CN108984841B - Method for calculating equivalent modulus of composite laminated plate and checking strength under given load - Google Patents
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Abstract
The invention relates to the field of composite material design, in particular to equivalent modulus calculation and strength check under given load of a composite material laminated plate. Comprises an information input module, an operation module and an information output module. The material performance information, the layering information and the load data information are input into the information input module, the calculation program can calculate three rigidity matrixes A, D and B of the composite material laminated plate according to the input data, and the equivalent modulus and the corresponding equivalent rigidity matrix of the laminated plate under the pure in-plane load action and the pure bending action are calculated according to the matrix A and the matrix D. And meanwhile, calculating the integral strain and the deflection rate of the laminated plate according to the rigidity matrix and the load information of the laminated plate, further obtaining the stress strain information of each single layer, and checking whether the laminated plate meets the strength requirement under the action of specified load by adopting three composite material failure criteria. The method greatly improves the calculation speed, can directly and quickly obtain the accurate numerical solution of the stress and the strain for the analysis of the laminated plate under the condition of simple stress, and improves the design efficiency.
Description
Technical Field
The invention relates to the field of structural design of composite materials, in particular to a checking program for calculating equivalent modulus and strength under a given load action of a composite material laminated plate.
Background
As is known, in the finite element analysis process of a composite material, due to the complexity of the structure of the composite material and the anisotropy of the material, tedious input of ply information is often required when defining the material properties, and especially, when analyzing a composite material part with more plies or a more complex structure, a large amount of time and cost are required for giving the material properties. Because the symmetrical balanced ply composite material laminated plate has no stretch bending and stretch twisting coupling and has smaller stretch shearing coupling coefficient, the material attribute endowing process is simplified by an equivalent modulus method, the time cost is saved for the plane stress problem or the pure bend twisting problem, the design efficiency is improved, and higher calculation precision can be ensured.
At present, the strength analysis of the laminated plate bearing the in-plane tension-compression shearing force or the bending-torsion action is generally realized by using a finite element analysis method. When finite element software is used for calculation and analysis, concentrated stress larger than real stress is obtained at the load application position, which is not desirable for designers. The concentrated stress causes that the stress condition of the laminated plate cannot be correctly and intuitively reflected by a finite element analysis result, and the force is only a local effect and has no influence on the stress of the whole structure according to the Saint-Venen principle. The numerical solution is used for calculating the internal force of the laminated plate in the stress state, so that the high calculation precision can be achieved, the input information is less, the calculation efficiency is high, and the calculation result can reflect the integral stress state of the laminated plate, so that the numerical solution is superior to finite element analysis for the problem.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a program for calculating the equivalent modulus and the strength of a composite material laminated plate under the action of a given load, which can calculate the equivalent modulus and the equivalent stiffness matrix of a symmetrical and balanced laminated plate, simplify the finite element analysis process, reduce the analysis complexity, improve the analysis efficiency, carry out high-efficiency numerical solution on the stress strain under the action of the in-plane load or the bending load borne by the laminated plate, adopt three common failure criteria to check the strength value of the laminated plate, and provide a design basis and basis for a designer to carry out the structural design of the composite material.
The technical scheme adopted by the invention for solving the technical problems is as follows: the utility model provides a composite material laminate equivalent modulus calculates and intensity check under the given load, includes information input module, operation module and information output module. After data is input and running, the calculation program firstly calculates the stiffness matrix of each single layer according to the data input in the information input module, and then integrates the stiffness matrix of the laminated plate according to the layering information. The method comprises the steps of calculating the equivalent modulus of the laminated plate under the pure in-plane load effect and the pure bending load effect and the equivalent stiffness matrix thereof through the laminated plate stiffness matrix, obtaining the total strain by combining load information, further obtaining the stress strain level of each single layer by combining layering information, and judging whether the laminated plate fails under the specified load effect according to the maximum stress criterion, the Tsai-Hill failure criterion and the Tsai-Wu failure criterion.
The information input module of the equivalent modulus and strength checking calculation program comprises three parts of material performance information, layering information and load data information: the material property information comprises the following contents: axial modulus E of the individual layers 1 Transverse modulus E 2 Poisson ratio mu 12 Shear modulus G 12 Axial tensile strength X of the individual layers t Transverse tensile Strength Y t Axial compressive strength X c Transverse compressive strength Y c The shear strength S; the layering information comprises the following contents: the laying sequence ord, the thickness t and the laying angle theta of each single layer; the payload data information includes contents of: axial tension and compression load N d x Transverse tension and compression load N d y In-plane shear load N d xy Axial bending load M d x Transverse bending load M d y Torsional load M d xy (the above loads are both internal force and internal moment per unit width (or length) of the cross section of the laminate).
The equivalent modulus and strength check calculation program has the following calculation principle of an operation module:
step 1: according to the input data information E 1 、E 2 、μ 12 、G 12 And calculating the rigidity matrix Q of each single layer by using the formulas (2-1) to (2-3).
Wherein,
the equation (2-1) is written as a relation expressing stress in terms of strain:
where Q is a two-dimensional stiffness matrix, inverted by a two-dimensional compliance matrix S.
And 2, step: and (3) calculating the overall stiffness matrixes A, D and B of the laminated plate by integrating the stacking angle theta, the sequence ord and the thickness t information and by formulas (2-4) - (2-9) according to the calculated single-layer stiffness matrix Q.
The stress-strain relationship of the monolayer in the overall coordinate x-y at a ply angle θ is as follows:
wherein T is a coordinate transformation matrix.
Considering that the laminated plate is formed by laminating a plurality of single-layer plates, the stress-strain relationship of the k-th single layer is as follows:
for laminated plate have
In the formula, K x 、K y For bending of the middle plane of the panel, K xy Is the plane torsion of the plate, epsilon 0 x 、ε 0 x 、γ 0 xy Mid plane strain.
Let N x 、N y 、N xy 、M x 、M x 、M xy The internal force and the internal moment per unit width (or length) of the cross section of the laminated plate, the stress of the laminated plate and the internal force and the internal moment per unit width (or length) of the cross section of the laminated plate should satisfy the formula (1-9):
therefore, the relationship between the internal force, the internal moment and the strain of the laminated plate is converted into
Is abbreviated as
A laminate stiffness matrix a, D, B is obtained.
And 3, step 3: according to the obtained A, D and B matrixes, as for the symmetrical balanced ply composite material laminated plate, stretch bending coupling does not exist, so that the B matrix is a hollow matrix; due to A 16 、A 26 、D 16 、D 26 The positive and negative alternative terms exist in the terms, so that the numerical value of the terms is much smaller than other rigidity coefficients, and the calculation can be simplified.
a. Under the condition of pure in-plane load, no bending load M exists, so that the relation between the internal force and the strain of the laminated plate is
N＝Aε 0 (2-10)
Thus, the equivalent modulus parameter E of the laminated plate can be obtained through calculation of the A matrix 1 、E 2 、μ 12 、G 12 And an equivalent stiffness matrix Q.
b. Under the condition of pure bending load, no in-plane load N exists, so that the relation between the internal moment and the strain of the laminated plate is
M＝DK (2-11)
So that the equivalent modulus parameter E of the laminated plate can be obtained through calculation of the D matrix 1W 、E 2W 、μ 12W 、G 12W And an equivalent stiffness matrix Q W 。
And 4, step 4: according to the obtained A, D and B matrixes and the specified external load N d x 、N d y 、N d xy 、M d x 、M d y 、M d xy The compliance relation formula of the internal force and the internal moment representing the strain and the curvature can be reversely deduced through the formula (2-9) as follows:
therefore, the strain component of the whole laminated plate can be calculated, and then the strain components epsilon of different single layers can be obtained by using the formula (2-6) x 、ε x 、γ xy Then, the stress level sigma of each layer under the overall coordinate x-y and the main direction coordinate 1-2 can be obtained by the formula (2-4) and the stress conversion formula x 、σ y 、τ xy 、σ 1 、σ 2 、τ 12 。
And 5: according to the calculated stress level data sigma in the main direction 1 、σ 2 、τ 12 And respectively adopting the following three strength judgment criteria to carry out strength check on the composite laminated plate:
a. maximum stress criterion:
in the formula, X t 、Y t For tensile strength in the axial and transverse directions, X c 、Y c Compressive strength in the axial and transverse directions, and shear strength.
Tsai-Hill failure criteria:
in the formula, X and Y correspond to the axial and transverse strengths (the tensile and compressive determinations depend on whether the stress is positive or negative), respectively, and S is the shear strength.
Tsai-Wu failure criteria:
in the formula
And judging whether each single layer fails according to each failure criterion, so as to obtain whether the composite material laminated plate meets the strength requirement under the action of the specified load.
The equivalent modulus and strength checking and calculating program includes the following information output by the information output module:
a. equivalent modulus E of the laminate under pure in-plane loading 1 、E 2 、μ 12 、G 12 And equivalent modulus E under pure bending and twisting load 1W 、E 2W 、μ 12W 、G 12W And stiffness matrices Q, Q under both loads W 。
b. Main stress S of each layer material under the action of specified load 11 (i.e.,. Sigma.) 1 )、S 22 (i.e.,. Sigma.) 2 )、S 12 (i.e.. Tau.) 12 )；
c. And (3) checking the strength based on three composite material failure criteria, namely the strength based on the maximum stress criterion, the Tsai-Hill criterion and the Tsai-Wu criterion.
The method has the advantages that three composite material strength failure criteria are used for judging whether the laminated plate meets the strength condition, and the program is systematically combined with a composite material laminated plate equivalent modulus calculation program. The invention integrates the calculation method of the equivalent modulus of the composite material laminated plate and the strength check method of the laminated plate, and uses the computer language to compile a complete calculation program comprising three parts of input, operation and output, and a user can quickly obtain the equivalent modulus data and the strength check result of the composite material laminated plate only by keying in material parameters, layering information and load information at corresponding positions in an input module, thereby avoiding the complex processes of model drawing, grid division, analysis step establishment, boundary condition setting and the like in finite element analysis software, and the calculation result obtained by a numerical solution has higher precision.
Detailed Description
The invention is further described below with reference to the following examples:
example 1: comprises an information input module, an operation module and an information output module. After data is input and running, the calculation program firstly calculates the stiffness matrix of each single layer according to the data input in the information input module, and then integrates the stiffness matrix of the laminated plate according to the layering information. The equivalent modulus and the equivalent stiffness matrix of the laminated plate under the pure in-plane load effect and the pure bending load effect can be calculated through the stiffness matrix of the laminated plate, the total strain is obtained through combining the load information, the stress strain level of each single layer is further obtained through combining the layering information, and whether the laminated plate fails under the specified load effect is judged according to the maximum stress criterion, the Tsai-Hill failure criterion and the Tsai-Wu failure criterion.
The information input module of the equivalent modulus and strength checking and calculating program comprises three parts of material performance information, layering information and load data information: the material property information comprises the following contents: axial modulus E of the individual layers 1 Transverse modulus E 2 Poisson ratio mu 12 Shear modulus G 12 Axial tensile strength X of the individual layers t Transverse tensile Strength Y t Axial compressive strength X c Transverse compressive strength Y c The shear strength S; the layering information comprises the following contents: the laying sequence ord, the thickness t and the laying angle theta of each single layer are determined, the laying sequence information is ordered from bottom to top according to the input sequence, namely the laying information in the first row corresponds to the first layer at the bottommost of the laminated plate, the second row corresponds to the second layer, and so on, the last row corresponds to the topmost layer; the load data information comprises the following contents: axial tension and compression load N d x Transverse tension and compression load N d y In-plane shear load N d xy Axial bending load M d x Transverse bending load M d y Torsional load M d xy (the above loads are both internal force and internal moment per unit width (or length) of the cross section of the laminate).
And after the input module is set, executing an operation program, sequentially and automatically calculating each single-layer rigidity matrix, the laminated plate integral rigidity matrix, the equivalent modulus, the integral strain and stress distribution and the strength check, and outputting the calculated result in a unified window.
The equivalent modulus and strength check calculation program has the following calculation principle of an operation module:
step 1: according to the input data information E 1 、E 2 、μ 12 、G 12 And calculating the rigidity matrix Q of each single layer by using the formulas (2-1) to (2-3).
Wherein,
the equation (2-1) is written as a relation expressing stress in terms of strain:
where Q is a two-dimensional stiffness matrix, inverted by a two-dimensional compliance matrix S.
Step 2: and (3) calculating the integral rigidity matrixes A, D and B of the laminated plate by integrating the information of the layering angle theta, the sequence ord and the thickness t and formulas (2-4) - (2-9) according to the calculated single-layer rigidity matrix Q.
The stress-strain relationship of the monolayer in the overall coordinate x-y at a ply angle θ is as follows:
wherein T is a coordinate transformation matrix.
Considering that the laminated plate is formed by laminating a plurality of single-layer plates, the stress-strain relationship of the k-th single layer is as follows:
for laminated plates have
In the formula, K x 、K y For bending of the middle plane of the panel, K xy Is the plane torsion of the plate, epsilon 0 x 、ε 0 x 、γ 0 xy Mid plane strain.
Let N x 、N y 、N xy 、M x 、M x 、M xy The internal force and the internal moment per unit width (or length) of the cross section of the laminated plate, the stress of the laminated plate and the internal force and the internal moment per unit width (or length) of the cross section of the laminated plate should satisfy the formula (1-9):
therefore, the relationship between the internal force, the internal moment and the strain of the laminated plate is converted into
Is abbreviated as
A laminate stiffness matrix a, D, B is obtained.
And 3, step 3: from the obtained A, D, B matrices, for symmetryThe composite material laminated plate is uniformly laid, and stretch bending coupling does not exist, so that the matrix B is a hollow matrix; due to A 16 、A 26 、D 16 、D 26 The positive and negative alternative terms exist in the terms, so that the numerical value of the terms is much smaller than other rigidity coefficients, and the calculation can be simplified.
a. Under the condition of pure in-plane load, no bending load M exists, so that the relation between the internal force and the strain of the laminated plate is
N＝Aε 0 (2-10)
Thus, the equivalent modulus parameter E of the laminated plate can be obtained through calculation of the A matrix 1 、E 2 、μ 12 、G 12 And an equivalent stiffness matrix Q.
b. Under the condition of pure bending load, no in-plane load N exists, so that the relation between the internal moment and the strain of the laminated plate is
M＝DK (2-11)
So that the equivalent modulus parameter E of the laminated plate can be obtained through calculation of the D matrix 1W 、E 2W 、μ 12W 、G 12W And an equivalent stiffness matrix Q W 。
And 4, step 4: according to the obtained A, D and B matrixes and the specified external load N d x 、N d y 、N d xy 、M d x 、M d y 、M d xy The compliance relation formula of the internal force and the internal moment representing the strain and the curvature can be reversely deduced through the formula (2-9) as follows:
therefore, the strain component of the whole laminated plate can be calculated, and then the strain components epsilon of different single layers can be obtained by using the formula (2-6) x 、ε x 、γ xy Then, the stress level sigma of each layer under the overall coordinate x-y and the main direction coordinate 1-2 can be obtained by the formula (2-4) and the stress conversion formula x 、σ y 、τ xy 、σ 1 、σ 2 、τ 12 。
And 5: from the calculated stress level data σ in the principal direction 1 、σ 2 、τ 12 And respectively adopting the following three strength judgment criteria to carry out strength check on the composite laminated plate:
a. maximum stress criterion:
in the formula, X t 、Y t For tensile strength in the machine and transverse directions, X c 、Y c Compressive strength in the axial and transverse directions, and shear strength.
Tsai-Hill failure criteria:
in the formula, X and Y correspond to the axial and transverse strengths (the tensile and compressive determinations depend on whether the stress is positive or negative), respectively, and S is the shear strength.
Tsai-Wu failure criteria:
in the formula
And judging whether each single layer fails according to each failure criterion, so as to obtain whether the composite material laminated plate meets the strength requirement under the action of the specified load.
The equivalent modulus and strength checking and calculating program includes the following information output by the information output module:
a. equivalent modulus E of the laminate under pure in-plane loading 1 、E 2 、μ 12 、G 12 Or equivalent modulus E under pure bending and twisting load 1W 、E 2W 、μ 12W 、G 12W And stiffness matrix Q or Q under both loads W 。
b. Main stress S of each layer material under the action of specified load 11 (i.e.,. Sigma.1), S 22 (i.e.,. Sigma.) 2 )、S 12 (i.e.. Tau.) 12 )；
c. And (3) checking the strength based on three composite material failure criteria, namely the strength based on the maximum stress criterion, the Tsai-Hill criterion and the Tsai-Wu criterion.
Example 2: on the basis of the embodiment 1, in order to meet the condition that part of the structural rigidity is required, the output structural rigidity data is added, wherein the output structural rigidity data comprises the following steps:
a. tensile stiffness EA:
wherein EA is the tensile stiffness, E is the elastic modulus, and A is the cross-sectional area; f is the tensile force, L is the rod length, Δ L is the rod elongation.
b. Bending stiffness EI:
wherein EI is bending rigidity, E is elastic modulus, and I is inertia moment of a section about a rotating shaft; f is the cantilever rod end concentrated force, l is the rod length, and omega is the rod end deflection.
c. Torsional stiffness GI p ：
Wherein GI p For torsional stiffness, G is the shear modulus, I p Is the polar moment of inertia; t is the torque, l is the rod length,
is the relative twist angle.
It should be noted that the three structural rigidities described above represent the resistance to deformation of a simple unit area laminate, and do not take into account the cross-sectional shape of the actual product. In practical use, especially the torsional rigidity, the sectional structure of the product is always considered, so that the structural rigidity can be changed as required in use.
Example 3: on the basis of the embodiment 2, in order to facilitate professional calculators to check the calculation details, matrix information A, matrix information D and matrix information B are added and output, and stress strain information sigma is added under the x-y coordinates and the 1-2 coordinates of each layer x 、σ y 、τ xy 、σ 1 、σ 2 、τ 12 . However, it should be noted that only 4 bits after the decimal point are reserved for the short type due to the data type in the calculation process, and therefore, correspondingly, data deviation occurs for the calculation result, and the data 0 is often calculated to be 10 -10 Numbers below the order of magnitude.
Example 4: on the basis of the method in example 3, in order to more intuitively express the distribution of the stress of the laminated plate in the thickness direction, the output stress distribution information is increased, wherein the output stress distribution information comprises axial stress, transverse stress and shear stress.
Example 5: on the basis of the description of the embodiment 4, the small term A neglected in the rigidity matrixes A and D is used 16 、A 26 、D 16 、D 26 And A 11 、D 11 With magnitude comparison therebetween, i.e. evaluation
And converted into a percentage system, and the result is examined by A 16 、A 26 、D 16 、D 26 Neglected to be reasonable. />
Claims (5)
1. A method for calculating equivalent modulus of a composite laminated plate and checking strength under a given load is characterized by comprising the following steps: comprises an information input module, an operation module and an information output module; transfusion deviceAfter data are input and run, the calculation program firstly calculates each single-layer rigidity matrix according to the data input in the information input module, and then integrates the single-layer rigidity matrix into the integral rigidity matrix of the laminated plate according to the layering information; calculating the integral stiffness matrix of the laminated plate to obtain the equivalent modulus and the equivalent stiffness matrix under the pure in-plane load effect and the pure bending load effect, obtaining the total strain by combining the load information, further obtaining the stress strain level of each single layer by combining the layering information, and judging whether the laminated plate fails under the specified load effect according to the maximum stress criterion, the Tsai-Hill failure criterion and the Tsai-Wu failure criterion; the information contained in the information input module is divided into three parts of material performance information, layering information and load data information; wherein the material performance information comprises the following contents: axial modulus E of the individual layers 1 Transverse modulus E 2 Poisson ratio mu 12 Shear modulus G 12 Axial tensile strength X of the individual layers t Transverse tensile Strength Y t Axial compressive strength X c Transverse compressive strength Y c The shear strength S, the layering information comprises the contents: the laying sequence ord, the thickness t and the laying angle theta of each single layer, and the load data information comprises the following contents: axial tension and compression load N d x Transverse tension and compression load N d y In-plane shear load N d xy Axial bending load M d x Transverse bending load M d y Torsional load M d xy (ii) a The loads are internal force and internal moment on the cross section of the laminated plate in unit width or length; calculating the stiffness matrix Q of each single layer by using the input data information according to formulas (1-1) to (1-3);
wherein,
the equation (1-1) is written as a relation expressing stress in terms of strain:
wherein Q is a two-dimensional stiffness matrix, inverted by a two-dimensional compliance matrix S;
calculating to obtain the single-layer stiffness matrix Q, and calculating to obtain integral stiffness matrixes A, D and B of the laminated plate through formulas (1-4) to (1-9) by integrating the information of the layering angle theta, the sequence ord and the thickness t;
the stress-strain relationship of the monolayer in the overall coordinates x-y at a ply angle θ is as follows:
wherein T is a coordinate transformation matrix;
considering that the laminated plate is formed by laminating a plurality of single-layer plates, the stress-strain relationship of the k-th single-layer plate is as follows:
for laminated plates have
In the formula, K x 、K y For bending of the middle plane of the panel, K xy Is the plane torsion of the plate, epsilon 0 x 、ε 0 x 、γ 0 xy Is mid-plane strain;
let N x 、N y 、N xy 、M x 、M x 、M xy The internal force and the internal moment per unit width on the cross section of the laminated plate satisfy the formula (1) with the stress of the laminated plate-7)：
Therefore, the relationship between the internal force, the internal moment and the strain of the laminated plate is converted into
Is abbreviated as
A laminate stiffness matrix a, D, B is obtained.
2. The method of claim 1 wherein, based on the obtained A, D, B matrices, for a symmetrical balanced ply composite laminate, no stretch-bending coupling exists, thus the B matrix is a null matrix; due to A 16 、A 26 、D 16 、D 26 Positive and negative alternative terms exist in the terms, so that the numerical value of the terms is much smaller than other rigidity coefficients, and the calculation can be simplified;
a, under the condition of pure in-plane load, no bending load M exists, so that the relation between the internal force and the strain of the laminated plate is
N＝Aε 0 (1-10)
Thereby obtaining the equivalent modulus parameter E of the laminated plate through calculation of the A matrix 1 、E 2 、μ 12 、G 12 And an equivalent stiffness matrix Q;
b, under the condition of pure bending and twisting load, no in-plane load N exists, so that the relation between the internal moment and the strain of the laminated plate is
M＝DK (1-11)
The equivalent of the laminated plate is calculated by the D matrixModulus parameter E 1W 、E 2W 、μ 12W 、G 12W And an equivalent stiffness matrix Q W 。
3. The method as claimed in claim 1, wherein the matrix A, D and B are obtained and the external load N is determined d x 、N d y 、N d xy 、M d x 、M d y 、M d xy The compliance relation formula of expressing strain and curvature by internal force and internal moment is reversely deduced through the formula (1-9) as follows:
therefore, the strain component of the whole laminated plate is calculated, and then the strain components epsilon of different single layers are obtained by using the formula (1-6) x 、ε x 、γ xy Then, the stress level sigma of each layer under the overall coordinate x-y and the main direction coordinate 1-2 is obtained by the formula (1-4) and the stress conversion formula x 、σ y 、τ xy 、σ 1 、σ 2 、τ 12 。
4. The method of claim 3, wherein the calculation of the equivalent modulus of the composite laminate and the calibration of the strength under a given load are based on the calculated stress level data σ in the principal direction 1 、σ 2 、τ 12 And respectively adopting the following three strength judgment criteria to carry out strength check on the composite laminated plate:
a maximum stress criterion:
in the formula, X t 、Y t For tensile strength in the axial and transverse directions, X c 、Y c The axial and transverse compressive strengths, and S the shear strength;
b Tsai-Hill failure criteria:
in the formula, X and Y respectively correspond to axial strength and transverse strength, and S is shear strength;
c Tsai-Wu failure criteria:
in the formula
And judging whether each single layer fails according to each failure criterion, so as to obtain whether the composite material laminated plate meets the strength requirement under the action of the specified load.
5. The method as claimed in claim 1, wherein the information output module outputs information including:
equivalent modulus E of a laminated plate under pure in-plane load 1 、E 2 、μ 12 、G 12 And equivalent modulus E under pure bending and twisting load 1W 、E 2W 、μ 12W 、G 12W And equivalence under both loadsStiffness matrices Q, Q W ；
B, a tension-shear stiffness matrix A, a bending-coupling stiffness matrix B and a bending-torsion stiffness matrix D of the laminated plate;
c main stress S of each layer material under the action of specified load 11 ；
d, strength checking results based on three composite material failure criteria, namely the strength checking results based on the maximum stress criterion, the Tsai-Hill criterion and the Tsai-Wu criterion.
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| CN114818372B (en) * | 2022-05-20 | 2024-10-15 | 中国航空工业集团公司西安飞机设计研究所 | Calculation method of composite material Tsai modulus |
| CN114818374B (en) * | 2022-05-20 | 2024-10-18 | 中国航空工业集团公司西安飞机设计研究所 | Calculation method of composite material Tsai modulus |
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