (mm) as repair parameters under the actual conditions for finite element verification:

8.1、在Hypermesh软件中，选择Geom中的nodes,在笛卡尔坐标系下建立两个节点分别为(0，0，105)和(0，0，-105),作为参考点；选择Geom中的surface,选中Cylinder Full,给出相应的半径r＝35mm和高度h＝210mm，以两节点作为地面中心和法向处置方向，点击创建，柱壳外表创建完成；点击菜单栏中2D中的automesh,根据真实模型，输入合适的网格尺寸，采用四边形的网格单元划分方式，点击创建，表面网格创建完成；创建柱壳两端网格，选择2D中的spline，以节点路径的方式(node path),按照一定的方向选择两端所有节点创建网格；选中网格类型(element type),将四边形网格类型调整为S4R，框选所有创建网格，点击更新；调整两端面网格的法向方向，选择Tool中normals,选中网格，点击“display”,统一法向堆栈方向由里往外；返回Geom,选择temp nodes，删除所有创建的节点，完成几何模型及其网格建立。8.1. In Hypermesh software, select nodes in Geom, and create two nodes (0, 0, 105) and (0, 0, -105) in the Cartesian coordinate system as reference points; select surface in Geom, select Cylinder Full, give the corresponding radius r = 35mm and height h = 210mm, use the two nodes as the ground center and normal direction, click Create, and the surface of the cylindrical shell is created; click Automesh in 2D in the menu bar, enter the appropriate mesh size according to the real model, use the quadrilateral mesh unit division method, click Create, and the surface mesh is created; create the mesh at both ends of the cylindrical shell, select spline in 2D, and select all nodes at both ends in a certain direction to create meshes in the node path method; select the mesh type (element type), adjust the quadrilateral mesh type to S4R, select all created meshes, and click Update; adjust the normal direction of the mesh at both ends, select normals in Tool, select the mesh, click "display", and unify the normal stack direction from inside to outside; return to Geom, select temp nodes, delete all created nodes, and complete the geometric model and its mesh establishment.

8.2、建立有限元模型计算模型，柱形耐压壳及碳纤维复合材料如表8所示：8.2. Establish the finite element model calculation model. The cylindrical pressure hull and carbon fiber composite material are shown in Table 8:

表8材料参数Table 8 Material parameters

Figure BDA0004119529210000191
Figure BDA0004119529210000191

选择Tool中的set,创建set集，将其柱壳模型分为端盖、完美、减薄以及修复区域，前三个区域建立连续均匀的壳单元截面属性，端盖厚度t0＝20mm，完美区域t1＝2mm,减薄区域t2＝0.6mm，厚度方向选取5个积分点，完美、减薄区域从顶面赋厚，端盖区域从底面赋厚；隐藏柱壳模型，仅显示修复区域的网格，进入Mesh模块，将修复区域的网格进行实体化，选择网格(mesh)中的编辑(edit),种类选择网格，方法选择创建实体层，从顶面由里往外进行偏置，其厚度为t3＝0.8mm，两个不同材料的接触面以共节点的方式进行连接。创建从顶面和底面新的单元，相应的网格类型需改成连续壳单元SC8R，再重新回到Property模块,定义修复区域网格的截面属性，创建复合材料铺层，给出铺层的数目4层，其网格单元类型与在mesh模块中保持一致，铺层方向以离散的方式进行定义，法向轴方向与初始轴方向分别选择方向3和1，其面和边则是选择网格面和以柱壳轴向的网格的一条边，堆栈方是向外进行铺层，输入每一层的材料都为复合材料、相对厚度为0.02mm以及选取角度为90°，每层选取三个积分点，完成创建。Select set in Tool to create a set set, and divide the cylindrical shell model into end cap, perfect, thinning and repair areas. Establish continuous and uniform shell unit section properties for the first three areas. The thickness of the end cap is t 0 = 20mm, the perfect area is t 1 = 2mm, and the thinning area is t 2 = 0.6mm. Select 5 integration points in the thickness direction. The perfect and thinning areas are thickened from the top surface, and the end cap area is thickened from the bottom surface. Hide the cylindrical shell model and only display the mesh of the repair area. Enter the Mesh module, solidify the mesh of the repair area, select Edit in Mesh, select Mesh as the type, and select Create a solid layer as the method. Offset from the top surface from the inside to the outside, and its thickness is t 3 = 0.8mm. The contact surfaces of two different materials are connected in the form of common nodes. Create new units from the top and bottom surfaces, and the corresponding mesh type needs to be changed to continuous shell unit SC8R. Then go back to the Property module, define the cross-sectional properties of the repair area mesh, create composite material plies, and give the number of plies as 4. The mesh unit type is consistent with that in the mesh module. The ply direction is defined in a discrete manner. The normal axis direction and the initial axis direction are selected as directions 3 and 1 respectively. The face and edge are the mesh face and an edge of the mesh in the axial direction of the cylindrical shell. The stacking direction is to lay the layers outward. The material of each layer is composite material, the relative thickness is 0.02mm, and the angle is 90°. Select three integration points for each layer to complete the creation.

8.3、采用Riks弧长分析步，考虑几何非线性选项，允许根据计算效率来自动选择弧长增量，考虑到分析不安全，其分析步中最大增量步数至少200步，在比例载荷——位移空间中沿静态平衡路径的初始弧长值一般设置为0.01，最大载荷增量设为0.1，最小载荷增量设为10-5；采用三点定位的方式限制模型的自由度，对于柱壳模型的两端面，选择其圆心处，固定其平面自由度，释放其法向自由度，对于柱壳表面，选择柱壳表面中心处一点，固定垂直于该点法向平面的自由度，释放其余自由度，并对整个模型的外表面施加均匀外压。8.3. Use the Riks arc length analysis step, consider the geometric nonlinearity option, and allow the arc length increment to be automatically selected based on the calculation efficiency. Considering the unsafe analysis, the maximum number of incremental steps in the analysis step is at least 200 steps. The initial arc length value along the static equilibrium path in the proportional load-displacement space is generally set to 0.01, the maximum load increment is set to 0.1, and the minimum load increment is set to 10-5; use three-point positioning to limit the degree of freedom of the model. For the two end faces of the cylindrical shell model, select the center of the circle, fix its plane degree of freedom, and release its normal degree of freedom. For the cylindrical shell surface, select a point at the center of the cylindrical shell surface, fix the degree of freedom perpendicular to the normal plane of the point, release the remaining degrees of freedom, and apply uniform external pressure to the outer surface of the entire model.

8.4、重复上述过程，只改变定义分析步方式，选择线性屈曲分(为非线性分析引入缺陷做准备)，采用子空间迭代法，分析六个特征值下的变形情况，特征向量选择12，最大的迭代次数选择3000。创建分析任务，导出文件，在非线性屈曲文件中加入缺陷扰动，调用线性屈曲分析文件，其扰动量一般是0.01t(t为壁厚)，进行求解；打开结果文件，查看后屈曲状态，得出随弧长增量变化的非线性屈曲载荷，提取最大临界载荷值，比较其理论设计的修复条件是否满足修复强度。8.4. Repeat the above process, only changing the definition of the analysis step mode, select linear buckling points (to prepare for the introduction of defects in nonlinear analysis), use the subspace iteration method, analyze the deformation under six eigenvalues, select 12 eigenvectors, and select 3000 for the maximum number of iterations. Create an analysis task, export the file, add defect perturbations to the nonlinear buckling file, call the linear buckling analysis file, and the perturbation amount is generally 0.01t (t is the wall thickness) for solution; open the result file, check the post-buckling state, obtain the nonlinear buckling load that changes with the arc length increment, extract the maximum critical load value, and compare whether the repair conditions of the theoretical design meet the repair strength.

实施例5：Embodiment 5:

提供一种采用复合材料修复内部损伤柱形耐压壳的设计方法如图9所示，具体包括如下步骤：A design method for repairing an internally damaged cylindrical pressure hull using composite materials is provided as shown in FIG9 , and specifically comprises the following steps:

表9初始柱形耐压壳尺寸参数Table 9 Dimensional parameters of initial cylindrical pressure shell

Figure BDA0004119529210000201
Figure BDA0004119529210000201

(一)根据柱形耐压壳的尺寸计算临界长度，当耐压壳设计长度≥临界长度时，为长柱壳；当耐压壳设计长度<临界长度，为短柱壳，代入公式(1)，此实施例5的临界长度为：(I) The critical length is calculated according to the size of the cylindrical pressure hull. When the design length of the pressure hull is ≥ the critical length, it is a long cylindrical hull; when the design length of the pressure hull is < the critical length, it is a short cylindrical hull. Substituting into formula (1), the critical length of this embodiment 5 is:

Figure BDA0004119529210000202
Figure BDA0004119529210000202

由此可得出该柱形耐压壳为短柱壳；It can be concluded that the cylindrical pressure shell is a short cylindrical shell;

(二)对于钢制柱形耐压壳，当处于深海中，外部压力均匀的作用在柱壳表面，按照耐压壳的分类进行壳体临界压力的计算(弹性范围内)，具体地，E为弹性模量，如图表2所示，该实施例为短轴柱形耐压壳，代入公式(3)，计算得出：(II) For a steel cylindrical pressure hull, when it is in the deep sea, the external pressure acts evenly on the surface of the cylindrical hull. The critical pressure of the hull is calculated (within the elastic range) according to the classification of the pressure hull. Specifically, E is the elastic modulus, as shown in Figure 2. This embodiment is a short-axis cylindrical pressure hull. Substituting it into formula (3), it is calculated:

Figure BDA0004119529210000203
Figure BDA0004119529210000203

由于柱壳在成型过程中，因加工操作、制造造成的误差及材料性能在其过程中存在硬化现象等因素会对耐压壳的临界压力造成不良影响，在计算时需要考虑安全系数m,即满足临界压力为设计压力的m倍，代入公式(4)，可得：During the forming process of the cylindrical shell, the errors caused by processing operations and manufacturing, as well as the hardening of material properties during the process, will have an adverse effect on the critical pressure of the pressure shell. Therefore, the safety factor m needs to be considered in the calculation, that is, the critical pressure is m times the design pressure. Substituting it into formula (4), we can get:

Figure BDA0004119529210000204
Figure BDA0004119529210000204

(三)选取如图9所示柱形耐压壳内部受损状态，引入缺陷当量长度z，代入公式(5)可得：(III) Select the damaged state of the cylindrical pressure hull as shown in Figure 9, introduce the defect equivalent length z, and substitute it into formula (5) to obtain:

Figure BDA0004119529210000205
Figure BDA0004119529210000205

根据缺陷当量的长度范围，代入公式(9)，计算缺陷在轴向穿壁平面的投影面积S:According to the length range of the defect equivalent, substitute it into formula (9) to calculate the projection area S of the defect on the axial through-wall plane:

Figure BDA0004119529210000211
Figure BDA0004119529210000211

对于缺陷区域原始管壁横街面积S0，可定义为：S0＝lt＝20×2＝40(mm2)；The original pipe wall cross-sectional area S 0 of the defective region can be defined as: S 0 = lt = 20 × 2 = 40 (mm 2 );

(四)计算柱形耐压壳缺陷程度，d/t＝20％，确定材料流变应力Sflow，代入公式(10),计算可得：(IV) Calculate the defect degree of the cylindrical pressure hull, d/t = 20%, determine the material flow stress S flow , and substitute it into formula (10) to obtain:

Sflow＝304×69＝373(MPa)；S flow =304×69=373(MPa);

(五)根据上述获得的S、S0、Sflow，以Dugdale塑性尺寸模型、受外压耐压壳的轴向缺陷的“Folias”分析和经验的缺陷深度与柱壳厚度关系为基础，计算环向断裂应力SF，代入公式(14)；其中，Mt为Folias系数，由柱形耐压壳内径、缺陷长度、柱壳壁厚确定，代入公式(13)计算可得：(V) Based on the above-obtained S, S0 , and Sflow , the circumferential fracture stress S F is calculated based on the Dugdale plastic size model, the "Folias" analysis of the axial defect of the pressure hull under external pressure, and the empirical relationship between the defect depth and the thickness of the cylindrical shell, and substituted into formula (14); where Mt is the Folias coefficient, which is determined by the inner diameter of the cylindrical pressure hull, the defect length, and the thickness of the cylindrical shell. Substituting it into formula (13) yields:

Figure BDA0004119529210000212
Figure BDA0004119529210000212

Figure BDA0004119529210000213
Figure BDA0004119529210000213

(六)根据内部损伤柱形耐压壳的环向断裂应力，确定缺陷柱壳设计压力PS为，代入公式(15)、(16)，计算可得：(VI) According to the circumferential fracture stress of the internally damaged cylindrical pressure shell, the design pressure PS of the defective cylindrical shell is determined as follows: Substituting into formulas (15) and (16), the following is obtained:

Figure BDA0004119529210000214
Figure BDA0004119529210000214

(七)设计复合材料修复层，计算缠绕复合材料的最小厚度tmin、长度l0，代入公式(17)(19)中，最小厚度tmin、长度分别为l0：(VII) Design the composite material repair layer, calculate the minimum thickness t min and length l 0 of the wrapped composite material, and substitute them into formulas (17) and (19). The minimum thickness t min and length l 0 are:

Figure BDA0004119529210000215
Figure BDA0004119529210000215

(八)通过理论计算求出的修复厚度和修复长度，在符合实际情况条件下，最终选取tmin＝0.8(mm)、l0＝32(mm)，作为修复参数，进行有限元验证:(VIII) The repair thickness and repair length obtained through theoretical calculations were finally selected as t min = 0.8 (mm) and l 0 = 32 (mm) as repair parameters under the actual conditions for finite element verification:

8.1、在Hypermesh软件中，选择Geom中的nodes,在笛卡尔坐标系下建立两个节点分别为(0，0，105)和(0，0，-105),作为参考点；选择Geom中的surface,选中Cylinder Full,给出相应的半径r＝35mm和高度h＝210mm，以两节点作为地面中心和法向处置方向，点击创建，柱壳外表创建完成；点击菜单栏中2D中的automesh,根据真实模型，输入合适的网格尺寸，采用四边形的网格单元划分方式，点击创建，表面网格创建完成；创建柱壳两端网格，选择2D中的spline，以节点路径的方式(node path),按照一定的方向选择两端所有节点创建网格；选中网格类型(element type),将四边形网格类型调整为S4R，框选所有创建网格，点击更新；调整两端面网格的法向方向，选择Tool中normals,选中网格，点击“display”,统一法向堆栈方向由里往外；返回Geom,选择temp nodes，删除所有创建的节点，完成几何模型及其网格建立。8.1. In Hypermesh software, select nodes in Geom, and create two nodes (0, 0, 105) and (0, 0, -105) in the Cartesian coordinate system as reference points; select surface in Geom, select Cylinder Full, give the corresponding radius r = 35mm and height h = 210mm, use the two nodes as the ground center and normal direction, click Create, and the surface of the cylindrical shell is created; click Automesh in 2D in the menu bar, enter the appropriate mesh size according to the real model, use the quadrilateral mesh unit division method, click Create, and the surface mesh is created; create the mesh at both ends of the cylindrical shell, select spline in 2D, and select all nodes at both ends in a certain direction to create meshes in the node path method; select the mesh type (element type), adjust the quadrilateral mesh type to S4R, select all created meshes, and click Update; adjust the normal direction of the mesh at both ends, select normals in Tool, select the mesh, click "display", and unify the normal stack direction from inside to outside; return to Geom, select temp nodes, delete all created nodes, and complete the geometric model and its mesh establishment.

8.2、建立有限元模型计算模型，柱形耐压壳及碳纤维复合材料如表10所示：8.2. Establish the finite element model calculation model. The cylindrical pressure hull and carbon fiber composite material are shown in Table 10:

表10材料参数Table 10 Material parameters

Figure BDA0004119529210000221
Figure BDA0004119529210000221

选择Tool中的set,创建set集，将其柱壳模型分为端盖、完美、减薄以及修复区域，前三个区域建立连续均匀的壳单元截面属性，端盖厚度t0＝20mm，完美区域t1＝2mm,减薄区域t2＝0.4mm，厚度方向选取5个积分点，完美、减薄区域从顶面赋厚，端盖区域从底面赋厚；隐藏柱壳模型，仅显示修复区域的网格，进入Mesh模块，将修复区域的网格进行实体化，选择网格(mesh)中的编辑(edit),种类选择网格，方法选择创建实体层，从顶面由里往外进行偏置，其厚度为t3＝0.8mm，两个不同材料的接触面以共节点的方式进行连接。创建从顶面和底面新的单元，相应的网格类型需改成连续壳单元SC8R，再重新回到Property模块,定义修复区域网格的截面属性，创建复合材料铺层，给出铺层的数目4层，其网格单元类型与在mesh模块中保持一致，铺层方向以离散的方式进行定义，法向轴方向与初始轴方向分别选择方向3和1，其面和边则是选择网格面和以柱壳轴向的网格的一条边，堆栈方是向外进行铺层，输入每一层的材料都为复合材料、相对厚度为0.2mm以及选取角度为90°，每层选取三个积分点，点击创建完成。Select set in Tool to create a set. Divide the cylindrical shell model into end cap, perfect, thinning and repair areas. Establish continuous and uniform shell unit section properties for the first three areas. The thickness of the end cap is t 0 = 20 mm, the perfect area is t 1 = 2 mm, and the thinning area is t 2 = 0.4 mm. Select 5 integration points in the thickness direction. The perfect and thinning areas are thickened from the top surface, and the end cap area is thickened from the bottom surface. Hide the cylindrical shell model and only display the mesh of the repair area. Enter the Mesh module to solidify the mesh of the repair area. Select Edit in Mesh, select Mesh as the type, and select Create a solid layer as the method. Offset from the top surface from the inside to the outside. The thickness is t 3 = 0.8 mm. The contact surfaces of two different materials are connected in the form of common nodes. Create new units from the top and bottom surfaces, and the corresponding mesh type needs to be changed to continuous shell unit SC8R. Then go back to the Property module, define the cross-sectional properties of the repair area mesh, create composite material plies, and give the number of plies as 4. The mesh unit type is consistent with that in the mesh module. The ply direction is defined in a discrete manner. The normal axis direction and the initial axis direction are selected as directions 3 and 1 respectively. The faces and edges are the mesh faces and one edge of the mesh in the axial direction of the cylindrical shell. The stacking direction is to lay the layers outward. Enter the material of each layer as composite material, the relative thickness is 0.2mm, and the angle is 90°. Select three integration points for each layer and click Create to complete.

8.3、采用Riks弧长分析步，考虑几何非线性选项，允许根据计算效率来自动选择弧长增量，考虑到分析不安全，其分析步中最大增量步数至少200步，在比例载荷——位移空间中沿静态平衡路径的初始弧长值一般设置为0.01，最大载荷增量设为0.1，最小载荷增量设为10-5；采用三点定位的方式限制模型的自由度，对于柱壳模型的两端面，选择其圆心处，固定其平面自由度，释放其法向自由度，对于柱壳表面，选择柱壳表面中心处一点，固定垂直于该点法向平面的自由度，释放其余自由度，并对整个模型的外表面施加均匀外压。8.3. Use the Riks arc length analysis step, consider the geometric nonlinearity option, and allow the arc length increment to be automatically selected based on the calculation efficiency. Considering the unsafe analysis, the maximum number of incremental steps in the analysis step is at least 200 steps. The initial arc length value along the static equilibrium path in the proportional load-displacement space is generally set to 0.01, the maximum load increment is set to 0.1, and the minimum load increment is set to 10-5; use three-point positioning to limit the degree of freedom of the model. For the two end faces of the cylindrical shell model, select the center of the circle, fix its plane degree of freedom, and release its normal degree of freedom. For the cylindrical shell surface, select a point at the center of the cylindrical shell surface, fix the degree of freedom perpendicular to the normal plane of the point, release the remaining degrees of freedom, and apply uniform external pressure to the outer surface of the entire model.

8.4、重复上述过程，只改变定义分析步方式，选择线性屈曲分(为非线性分析引入缺陷做准备)，采用子空间迭代法，分析六个特征值下的变形情况，特征向量选择12，最大的迭代次数选择3000。创建分析任务，导出文件，在非线性屈曲文件中加入缺陷扰动，调用线性屈曲分析文件，其扰动量一般是0.01t(t为壁厚)，进行求解；打开结果文件，查看后屈曲状态，得出随弧长增量变化的非线性屈曲载荷，提取最大临界载荷值，比较其理论设计的修复条件是否满足修复强度。8.4. Repeat the above process, only changing the definition of the analysis step mode, select linear buckling points (to prepare for the introduction of defects in nonlinear analysis), use the subspace iteration method, analyze the deformation under six eigenvalues, select 12 eigenvectors, and select 3000 for the maximum number of iterations. Create an analysis task, export the file, add defect perturbations to the nonlinear buckling file, call the linear buckling analysis file, and the perturbation amount is generally 0.01t (t is the wall thickness) for solution; open the result file, check the post-buckling state, obtain the nonlinear buckling load that changes with the arc length increment, extract the maximum critical load value, and compare whether the repair conditions of the theoretical design meet the repair strength.

实施例6：Embodiment 6:

提供一种采用复合材料修复内部损伤柱形耐压壳的设计方法如图10所示，具体包括如下步骤：A design method for repairing an internally damaged cylindrical pressure hull using composite materials is provided as shown in FIG10 , and specifically comprises the following steps:

表11初始柱形耐压壳尺寸参数Table 11 Dimensional parameters of initial cylindrical pressure hull

Figure BDA0004119529210000231
Figure BDA0004119529210000231

(一)根据柱形耐压壳的尺寸计算临界长度，当耐压壳设计长度≥临界长度时，为长柱壳；当耐压壳设计长度<临界长度，为短柱壳，代入公式(1)，此实施例6的临界长度为：(I) The critical length is calculated according to the size of the cylindrical pressure hull. When the design length of the pressure hull is ≥ the critical length, it is a long cylindrical hull; when the design length of the pressure hull is < the critical length, it is a short cylindrical hull. Substituting into formula (1), the critical length of this embodiment 6 is:

Figure BDA0004119529210000232
Figure BDA0004119529210000232

由此可得出该柱形耐压壳为短柱壳；It can be concluded that the cylindrical pressure shell is a short cylindrical shell;

(二)对于钢制柱形耐压壳，当处于深海中，外部压力均匀的作用在柱壳表面，按照耐压壳的分类进行壳体临界压力的计算(弹性范围内)，具体地，E为弹性模量，如图表2所示，该实施例为短轴柱形耐压壳，代入公式(3)，计算得出：(II) For a steel cylindrical pressure hull, when it is in the deep sea, the external pressure acts evenly on the surface of the cylindrical hull. The critical pressure of the hull is calculated (within the elastic range) according to the classification of the pressure hull. Specifically, E is the elastic modulus, as shown in Figure 2. This embodiment is a short-axis cylindrical pressure hull. Substituting it into formula (3), it is calculated:

Figure BDA0004119529210000233
Figure BDA0004119529210000233

由于柱壳在成型过程中，因加工操作、制造造成的误差及材料性能在其过程中存在硬化现象等因素会对耐压壳的临界压力造成不良影响，在计算时需要考虑安全系数m,即满足临界压力为设计压力的m倍，代入公式(4)，可得：During the forming process of the cylindrical shell, the errors caused by processing operations and manufacturing, as well as the hardening of material properties during the process, will have an adverse effect on the critical pressure of the pressure shell. Therefore, the safety factor m needs to be considered in the calculation, that is, the critical pressure is m times the design pressure. Substituting it into formula (4), we can get:

Figure BDA0004119529210000234
Figure BDA0004119529210000234

(三)选取如图10所示柱形耐压壳内部受损状态，引入缺陷当量长度z，代入公式(5)可得：(III) Select the damaged state of the cylindrical pressure hull as shown in Figure 10, introduce the defect equivalent length z, and substitute it into formula (5) to obtain:

Figure BDA0004119529210000235
Figure BDA0004119529210000235

根据缺陷当量的长度范围，代入公式(9)，计算缺陷在轴向穿壁平面的投影面积S:According to the length range of the defect equivalent, substitute it into formula (9) to calculate the projection area S of the defect on the axial through-wall plane:

Figure BDA0004119529210000241
Figure BDA0004119529210000241

对于缺陷区域原始管壁横街面积S0，可定义为：S0＝lt＝20×2＝40(mm2)；The original pipe wall cross-sectional area S 0 of the defective region can be defined as: S 0 = lt = 20 × 2 = 40 (mm 2 );

(四)计算柱形耐压壳缺陷程度，d/t＝50％，确定材料流变应力Sflow，代入公式(10),计算可得：Sflow＝304×1.1＝334.4(MPa)；(iv) Calculate the defect degree of the cylindrical pressure hull, d/t = 50%, determine the material flow stress S flow , substitute it into formula (10), and calculate: S flow = 304 × 1.1 = 334.4 (MPa);

(五)根据上述获得的S、S0、Sflow，以Dugdale塑性尺寸模型、受外压耐压壳的轴向缺陷的“Folias”分析和经验的缺陷深度与柱壳厚度关系为基础，计算环向断裂应力SF，代入公式(14)；其中，Mt为Folias系数，由柱形耐压壳内径、缺陷长度、柱壳壁厚确定，代入公式(13)计算可得：(V) Based on the above-obtained S, S0 , and Sflow , the circumferential fracture stress S F is calculated based on the Dugdale plastic size model, the "Folias" analysis of the axial defect of the pressure hull under external pressure, and the empirical relationship between the defect depth and the thickness of the cylindrical shell, and substituted into formula (14); where Mt is the Folias coefficient, which is determined by the inner diameter of the cylindrical pressure hull, the defect length, and the thickness of the cylindrical shell. Substituting it into formula (13) yields:

Figure BDA0004119529210000242
Figure BDA0004119529210000242

Figure BDA0004119529210000243
Figure BDA0004119529210000243

(六)根据内部损伤柱形耐压壳的环向断裂应力，确定缺陷柱壳设计压力PS为，代入公式(15)、(16)，计算可得：

Figure BDA0004119529210000244
(VI) According to the circumferential fracture stress of the internally damaged cylindrical pressure shell, the design pressure PS of the defective cylindrical shell is determined as follows: Substituting into formulas (15) and (16), the following is obtained:
Figure BDA0004119529210000244

(七)设计复合材料修复层，计算缠绕复合材料的最小厚度tmin、长度l0，代入公式(17)(19)中，最小厚度tmin、长度分别为l0：(VII) Design the composite material repair layer, calculate the minimum thickness t min and length l 0 of the wrapped composite material, and substitute them into formulas (17) and (19). The minimum thickness t min and length l 0 are:

Figure BDA0004119529210000245
Figure BDA0004119529210000245

Figure BDA0004119529210000246
Figure BDA0004119529210000246

(八)通过理论计算求出的修复厚度和修复长度，在符合实际情况条件下，最终选取tmin＝1.8(mm)、l0＝52(mm)，作为修复参数，进行有限元验证:(VIII) The repair thickness and repair length obtained through theoretical calculations were finally selected as t min = 1.8 (mm) and l 0 = 52 (mm) as repair parameters under the actual conditions for finite element verification:

8.1、在Hypermesh软件中，选择Geom中的nodes,在笛卡尔坐标系下建立两个节点分别为(0，0，105)和(0，0，-105),作为参考点；选择Geom中的surface,选中Cylinder Full,给出相应的半径r＝35mm和高度h＝210mm，以两节点作为地面中心和法向处置方向，点击创建，柱壳外表创建完成；点击菜单栏中2D中的automesh,根据真实模型，输入合适的网格尺寸，采用四边形的网格单元划分方式，点击创建，表面网格创建完成；创建柱壳两端网格，选择2D中的spline，以节点路径的方式(node path),按照一定的方向选择两端所有节点创建网格；选中网格类型(element type),将四边形网格类型调整为S4R，框选所有创建网格，点击更新；调整两端面网格的法向方向，选择Tool中normals,选中网格，点击“display”,统一法向堆栈方向由里往外；返回Geom,选择temp nodes，删除所有创建的节点，完成几何模型及其网格建立。8.1. In Hypermesh software, select nodes in Geom, and create two nodes (0, 0, 105) and (0, 0, -105) in the Cartesian coordinate system as reference points; select surface in Geom, select Cylinder Full, give the corresponding radius r = 35mm and height h = 210mm, use the two nodes as the ground center and normal direction, click Create, and the surface of the cylindrical shell is created; click Automesh in 2D in the menu bar, enter the appropriate mesh size according to the real model, use the quadrilateral mesh unit division method, click Create, and the surface mesh is created; create the mesh at both ends of the cylindrical shell, select spline in 2D, and select all nodes at both ends in a certain direction to create meshes in the node path method; select the mesh type (element type), adjust the quadrilateral mesh type to S4R, select all created meshes, and click Update; adjust the normal direction of the mesh at both ends, select normals in Tool, select the mesh, click "display", and unify the normal stack direction from inside to outside; return to Geom, select temp nodes, delete all created nodes, and complete the geometric model and its mesh establishment.

8.2、建立有限元模型计算模型，柱形耐压壳及碳纤维复合材料如表12所示：8.2. Establish the finite element model calculation model. The cylindrical pressure hull and carbon fiber composite material are shown in Table 12:

表12材料参数Table 12 Material parameters

Figure BDA0004119529210000251
Figure BDA0004119529210000251

选择Tool中的set,创建set集，将其柱壳模型分为端盖、完美、减薄以及修复区域，前三个区域建立连续均匀的壳单元截面属性，端盖厚度t0＝20mm，完美区域t1＝2mm,减薄区域t2＝1mm，厚度方向选取5个积分点，完美、减薄区域从顶面赋厚，端盖区域从底面赋厚；隐藏柱壳模型，仅显示修复区域的网格，进入Mesh模块，将修复区域的网格进行实体化，选择网格(mesh)中的编辑(edit),种类选择网格，方法选择创建实体层，从顶面由里往外进行偏置，其厚度为t3＝1.8mm，两个不同材料的接触面以共节点的方式进行连接。创建从顶面和底面新的单元，相应的网格类型需改成连续壳单元SC8R，再重新回到Property模块,定义修复区域网格的截面属性，创建复合材料铺层，给出铺层的数目9层，其网格单元类型与在mesh模块中保持一致，铺层方向以离散的方式进行定义，法向轴方向与初始轴方向分别选择方向3和1，其面和边则是选择网格面和以柱壳轴向的网格的一条边，堆栈方是向外进行铺层，输入每一层的材料都为复合材料、相对厚度为0.2mm以及选取角度为90°，每层选取三个积分点，完成创建。Select set in Tool to create a set set, and divide the cylindrical shell model into end cap, perfect, thinning and repair areas. Establish continuous and uniform shell unit section properties for the first three areas. The thickness of the end cap is t 0 = 20mm, the perfect area is t 1 = 2mm, and the thinning area is t 2 = 1mm. Select 5 integration points in the thickness direction. The perfect and thinning areas are thickened from the top surface, and the end cap area is thickened from the bottom surface. Hide the cylindrical shell model and only display the mesh of the repair area. Enter the Mesh module, solidify the mesh of the repair area, select Edit in Mesh, select Mesh as the type, and select Create a solid layer as the method. Offset from the top surface from the inside to the outside, and its thickness is t 3 = 1.8mm. The contact surfaces of two different materials are connected in the form of common nodes. Create new units from the top and bottom surfaces, and the corresponding mesh type needs to be changed to continuous shell unit SC8R. Then go back to the Property module, define the cross-sectional properties of the repair area mesh, create composite material plies, and give the number of plies as 9. The mesh unit type is consistent with that in the mesh module. The ply direction is defined in a discrete manner. The normal axis direction and the initial axis direction are selected as directions 3 and 1 respectively. The faces and edges are the mesh faces and one edge of the mesh in the axial direction of the cylindrical shell. The stacking direction is to ply outwards. The material of each layer is composite material, the relative thickness is 0.2mm, and the angle is 90°. Three integration points are selected for each layer to complete the creation.

8.3、采用Riks弧长分析步，考虑几何非线性选项，允许根据计算效率来自动选择弧长增量，考虑到分析不安全，其分析步中最大增量步数至少200步，在比例载荷——位移空间中沿静态平衡路径的初始弧长值一般设置为0.01，最大载荷增量设为0.1，最小载荷增量设为10-5；采用三点定位的方式限制模型的自由度，对于柱壳模型的两端面，选择其圆心处，固定其平面自由度，释放其法向自由度，对于柱壳表面，选择柱壳表面中心处一点，固定垂直于该点法向平面的自由度，释放其余自由度，并对整个模型的外表面施加均匀外压。8.3. Use the Riks arc length analysis step, consider the geometric nonlinearity option, and allow the arc length increment to be automatically selected based on the calculation efficiency. Considering the unsafe analysis, the maximum number of incremental steps in the analysis step is at least 200 steps. The initial arc length value along the static equilibrium path in the proportional load-displacement space is generally set to 0.01, the maximum load increment is set to 0.1, and the minimum load increment is set to 10-5; use three-point positioning to limit the degree of freedom of the model. For the two end faces of the cylindrical shell model, select the center of the circle, fix its plane degree of freedom, and release its normal degree of freedom. For the cylindrical shell surface, select a point at the center of the cylindrical shell surface, fix the degree of freedom perpendicular to the normal plane of the point, release the remaining degrees of freedom, and apply uniform external pressure to the outer surface of the entire model.

8.4、重复上述过程，只改变定义分析步方式，选择线性屈曲分(为非线性分析引入缺陷做准备)，采用子空间迭代法，分析六个特征值下的变形情况，特征向量选择12，最大的迭代次数选择3000。创建分析任务，导出文件，在非线性屈曲文件中加入缺陷扰动，调用线性屈曲分析文件，其扰动量一般是0.01t(t为壁厚)，进行求解；打开结果文件，查看后屈曲状态，得出随弧长增量变化的非线性屈曲载荷，提取最大临界载荷值，比较其理论设计的修复条件是否满足修复强度。8.4. Repeat the above process, only changing the definition of the analysis step mode, select linear buckling points (to prepare for the introduction of defects in nonlinear analysis), use the subspace iteration method, analyze the deformation under six eigenvalues, select 12 eigenvectors, and select 3000 for the maximum number of iterations. Create an analysis task, export the file, add defect perturbations to the nonlinear buckling file, call the linear buckling analysis file, and the perturbation amount is generally 0.01t (t is the wall thickness) for solution; open the result file, check the post-buckling state, obtain the nonlinear buckling load that changes with the arc length increment, extract the maximum critical load value, and compare whether the repair conditions of the theoretical design meet the repair strength.

基于上述六个实施例的验证，得出如图11所示效果图，如表13所示为综上修复的理论设计及有限元仿真综合：Based on the verification of the above six embodiments, the effect diagram shown in FIG11 is obtained, and the theoretical design and finite element simulation synthesis of the above repair are shown in Table 13:

表13理论设计于有限元仿真Table 13 Theoretical design and finite element simulation

Figure BDA0004119529210000261
Figure BDA0004119529210000261

通过提出一种内部损伤耐压壳在外压作用下利用复合材料进行修复的方式，将修复的厚度和长度作为仿真的条件，建立初始，缺陷、修复仿真模型得出数值解进行对比，三者结果比较，验证该评估方法满足内部损伤柱形耐压壳修复条件的正确性。A method of repairing the internally damaged pressure hull using composite materials under external pressure is proposed. The thickness and length of the repair are used as simulation conditions, and the initial, defect and repair simulation models are established to obtain numerical solutions for comparison. The comparison of the three results verifies the correctness of the evaluation method in meeting the repair conditions of the internally damaged cylindrical pressure hull.

Claims (7)

1.一种采用复合材料修复内部损伤柱形耐压壳的设计方法，其特征在于包括以下步骤：1. A design method adopting composite materials to repair internal damage cylindrical pressure vessel, is characterized in that comprising the following steps: 第一步：判断长短壳；The first step: judge the length of the shell; 根据耐压壳的外径D和壁厚t计算临界长度Lcr,对于耐压壳进行判断分类，其中：Calculate the critical length L cr according to the outer diameter D and wall thickness t of the pressure vessel, and judge and classify the pressure vessel, where:
Figure FDA0004119529190000011
Figure FDA0004119529190000011
 当耐压壳计算长度≥临界长度时，为长柱壳；当耐压壳计算长度<临界长度，为短柱壳；When the calculated length of the pressure hull ≥ the critical length, it is a long cylindrical shell; when the calculated length of the pressure hull < the critical length, it is a short cylindrical shell; 第二步：确定完美柱壳设计压力；Step 2: Determine the design pressure of the perfect cylindrical shell; 对于钢制柱形耐压壳，当处于深海中，外部压力均匀的作用在柱壳表面，按照耐压壳的分类按以下公式进行壳体临界压力的计算：For the steel cylindrical pressure hull, when it is in the deep sea, the external pressure acts uniformly on the surface of the cylindrical shell, and the critical pressure of the shell is calculated according to the following formula according to the classification of the pressure hull: 长柱壳：
Figure FDA0004119529190000012
Long cylindrical shell:
Figure FDA0004119529190000012
 短柱壳：
Figure FDA0004119529190000013
Short cylindrical shell:
Figure FDA0004119529190000013
 其中，L为柱壳长度，E为柱壳的弹性模量，Pcr为临界压力；Among them, L is the length of the cylindrical shell, E is the elastic modulus of the cylindrical shell, and P cr is the critical pressure; 考虑耐压壳成型过程中多种因素对临界压力造成的不良影响，引入安全系数m，则满足临界压力为设计压力为：Considering the adverse effects of various factors on the critical pressure during the pressure shell forming process, and introducing the safety factor m, the critical pressure is satisfied as the design pressure is:
Figure FDA0004119529190000014
Figure FDA0004119529190000014
 第三步：确定缺陷柱壳断裂应力；Step 3: Determine the fracture stress of the defective cylindrical shell; S1：确定缺陷区域的具体形态，引入缺陷当量长度z,求出缺陷在轴向穿壁平面的投影面积S：S1: Determine the specific shape of the defect area, introduce the defect equivalent length z, and calculate the projected area S of the defect on the axial wall-through plane:
Figure FDA0004119529190000015
Figure FDA0004119529190000015
 其中，l为损失最大轴向长度，d为损失的最大深度，davg为损失平均厚度；Among them, l is the maximum axial length of loss, d is the maximum depth of loss, and d avg is the average thickness of loss; S2：根据缺陷程度，γ＝d/t，确定材料的流变应力Sflow：S2: According to the defect degree, γ=d/t, determine the flow stress S flow of the material:
Figure FDA0004119529190000016
Figure FDA0004119529190000016
 其中，SMYS为最小屈服强度；Among them, SMYS is the minimum yield strength; S3：计算内部损失柱壳环向断裂应力：S3: Calculate the circumferential fracture stress of the cylindrical shell with internal loss: 以Dugdale塑性尺寸模型、受外压耐压壳的轴向缺陷的Folias分析和经验的缺陷深度与柱壳厚度关系为基础，得到环向断裂应力为：Based on the Dugdale plastic size model, the Folias analysis of the axial defects of the pressure vessel subjected to external pressure, and the empirical relationship between the defect depth and the thickness of the cylindrical shell, the circumferential fracture stress is obtained as:
Figure FDA0004119529190000021
Figure FDA0004119529190000021
 其中，SF为环向断裂应力，S0为缺陷处原始管壁的横截面积，S0＝lt，Mt为Flias系数，代入投影面积S，则：Among them, S F is the circumferential fracture stress, S 0 is the cross-sectional area of the original pipe wall at the defect, S 0 =lt, and M t is the Flias coefficient, which is substituted into the projected area S, then:
Figure FDA0004119529190000022
Figure FDA0004119529190000022
 第四步：确定缺陷柱壳设计压力；Step 4: Determine the design pressure of the defective cylindrical shell; 柱形耐压壳失效压力PF：Failure pressure P F of cylindrical pressure vessel: PF＝SF2t/D；P F = S F 2t/D; 柱形耐压壳设计压力PS：Cylindrical pressure vessel design pressure P S : PS＝PF/SF；P S =P F /SF; 其中，SF为常数，SF＝1.2～1.6；Among them, SF is a constant, SF=1.2～1.6; 第五步：设计复合材料修复层；Step 5: Design the composite repair layer; 修复厚度：Repair thickness:
Figure FDA0004119529190000023
Figure FDA0004119529190000023
 其中，Ep为柱壳的拉伸模量，Ea为纤维增强聚合物轴向的拉伸模量，Pd为设计压力；Among them, E p is the tensile modulus of the cylindrical shell, E a is the axial tensile modulus of the fiber reinforced polymer, and P d is the design pressure; 修复长度：Repair length: F＝2πrtσy；F=2πrtσ y ;
Figure FDA0004119529190000024
Figure FDA0004119529190000024
 其中，F为柱形耐压壳轴向屈服载荷；l0为修复长度；σy柱形耐压壳的屈服强度，τ为粘合剂的剪切强度，r为柱形耐压壳外部半径。Among them, F is the axial yield load of the cylindrical pressure vessel; l 0 is the repair length; σy is the yield strength of the cylindrical pressure vessel, τ is the shear strength of the adhesive, and r is the outer radius of the cylindrical pressure vessel . 2.根据权利要求1所述的采用复合材料修复内部损伤柱形耐压壳的设计方法，其特征在于：在第二步中，耐压壳成型过程中考虑的因素包括因加工操作、制造造成的误差及材料性能在加工过程中存在硬化现象，安全系数m的取值范围为1.2～1.5。2. The design method for using composite materials to repair internally damaged cylindrical pressure vessel according to claim 1, characterized in that: in the second step, the factors considered in the forming process of the pressure vessel include the factors caused by processing operations and manufacturing There is hardening phenomenon in the processing process of the errors and material properties, and the value range of the safety factor m is 1.2 to 1.5. 3.根据权利要求1所述的采用复合材料修复内部损伤柱形耐压壳的设计方法，其特征在于：在第三步的步骤S1中，缺陷当量长度z为：3. The design method for using composite materials to repair internal damaged cylindrical pressure vessel according to claim 1, characterized in that: in the third step S1, the defect equivalent length z is:
Figure FDA0004119529190000031
Figure FDA0004119529190000031
 当z≤20时；When z≤20;
Figure FDA0004119529190000032
Figure FDA0004119529190000032
 当z＞20时；When z>20; 沿着轴向等间距h测量缺陷深度分别为d0、d1、d2…dn、dn+1，共测量n+1次构成n个梯形：Measure the defect depth along the axial equidistant h as d 0 , d 1 , d 2 ...d n , d n+1 respectively, and measure n+1 times in total to form n trapezoids:
Figure FDA0004119529190000033
Figure FDA0004119529190000033
 其中，d0、dn为两端的深度，在理想情况下可视为0，则有：Among them, d 0 and d n are the depths at both ends, which can be regarded as 0 under ideal conditions, then:
Figure FDA0004119529190000034
Figure FDA0004119529190000034
 4.根据权利要求1所述的采用复合材料修复内部损伤柱形耐压壳的设计方法，其特征在于：在第三步的步骤S3中，Mt由l、Di、t确定：4. The design method of using composite materials to repair internal damage cylindrical pressure vessel according to claim 1, characterized in that: in the third step S3, M t is determined by l, D i , t:
Figure FDA0004119529190000035
Figure FDA0004119529190000035
Figure FDA0004119529190000036
Figure FDA0004119529190000036
 其中，Di为耐压壳内径；Among them, D i is the inner diameter of the pressure vessel; 将Mt进行修正，其表达式可分为：To modify M t , its expression can be divided into:
Figure FDA0004119529190000037
Figure FDA0004119529190000037
 其中，λ为缺陷柱壳系数。where λ is the defective cylindrical shell coefficient. 5.根据权利要求1所述的采用复合材料修复内部损伤柱形耐压壳的设计方法，其特征在于，还包括第六步，有限元验证：分别建立初始、缺陷和修复的几何模型与有限元模型，确定模型各部分的截面参数，对复合材料赋予相应的铺层角度；采用非线性屈曲分析，定义有限元模型边界条件，在给予微小缺陷模拟真实耐压壳极限屈曲载荷，比较三者的屈曲载荷，验证理论计算的修复条件满足内部损伤柱形耐压壳修复状态。5. The design method for repairing internally damaged cylindrical pressure vessels using composite materials according to claim 1, further comprising the sixth step, finite element verification: establishing initial, defect and repaired geometric models and finite element models respectively. The element model, determine the section parameters of each part of the model, and assign the corresponding ply angle to the composite material; use nonlinear buckling analysis, define the boundary conditions of the finite element model, and simulate the ultimate buckling load of the real pressure shell by giving small defects, and compare the three The buckling load is verified to verify that the repair condition calculated by the theory meets the repair state of the internally damaged cylindrical pressure vessel. 6.一种如1～5任一所述的采用复合材料修复内部损伤柱形耐压壳设计方法得到的修复结构，其特征在于：包括柱形耐压壳(1)、复合材料修复层(3)，柱形耐压壳(1)上厚板(1)的内壁上具有损伤缺口，复合材料修复层(3)在损伤缺口的位置处固定于厚板(1)的外壁上，复合材料修复层(3)覆盖损伤缺口，且其沿柱形耐压壳(1)轴向的长度大于损伤缺口沿柱形耐压壳(1)轴向的长度。6. A repair structure as described in any one of 1 to 5 using composite materials to repair internal damaged cylindrical pressure vessel design methods, characterized in that: comprising a cylindrical pressure vessel (1), a composite material repair layer ( 3), there is a damage gap on the inner wall of the thick plate (1) on the cylindrical pressure vessel (1), and the composite material repair layer (3) is fixed on the outer wall of the thick plate (1) at the position of the damage gap, and the composite material The repair layer (3) covers the damaged notch, and its length along the axial direction of the cylindrical pressure vessel (1) is greater than the length of the damaged notch along the axial direction of the cylindrical pressure vessel (1). 7.根据权利要求6所述的采用复合材料修复结构，其特征在于：复合材料修复层(3)的材料为纤维增强聚合物复合材料。7. The repair structure using composite material according to claim 6, characterized in that: the composite material repair layer (3) is made of fiber reinforced polymer composite material.
CN202310229041.7A 2023-03-10 2023-03-10 Design method and structure for repairing internal damaged cylindrical pressure-resistant shell by adopting composite material Pending CN116432338A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN118150307A (en) * 2024-03-19 2024-06-07 中国船舶集团有限公司第七一九研究所 Test verification method for pressure-resistant structure of deep-sea composite material
CN119827312A (en) * 2025-03-14 2025-04-15 天津爱思达航天科技股份有限公司 Method for obtaining composite material deep sea pressure-resistant cabin barrel column section biaxial compression strength prediction curve

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN118150307A (en) * 2024-03-19 2024-06-07 中国船舶集团有限公司第七一九研究所 Test verification method for pressure-resistant structure of deep-sea composite material
CN119827312A (en) * 2025-03-14 2025-04-15 天津爱思达航天科技股份有限公司 Method for obtaining composite material deep sea pressure-resistant cabin barrel column section biaxial compression strength prediction curve
CN119827312B (en) * 2025-03-14 2025-07-04 天津爱思达航天科技股份有限公司 Method for obtaining composite material deep sea pressure-resistant cabin barrel column section biaxial compression strength prediction curve

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