CN101241520A - Model State Generation Method Based on Feature Suppression in Finite Element Modeling - Google Patents

Abstract

The model state generation method based on feature suppression in finite element modeling is characterized by providing the model to be simplified by the user; identifying the features that can be simplified in the model to be simplified; determining the number of features to be simplified; obtaining the sensitivity of the feature to be simplified after it is suppressed value; represent the model state error level by the sum of all suppressed feature sensitivity values; estimate the number of units after the model state is meshed; select the model state according to the error level of the model and the number of units _Ne to obtain a simplified model code; The feature suppression method is then applied to generate a simplified model corresponding to the code of the simplified model. The method of the invention realizes the objective evaluation of the sensitivity of the change of each feature in the model to the finite element calculation result, establishes the sensitivity evaluation system of the choice and change of each element in the model to the calculation result, and provides an objective and accurate model state consumption time Estimation method based on which the model state is generated.

Description

Model State Generation Method Based on Feature Suppression in Finite Element Modeling

technical field

The invention relates to a computer-aided modeling method, more specifically a method for generating model states applied in finite element modeling.

Background technique

Computers play an increasingly important role in improving social productivity, especially computer-aided design CAD, aided engineering CAE, and aided manufacturing CAM are becoming increasingly mature and popular in the industry, which greatly improves the efficiency of industrial design and production. The use of finite element analysis and optimization processing based on finite element analysis can improve the structural design of the product, so that the product has the most reasonable structure under the condition of satisfying the strength and rigidity.

Finite element analysis (FEA) was first applied in the field of continuum mechanics in the 1950s, such as in the analysis of static and dynamic characteristics of aircraft structures, and was soon applied to analyze continuous problems such as heat conduction, electromagnetic field and fluid mechanics.

The physical essence of finite element analysis is to approximately replace a continuum with a combination composed of a finite number of elements connected at nodes, so that the analysis problem of the continuum is transformed into the analysis problem of unit analysis and unit combination. The combination of finite element analysis and computer's powerful data processing ability makes the analysis of some large and complex structures that were impossible in the past become routine computing tasks.

To perform finite element analysis, the geometric model of the object to be analyzed must first be established. The actual model is usually very complicated, which is mainly reflected in the huge number and types of features it contains. In addition to the common hole and groove features, it also contains a large number of transition features. If the modeling accuracy is too high, it will undoubtedly bring a huge burden to the calculation, especially the existence of transitional features will greatly increase the amount of calculation. Therefore, it is necessary to simplify the features of the actual model. The following two core issues are involved in the simplification of the features in the actual model: one is how to estimate the influence of the simplified small holes, grooves and transition features on the original calculation results; the other is how to estimate the simplified model The calculation time required to determine whether the simplified model can improve the calculation efficiency.

In view of this problem, in the journal "Computer-Aided Design", 2001, Volume 33, Issue 13, Page 925-934, A Sheffer.'s article "Model Simplification for Meshing Using Face Clustering" (hereinafter referred to as Document 1), analyzed Negative effects of several common transitional features on grid division; however, transitional features are not dealt with, let alone the impact on results after feature simplification and the calculation time consumed by the simplified model are not estimated.

"Computer-Aided Design" 2002, Volume 34, Issue 22, Page 109-123, another document "B-Rep Model Simplification by Automatic Fillet/Round Suppressing for Efficient Automatic Feature Recognition" by H Zhu, C H Menq (hereinafter referred to as Document 2) and Cui Xiufen's article "An Efficient Algorithm for Recognizing and Suppressing Blend Features" (hereinafter referred to as Document 3) on pages 24-28 of "Computer-Aided Design" No. 5, 2004, although a relatively complete transition feature is proposed identification and simplification methods, but also did not estimate the impact of suppressed transition features on the results and the computational time consumed by the simplified model.

The article "Feature-based multiresolution techniques for product design" by LEE Sang Hun on pages 1535-1543, Vol. 7, No. 9, 2006, Vol. 7, No. 9, Journal of Zhejiang University, Natural Science Edition (hereinafter referred to as Document 4) proposes a method based on LOD in product manufacturing. In this method, the features in the geometric model are simply divided into adding features and subtracting features, and the user decides the value of LOD to determine whether each feature in the model exists, so as to reduce the amount of calculation. . However, this method relies too much on user experience; at the same time, due to the large geometric differences between the model levels, repeated experiments are required to verify whether the model is suitable after selecting the model level. The process is too complicated, and the estimation error corresponding to the level model is not given, nor Estimate the time consumed by the simplified model.

In the 2005 master's degree thesis of Hefei University of Technology, "A Preliminary Study on Geometric Polymorphic Models in Scientific Computing" (hereinafter referred to as Document 5), the neutron transport program MCNP is taken as the research object, and a certain model state is used in the field of scientific computing to replace the original Preliminary research was done on the influencing factors of the calculation error generated by the model, and based on the experimental data, the law between the calculation error and the characteristic volume was summarized. According to the summarized rules, the method of feature suppression is used to form the model state. Each model state corresponds to an estimation error, which provides users with a very good auxiliary modeling function. The research method has some references, but there are limitations in the field, that is, the summary method of the error elements does not consider the characteristics of the finite element field, the reliability and generality of the conclusion are not strong, and the calculation efficiency of the model state is not given. estimation method.

In the 2007 master's degree thesis of Hefei University of Technology "Research on the Selection of Model States in the Finite Element Field" (hereinafter referred to as Document 6), based on experiments, it was summarized from the experimental data that the replacement of the original model with a certain model state in the field of heat conduction produces The law of the calculation error, and the factors that affect the calculation time are initially analyzed and summarized; on the basis of the formal expression of the calculation accuracy and calculation time, the fitness function of the genetic algorithm is constructed, through a certain number of iterations Select the model state with the highest fitness; finally, according to the model state code, use the feature suppression algorithm to transform the original model to obtain the final geometric model. The specific steps of model state generation described in the paper are:

a. For different application fields of finite element, establish a simple model containing only one feature to be simplified. The feature to be simplified here is the most common transition feature of groove, hole or cylinder in the machined parts, establish a model containing them, and construct Steady-state heat transfer protocol.

b. Construct the experimental plan according to the characteristic volume parameters and position parameters, that is, analyze and calculate the model of the groove and hole features containing several groups of different characteristic volume ratios V and the distance D between the feature and the load surface, and analyze the error ratio EP, according to the calculation results The intrinsic relationship between the feature volume ratio V and the distance D between the feature and the load surface is used to fit the relationship.

c. Users use their own domain knowledge to judge the degree of influence of the existence of transition features in the model on the results. If the influence of a certain transition feature on the calculation results can be ignored, the quality of the grid division is used as the standard to determine the transition features. The deleted geometric attribute threshold avoids unpredictable problems during calculation; the transitional features that cannot be deleted will be retained.

d. According to the function relationship between the fitted characteristic volume ratio V of the groove and hole features, the distance D between the feature and the load surface, and the error ratio EP, determine the groove and hole features that can be suppressed to further improve the calculation efficiency.

是平均特征体积比，EP_max是用户输入的可接受的最大误差。e. Construct the expression P=1-∑EP _i of reaction precision element and the expression of time element $\stackrel{\‾}{V}=\frac{1}{\mathrm{no}}\mathrm{\Σ}{V}_i$ , and construct the genetic algorithm fitness function based on it $f=\left\{\begin{array}{cc}\mathrm{\α}\×\stackrel{\‾}{V}+(1-\mathrm{\α})\×P& \mathrm{EP}\≤{\mathrm{EP}}_{\max }\\ 0& \mathrm{EP}>{\mathrm{EP}}_{\max }\end{array}\right.$ , select other parameters of the genetic algorithm. Here EP _i is the error ratio generated after the ith feature is suppressed,

is the average feature volume ratio, and EP _max is the maximum acceptable error entered by the user.

f. Process the geometric model according to the coding to obtain the final selected model state.

In the above steps ad, the functional relationship between the error ratio EP, the characteristic volume ratio V, and the distance D between the characteristic and the load surface is obtained by fitting the experimental data. However, this method has two disadvantages: first, the relationship between the error ratio, feature volume ratio, and the distance between the feature and the load surface is only obtained from the data of a limited number of experiments, which is random; second, there is no guarantee that the error will be affected The comprehensiveness of the element summary. In step (e), according to the average volume ratio of the features contained in the model state $\stackrel{\‾}{V}=\frac{1}{\mathrm{no}}\mathrm{\Σ}{V}_i$ To estimate the time consumed by the model state obviously lacks objectivity and accuracy.

Contents of the invention

In order to avoid the shortcomings of the above-mentioned prior art, the present invention provides a model state generation method based on feature suppression in finite element modeling, and fully considers the factors that affect the finite element calculation results after model simplification, so as to realize the model The objective evaluation of the sensitivity of the change of each feature in the model to the calculation result of the finite element is established, and the sensitivity evaluation system of the choice and change of each element in the model to the calculation result is established, and an objective and accurate estimation method of the model state consumption time is given. On this basis, the model state is generated.

The present invention solves technical problem and adopts following technical scheme:

The feature of the model state generation method based on feature suppression in the finite element modeling of the present invention is to carry out as follows:

a. The model to be simplified is provided by the user, and the model to be simplified has load conditions during finite element analysis and meshing conditions, and the meshing conditions are the maximum mesh diameter h _max and the minimum mesh diameter _hmin ;

b. Identify the simplification features in the model to be simplified, and store them in the feature list;

c. Select the feature to be simplified in the feature linked list, determine the number of features to be simplified n; number the selected n features to be simplified in any order, and calculate and obtain the volume V _i of each selected feature to be simplified positional parameter P _i ;

d. According to the volume V _i of each selected feature to be simplified, the position parameter P _i , and the mesh diameter change of each selected feature to be simplified after it is suppressed, obtain the corresponding feature to be simplified in its The suppressed sensitive value E _i =V _i P _i H _i ; the error level of the model state is represented by the sum of the sensitive values of all suppressed features;

e. By estimating the number _of grid cells in the model state, it is estimated that the number of cells in the model state after grid division _Ne is linearly related to the order of the stiffness matrix in the model state. N _e reflects the finite element calculation time required for the model state;

f. According to the error level of the model and the number of units N _e , the genetic algorithm is used to select the model state to obtain the simplified model code;

g. Applying feature suppression to generate a simplified model corresponding to said simplified model code.

The inventive method is also characterized in that:

In the step c, the simplified feature position parameter P _i is obtained in the following way:

a. Given the weight of the influence of each feature to be simplified on the finite element calculation result after simplification, set it as q ₁ , q ₂ , ... q _n , where q _i ∈ [0, 1], (i=0, 1, ... n), q _i =0 indicates that the presence or absence of the i-th feature to be simplified has no effect on the finite element calculation results; q _i =1 indicates that the existence or non-existence of the ith feature to be simplified has the greatest impact on the finite element calculation results _, The closer to 1, the greater the influence of the characteristic features on the finite element calculation results;

b. Let i=1;

c. Set the distance d _i from the i-th feature to be simplified to the load surface;

d. Calculate the position parameter P _i =q _i /d _i of the i-th feature to be simplified;

e. Set i=i+1, repeat steps c-d until the calculation of position parameters P _i of all features to be simplified in the model is completed.

In the step d, the amount of mesh diameter change is obtained as follows:

a. If the features to be simplified are all composed of planes, obtain the minimum side length h _i of the features to be simplified, and calculate the mesh diameter change H _temp = h _max -min(h _max , h _i ), if H _temp >0, Then adopt this feature simplification scheme, the corresponding mesh diameter change $h_{i,c_i}=h_{\mathrm{temp}},$ Otherwise, go to the next step;

b. If there is a curved surface in the feature to be simplified, obtain the average Gaussian curvature θ _avgi of all high-curvature surfaces contained in the current feature i to be simplified, and calculate the mesh diameter change $h_{\mathrm{temp}}=h_{\max }-\min (h_{\max },\frac{\mathrm{\ϵ}}{{\mathrm{\θ}}_{\mathrm{avgi}}})$ , if H _temp >0, then adopt this feature simplification scheme, the corresponding mesh diameter change $h_{i,c_i}=h_{\mathrm{temp}}.$

In the step e, the estimation of the quantity of the model state grid units is carried out as follows:

a. According to the maximum grid diameter h _max and the minimum grid diameter h _min provided by the user, take the grid unit side length h=(h _max +h _min )/2;

b. Combining the type of grid unit and the side length of the grid unit, calculate the actual volume ve occupied by a grid unit, and the volume calculation formula varies from unit to unit;

c. Calculate the actual volume v of the model state, and obtain the number of units _Ne = v/v _e of the model mesh;

Adopt genetic algorithm to carry out model state selection in the described step f and carry out as follows:

a. Use binary code to represent the model state, the code length is the number of features, and each feature corresponds to a binary bit in the individual; 0 means that a certain feature does not exist in the model state, and 1 represents that a certain feature exists in the model state;

b. The user inputs the tolerable error level level m, m∈[1,n], forming the maximum allowable error ${\mathrm{E.}}_{\max }=\frac{1}{\mathrm{no}-\mathrm{<figure-callout\; id="1"\; label="m\; +"\; filenames="S2008100205612E00011.png,S2008100205612E00041.png"\; state="\{\{state\}\}">m</figure-callout>}+1}\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}{\mathrm{E.}}_i$ , where n is the number of features;

c. The number of randomly generated individuals is $N=\left\{\begin{array}{cc}{2}^{N_f}& N_f\&le;6\\ 100& N_f>6\end{array}\right.$ , where _NF is the number of features; set the crossover probability P _c ∈ [0.6, 0.8], the mutation probability P _m ∈ [0.01, 0.02], the fitness calculation formula of each individual is $f=\left\{\begin{array}{cc}\mathrm{\&alpha;}\&times;N_e+(1-\mathrm{\&alpha;})\&times;\widehat{{\mathrm{E.}}_m}& {\mathrm{E.}}_m\&le;{\mathrm{<figure-callout\; id="0"\; label="E.\; max"\; filenames="S2008100205612E00011.png"\; state="\{\{state\}\}">E.</figure-callout>}}_{\max }\\ 0& {\mathrm{E.}}_m>{\mathrm{E.}}_{\max }\end{array}\right.$ ,in $\widehat{{\mathrm{E.}}_m}={\mathrm{E.}}_m\&times;{\lg }^{N/{\mathrm{E.}}_m},$ E _M ＝∑E _i , i is the feature serial number of 0 in the model state code; α is the weight factor, where α is selected as 0.3;

d. The number of iterations is , each iteration, estimate the number of grid cells corresponding to the model state for all individuals in this generation, and calculate the fitness function on this basis; The individual with the greatest fitness in the first generation population is the obtained simplified model code.

Compared with the prior art, the beneficial effects of the present invention are reflected in:

1. The objectivity of error factor analysis

The method of the present invention analyzes the cause of calculation errors using a certain model state instead of the original model, and obtains the elements related to errors: volume, feature position parameters, and grid diameter change after feature simplification; abandoning experience , using experimental data to find the randomness of the error-related element method.

2. Calculate the accuracy of time consumption estimates

Among the existing methods, only literature 7 initially summarizes the elements to measure the time-consuming calculation, but it proposes to use the average characteristic volume in the model as a parameter to measure the time-consuming calculation, which is not accurate enough. The method of the present invention uses the element that can accurately reflect the time-consuming calculation, that is, the number of units _Ne after the model is divided into grids, as the time element in the model state evaluation element, which can accurately reflect the calculation time corresponding to the model state, and is beneficial to the optimal model The choice of state code.

3. Rationality of Genetic Algorithm Fitness Function Construction

The construction of the fitness function fully considers the balance between the calculation time of the model state and the calculation accuracy. In order to balance the influence factors of the two elements, the error level E _M in the fitness function is corrected by an order of magnitude.

Description of drawings

Fig. 1 is a schematic diagram of the mathematical model of the selection transition of the model state in the method of the present invention.

Fig. 2 is a schematic diagram of the external normal vector of the corresponding point of the mesh vertex on the surface.

Figure 3 is a schematic diagram of the relationship between the surface curvature of the model and the grid.

Figure 4 is a schematic diagram of model state encoding.

Figure 5 is a schematic diagram of model state selection.

Fig. 6 is a schematic diagram of the feature composition surface of slots, holes and rounded corners. Among them, Fig. 6(a1) is a model containing groove features; Fig. 6(a2) is the surface and edge diagram corresponding to the model shown in Fig. 6(a1); Fig. 6(b1) is a model containing hole features; Fig. 6(b2 ) is the surface-edge graph corresponding to the model shown in Figure 6(b1); Figure 6(c1) is the model with rounded corner features; Figure 6(c2) is the surface-edge graph corresponding to the model shown in Figure 6(c1).

Figure 7(a) is a model containing a blind hole, a through hole and a slot feature, and Figure 7(b) is the corresponding feature subgraph of Figure 7(a).

Figure 8(a), Figure 8(b), Figure 8(c), Figure 8(d) and Figure 8(e) are the eigenvalues of square through holes, square blind holes, round through holes, round blind holes and slots, respectively Graph Classification Diagram.

Figure 9 is a schematic diagram of the model feature tree.

Fig. 10 is a schematic diagram of an actual model to be simplified in the method of the present invention.

Fig. 11 is a schematic diagram of a simplified model obtained by the method of the present invention.

Symbols in the figure: 1 base, 2 inner cylinder A, 3 inner cylinder B, 4 inner cylinder C, 5 inner hexagonal prism A, 6 inner octagonal prism A, 7 inner octagonal prism B, 8 inner hexagonal prism B, 9 slot A , 10 slot B, 11 slot C, 12 slot D, 13 slot E, 14 slot F, 15 fillet A, 16 fillet B, 17 fillet C, 18 fillet D.

The present invention will be further described below in conjunction with the accompanying drawings by way of specific embodiments:

Detailed ways

This embodiment provides a method for constructing the model error level according to the following steps:

1. The model to be simplified is provided by the user. The model to be simplified has load conditions during finite element analysis and grid division conditions. The grid division conditions are the maximum grid diameter h _max and the minimum Mesh diameter h _min ;

2. Perform feature recognition on it, classify and store the identified features into the feature linked list; traverse the feature linked list, calculate and obtain the volume V _i of each feature, and the position parameter P _i of each feature;

Among them, the linked list is a conventional computer data structure;

In this step, the volume V _i of the feature to be simplified is calculated according to the conventional volume formula, and the position parameter P _i of the feature is obtained as follows:

a. Given the weight of the influence of each feature to be simplified on the finite element calculation result after simplification, set it as q ₁ , q ₂ , ... q _n , where q _i ∈ [0, 1], (i=0, 1, ... n), q _i =0 indicates that the presence or absence of the i-th feature to be simplified has no effect on the finite element calculation results; q _i =1 indicates that the existence or non-existence of the ith feature to be simplified has the greatest impact on the finite element calculation results _, The closer to 1, the greater the influence of the characteristic features on the finite element calculation results;

b: let i=1;

c: Find the centroid of the bounding box of the i-th feature to be simplified, if the load is a body load, then obtain the centroid of the load body; calculate the distance d _i from the centroid of the i-th feature to be simplified to the load surface, if it is a body load , then calculate the distance d _i from the centroid of the i-th feature to be simplified to the centroid of the load body; if there are multiple load surfaces, calculate the distance from the centroid of the i-th feature to be simplified to each load, and then take the average value;

d: Calculate the position parameter P _i =q _i /d _i of the i-th feature to be simplified;

e: set i=i+1, repeat steps c~d until the position parameter P _i of all features to be simplified in the model is calculated;

3. Calculate and obtain the maximum Gaussian curvature θ _max of all feature composition surfaces of all features to be simplified;

4. According to the calculation method of the mesh diameter change, calculate the mesh diameter change H _i after the feature is simplified;

According to the maximum curvature θ _max , the maximum grid diameter h _max and the minimum grid diameter h _min , the grid diameter change is obtained as follows;

a. Set i=1, calculate ε=θ _max h _min ; if the feature composition surfaces are all planes, then obtain the minimum side length h _i of the feature to be simplified, and calculate the grid diameter change H _temp =h _max -min( h _max , h _i ), if H _temp >0, the corresponding mesh diameter change H _i =H _temp , otherwise go to the next step;

b. If there is a curved surface in the feature composition surface, then obtain the average Gaussian curvature θ _avgi of all the surfaces contained in the current feature i to be simplified, and calculate the mesh diameter change $h_{\mathrm{temp}}=h_{\max }-\min (h_{\max },\frac{\mathrm{\&epsiv;}}{{\mathrm{\&theta;}}_{\mathrm{avgi}}})$ , if H _temp >0, then the corresponding mesh diameter change amount H _i =H _temp , otherwise go to the next step;

c. Let i=i+1, repeat steps a and b until all the features to be simplified in the model and the grid diameter change amount H i corresponding to the simplification method, _i =1, 2, ..., n, the calculation is completed;

5. Estimate the sensitive value of the feature after the feature is suppressed by the error level estimation formula E _i =V _i P _i H _i , and use the sum of the sensitive values of all suppressed features to represent the error level of the model state;

6. Construct the parameters of the genetic algorithm and select the model state;

The construction steps of the genetic algorithm are as follows:

a. Use the conventional binary code to represent the model state, the code length is the number of features, and each feature corresponds to a binary bit in the individual; 0 means that a certain feature does not exist in the model state, and 1 means that a certain feature exists in the model state;

b. The user inputs the tolerable error level level m, m∈[1,n], forming the maximum allowable error ${\mathrm{E.}}_{\max }=\frac{1}{\mathrm{no}-\mathrm{<figure-callout\; id="1"\; label="m\; +"\; filenames="S2008100205612E00011.png,S2008100205612E00041.png"\; state="\{\{state\}\}">m</figure-callout>}+1}\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}{\mathrm{E.}}_i$ , where n is the number of features;

c. The number of randomly generated individuals is $N=\left\{\begin{array}{cc}{2}^{N_f}& N_f\&le;6\\ 100& N_f>6\end{array}\right.$ , where _NF is the number of features; set the crossover probability P _c ∈ [0.6, 0.8], the mutation probability P _m ∈ [0.01, 0.02], the fitness calculation formula of each individual is $f=\left\{\begin{array}{cc}\mathrm{\&alpha;}\&times;N_e+(1-\mathrm{\&alpha;})\&times;\widehat{{\mathrm{E.}}_m}& {\mathrm{E.}}_m\&le;{\mathrm{<figure-callout\; id="0"\; label="E.\; max"\; filenames="S2008100205612E00011.png"\; state="\{\{state\}\}">E.</figure-callout>}}_{\max }\\ 0& {\mathrm{E.}}_m>{\mathrm{E.}}_{\max }\end{array}\right.$ ,in $\widehat{{\mathrm{E.}}_m}={\mathrm{E.}}_m\&times;{\lg }^{N/{\mathrm{E.}}_m},$ E _M ＝∑E _i , i is the feature serial number of 0 in the model state code; α is the weight factor, where α is selected as 0.3;

，每迭代一次，估计出这代中所有个体编码对应模型态的网格单元数量，以此为基础计算适应度函数；若连续三代没有出现更优秀的个体或者到达最大迭代次数，则遗传算法结束，获得最优模型态编码；d. The number of iterations is

, each iteration, estimate the number of grid cells corresponding to the model state for all individuals in this generation, and calculate the fitness function based on this; if there are no better individuals in three consecutive generations or the maximum number of iterations is reached, the genetic algorithm ends , to obtain the optimal model state code;

In this step, the number of grid cells corresponding to the model state encoded by all individuals in a certain generation of the population is obtained by the following method:

(1) According to the maximum grid diameter h _max and the minimum grid diameter h _min input by the user, take the element side length h=(h _max +h _min )/2;

(2) Combining the element type and the side length of the element, the actual volume v _e occupied by an element is calculated according to geometric knowledge, and the volume calculation formula varies from element to element;

(3), calculate the actual volume v of the model state in a conventional manner, and obtain the number of units N _e =v/v _e of the model grid division;

7. According to the optimal model state encoding, traverse the feature linked list, and use feature suppression technology to obtain the geometric model corresponding to the encoding.

The principles on which the model state generation method based on feature suppression in the finite element field of the present invention is based include:

，则模型态M_i到模型态M_j的最小转化代价记为。根据给定的转化代价阈值c_ε，可以取定满足转化代价阈值的模型态集合T_minct＝{M_j|C_Tmin(M₀→M_j)＜c_ε}，再根据T_minct取定满足最小计算代价的模型态M_f，即M_f满足条件 $C_c\left(M_f\right)=\underset{M_j\&Element;T_{\min \mathrm{ct}}}{\min }\left\{C_c\left(M_j\right)\right\}.$ The polymorphic model theory on which the present invention is based analyzes and studies the models in scientific computing from the perspective of system theory, takes the model as a system, and the features contained in the model as elements constituting the system. The variability of the elements themselves means that each element has polymorphic characteristics. At the same time, changes in the composition of elements will cause changes in the state of the system. Therefore, when the model is regarded as a system, it itself presents polymorphic characteristics. Through the study of the characteristic elements contained in the polymorphic model and their composition methods, a corresponding system is established for the actual model, and the characteristics are used as the constituent elements of the system to study the sensitivity of various characteristics and establish a quantitative evaluation standard for characteristic sensitivity. Find the state of the model and the regularity implied in its change process, and establish a polymorphic theoretical system to describe the various states of complex models due to changes in model accuracy, calculation time, and calculation accuracy. The core idea of the polymorphic theoretical system is state transition, that is, the dynamic process of the original model state reaching the target model state: as shown in Figure 1, the system model state is recorded as M, which can be described as M{f ₁ , f ₂ ,… , f _n }, where f _i (i=1, 2,...n) is its included features, for convenience it is denoted as $m=\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}{f}_i$ . set up ${\mathrm{<figure-callout\; id="0"\; label="m"\; filenames="S2008100205612E00011.png"\; state="\{\{state\}\}">m</figure-callout>}}_0=\underset{i=1}{\overset{m_0}{\mathrm{\&Sigma;}}}{f}_{0i}$ for the prototype state, $m_j=\underset{i=1}{\overset{m_j}{\mathrm{\&Sigma;}}}{f}_{\mathrm{the\; ji}},(j=\mathrm{1,2},\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;\mathrm{no})$ is the transition model state. Record the calculation cost of each state (such as calculation time) as C _c (M _j ), (j=0, 1, 2, . . . , n). If there is a transformation path from model state M _i to model state M _j (i, j=0, 1,...n, i≠j) (the path may not be unique), let the transformation path set be P _ij , and model state M _i follows the path The conversion cost of p(p∈P _ij ) into the model state M _j (such as the error of the calculation result) is denoted as

, then the minimum conversion cost from model state M _i to model state M _j is recorded as . According to the given conversion cost threshold c _ε , the model state set T _minct ＝{M _j |C _Tmin (M ₀ →M _j )＜c _ε } that satisfies the conversion cost threshold can be determined, and then according to T _minct , the minimum Calculate the model state M _f of the cost, that is, M _f satisfies the condition $C_c\left(m_f\right)=\underset{m_j\&Element;T_{\min \mathrm{ct}}}{\min }\left\{C_c\left(m_j\right)\right\}.$

In the method of the present invention, the principle of estimating the error level of the error generated by using the model state instead of the original model for calculation is based on:

When the finite element type and interpolation method are determined, only three factors need to be considered in calculating the sensitivity of features in the model to simplification: ΔT, ΔH and ΔU

Among them, ΔT is the element reflected by the regional measure that the feature simplification affects the grid division.

ΔH is the element reflected by the mesh diameter change after feature simplification.

ΔU is an element reflected by the semi-norm of the field function in the region where feature simplification affects grid division.

When calculating the sensitivity value of each feature in the model to the simplification, it is necessary to calculate the three elements ΔT, ΔH and ΔU; but the precise values of the elements ΔT and ΔH need to be known after the grid is divided, and the precise value of the element ΔU It is possible to know after the finite element calculation. It is difficult to obtain their precise values before the finite element calculation, and the time required for their precise calculation may be greater than the calculation time saved after the model is simplified. Considering the cost Exact calculations are not amenable, so a way to value them needs to be found. An obvious fact is that the feature simplification affects the mesh subdivision. The element ΔT reflected by the area measure is proportional to the model feature volume, so the feature volume V can be used to replace the element ΔT. In the method of the present invention, the feature volume V is used to replace the element ΔT, and the feature position parameter P is used to replace the element ΔU, so the calculation method of the error estimation formula is: E _i =V _i P _i H _i , where E _i , V _i , P _i , H _i represent the simplification error, feature volume, position parameter and grid diameter change amount produced by the i-th simplification mode of the feature respectively.

The principle on which the grid diameter variation calculation method is based in the method of the present invention:

It is known that the model established by the CAD system usually contains some complex features, such as small features and high curvature features, and the meshing density of these complex features will be increased when the finite element analysis is performed. , so that the mesh diameter at these complex features is relatively small. The purpose of deleting or replacing complex features with simple features is to reduce the mesh density at these features, that is, to increase the mesh diameter at these features. In the principle of the error estimation formula calculation method, it is pointed out that the change of the grid diameter before and after feature simplification is one of the factors affecting the sensitivity of the feature to simplification. The method of the present invention uses two methods of replacement and deletion to simplify the feature. Different simplification methods The calculation methods for the mesh diameter change are as follows:

1. Calculation method of mesh diameter change after deletion of features without high curvature components

If the feature does not contain high-curvature features to form surfaces, the mesh diameter on the feature will depend on the maximum mesh diameter that the user can tolerate and the mesh diameter that meets the geometric properties of this feature when performing meshing in finite element analysis The minimum value, and the mesh diameter that conforms to the geometric properties of this feature should be the minimum edge length in the component faces of this feature. When the feature is deleted and the feature does not exist in the model, the mesh division of the finite element analysis should be performed according to the maximum mesh diameter specified by the user, that is, the h _max input by the user, so there is no high curvature component surface After the feature of is deleted, the mesh diameter change amount should be h _max -min(h _max , h), where h is the minimum side length in the feature composition surface of this feature.

2. Calculation method of the mesh diameter change amount after the feature with high curvature composition surface is deleted

If the feature contains faces with high curvature features, you should first estimate the mesh diameter at the faces with high curvature features. We first describe how to estimate the mesh diameter at high curvature features.

In the process of finite element mesh generation, there are two kinds of mesh density control: one is the prior control of mesh density according to the geometric characteristics and physical characteristics of the analysis object, and the other is based on the calculation of the current mesh As a result, the posterior control of increasing the meshing density in areas where the calculated data varies greatly and decreasing the meshing density where the calculated data changes gently. This method is aimed at the preprocessing of the model prior to finite element analysis, so only a priori control of the mesh density is considered. Mesh control based on the geometric characteristics of the analysis object mainly refers to determining the size of the mesh diameter according to the degree of fitting of the mesh to the model surface. The fitting degree of the mesh to the model surface can be approximated by the angle between the mesh vertices on the surface and the corresponding point external normal vector. As shown in Figure 2, a certain surface of the model is fitted by a triangular unit, and the angle between the fingertips of the outer normal vector corresponding to the vertices of the triangle determines the degree of fitting of the unit to the model surface. For a given allowable error η of the fitting degree of the model surface, each external normal vector is required to satisfy (1-N _i N _j )≤η, i≠j and i, j∈(1, 2, 3).

When the meshing algorithm is used to subdivide a certain local area ΔS on the surface of the model, the average normal curvature is considered, which is set to ρ, and the radius of the curvature sphere is r, and the ΔS can be considered on the spherical surface with r as the radius mesh diameter. Let △ABC be a triangular mesh. Since the normal curvature is the same everywhere on the spherical surface, △ABC is an equilateral triangle. Without loss of generality, discuss the side length of △ABC with side AB.

As shown in Figure 3, assuming that in the coordinate system XOY, the coordinates of A and B are (x ₁ , y ₁ , z ₁ ), (x ₂ , y ₂ , z ₂ ) respectively, when the allowable error of the fitting degree of the model surface ε At a certain time, there is the following equation:

(x ₁ -x ₂ ) ² +(y ₁ -y ₂ ) ² +(z ₁ -z ₂ ) ² ＝h ²

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="1"\; label="y"\; filenames="S2008100205612E00011.png,S2008100205612E00041.png"\; state="\{\{state\}\}">y</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="z"\; filenames="S2008100205612E00011.png,S2008100205612E00041.png"\; state="\{\{state\}\}">z</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="r"\; filenames="S2008100205612E00011.png"\; state="\{\{state\}\}">r</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="y"\; filenames="S2008100205612E00011.png"\; state="\{\{state\}\}">y</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="z"\; filenames="S2008100205612E00011.png"\; state="\{\{state\}\}">z</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="r"\; filenames="S2008100205612E00011.png"\; state="\{\{state\}\}">r</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

$\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="1"\; label="y"\; filenames="S2008100205612E00011.png,S2008100205612E00041.png"\; state="\{\{state\}\}">y</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="y"\; filenames="S2008100205612E00011.png"\; state="\{\{state\}\}">y</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="1"\; label="y"\; filenames="S2008100205612E00011.png,S2008100205612E00041.png"\; state="\{\{state\}\}">y</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="z"\; filenames="S2008100205612E00011.png,S2008100205612E00041.png"\; state="\{\{state\}\}">z</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="y"\; filenames="S2008100205612E00011.png"\; state="\{\{state\}\}">y</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="z"\; filenames="S2008100205612E00011.png"\; state="\{\{state\}\}">z</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}$

ρ=1/r

thus have

$\mathrm{<span\; class="notranslate">\; \&rho;h</span>}<span\; class="notranslate">\; \&le;</span>\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&eta;</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2.1</span>}<span\; class="notranslate">\; )</span>$

When meshing for finite element analysis, when once detected $\mathrm{\&rho;h}\&le;\sqrt{2\mathrm{\&eta;}}$ That is, stop refining the mesh, so it can be considered that $\mathrm{\&rho;h}=\sqrt{2\mathrm{\&eta;}}$ . Assuming that the maximum curvature of the feature surface of all the features to be simplified in the model is ρ _max , then there should be a minimum mesh diameter h _min on this feature, so $\sqrt{2\mathrm{\&eta;}}={\mathrm{\&rho;}}_{\max }{h}_{\min }$ , when the average curvature of the feature composition surface of the feature to be simplified is ρ _avg , the mesh diameter on the feature to be simplified should be estimated as $\frac{\sqrt{2\mathrm{\&eta;}}}{{\mathrm{\&rho;}}_{\mathrm{avgi}}}=\frac{{\mathrm{\&rho;}}_{\max }\&CenterDot;h_{\min }}{{\mathrm{\&rho;}}_{\mathrm{avgi}}}.$

Similarly, when this feature is deleted and the feature does not exist in the model, the finite element software should divide the grid according to the maximum grid diameter specified by the user, that is, the h _max input by the user, so it does not contain After the features of the high-curvature component surface are deleted, the change in mesh diameter should be $h_{\max }-\min (h_{\max },\frac{{\mathrm{\&rho;}}_{\max }\&Center\; Dot;h_{\min }}{{\mathrm{\&rho;}}_{\mathrm{avgi}}}).$

3. Calculation method of mesh diameter change after feature replacement with high curvature component surfaces

For this type of feature to be simplified, the mesh diameter estimation method on the feature is the same as the estimation method in the previous type, the difference is that this type of feature will have multiple simplification schemes. For a surface with average curvature _ρavg , the mesh diameter of its surface is $\frac{{\mathrm{\&rho;}}_{\max }\&Center\; Dot;h_{\min }}{{\mathrm{\&rho;}}_{\mathrm{avgi}}}$ , the mesh diameter after replacing with positive k deformation should be $\frac{2}{{\mathrm{\&rho;}}_{\mathrm{avgi}}}\sin \frac{\mathrm{\&pi;}}{j}$ , so the change in mesh diameter is $\min (h_{\max },\frac{2}{{\mathrm{\&rho;}}_{\mathrm{avgi}}}\sin \frac{\mathrm{\&pi;}}{j})-\min (h_{\max },\frac{\mathrm{\&epsiv;}}{{\mathrm{\&rho;}}_{\mathrm{avgi}}}).$

The principle of the location parameter calculation method basis of the feature in the method of the present invention:

As stated in the principle on which the calculation method of the error estimation formula is based, in areas where the field function changes drastically, one of the three elements of the simplified error, ΔU, will also be larger. Simplifying the features in these areas will lead to larger errors. Therefore, the features that can be simplified in the model must be limited to the area where the field function changes smoothly, that is, the drastic change of the field function of the area where the feature belongs to in the model is an important factor that affects the finite element calculation results after feature simplification. Before the actual finite element calculation, the following two methods can be used to obtain the severity of the change of the field function of the area where the feature belongs to in the model.

1. Based on experience

It is a very important reference value to specify the severity of field function changes in the area where the model features belong to by the user. In finite element analysis, the physical properties of the feature, that is, the properties given to the feature by the external load and boundary conditions - the intensity of the field function change in the area where the feature is located, have the same important influence as the feature geometry, and these physical properties are in the finite element. Precise values cannot be obtained before element calculation, and the order of characteristic physical attribute values can be given according to past analysis experience, which is an important reference for the influence of simplified analysis features on finite element calculation results.

2. The role of distance

According to St. Venant's principle, in a balanced force system, the farther away from the load the field function changes more smoothly, so the method of the present invention regards the distance from the feature to the load as one of the factors reflecting the severity of the field function change, and the distance and the expert-specified The weight product of is used as an estimate of ΔU.

According to conventional theory, the sensitivity of features to simplification is inversely proportional to the distance and proportional to the weight specified by the user, so the ratio of the weight specified by the user to the distance from the feature to the load is taken as the position parameter of the feature to reflect the feature The severity of the change of the field function u of the area to which it belongs.

The principle of selecting the number of cells after the model is divided into grids as the time element

In the finite element field, the solution process of each problem is the same, the steps are as follows:

a. Subdivide the solution area of the problem, the result of the subdivision is a unit, and the solution area is discretized into a set of units.

b. Construct a trial function space.

c. Calculate the element stiffness matrix and element load vector.

d. Compute the overall stiffness matrix and the overall load vector.

e. Handle constraints and solve them.

的第(i-1)行和i行的2阶对角块中，而其他元素均为0。同理，可以将单元载荷向量F_ei扩展成为(n+1)阶的向量 ${\stackrel{\&OverBar;}{F_{e_i}}=\left[\begin{array}{c}\&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ F_{i-1}^{e_i}\\ F_i^{e_i}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\end{array}\right]}_{(n+1)}$ ，那么总体刚度矩阵 $K=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{K_{e_i}}$ ，总载荷向量 $F=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{F_{e_i}}$ ，考虑约束条件的前提下解代数方程组v^T(Ku-F)＝0，即可得到有限元解。若认为这个近似解不够精确，可以使得剖分更细，即节点取的更多。从整个求解过程可以看出，有限元求解就是解一个代数方程组，显然，这个代数方程组内方程的多少决定了求解所需要的时间，而方程的数量就是总体刚度矩阵K的阶数，即问题域剖分得到的节点数量。虽然节点数量和计算所需要的时间不一定成线性关系，但是它是最能够反映所需计算时间的参数。而模型划分网格后的单元数量与节点数量成线性关系，所以通过算法来估计出单元数量从而反映出模型态计算消耗时间。Taking the one-dimensional finite element problem as an example, in the solution area [a, b], first divide [a, b] into n parts, and set the nodes x ₀ , x ₁ ,..., x _n to satisfy a=x ₀ <x ₁ <...<x _n =b, the subinterval e _i =[x _i-1 , x _i ] (i=1, 2, ..., n) obtained in this way is the unit. The length h _i =x _i -xi _-1 of the unit e _i . Consider constructing a relatively simple basis function v _h , which satisfies: it is continuous on [a, b], and it is a linear function on each e _i , and all functions satisfying these conditions form a trial function space. Recalculate the element stiffness matrix $K_{e_i}={\&Integral;}_{x_{i-1}}^{x_i}(p{B}^{T}B+q{N}^{T}N)\mathrm{dx}=\left[\begin{array}{cc}{k}_{i-1,i-1}^{e_i}& k_{i-1,i}^{e_i}\\ k_{i,i-1}^{e_i}& k_{i,i}^{e_i}\end{array}\right]$ and element load vector $f_{e_i}={\&Integral;}_{x_{i-1}}^{x_i}{N}^T\mathrm{fdx}=\left[\begin{array}{c}{f}_{i-1}^{e_i}\\ f_i^{e_i}\end{array}\right].$ Extend the element stiffness matrix k _ei to a matrix of order (n+1) $\stackrel{\&OverBar;}{K_{e_i}}={\left[\begin{array}{cccccccc}& & & \&CenterDot;& \&CenterDot;& & & \\ & & & \&CenterDot;& \&CenterDot;& & & \\ & & & \&CenterDot;& \&CenterDot;& & & \\ \&CenterDot;& \&CenterDot;& \&CenterDot;& k_{i-1,i-1}^{e_i}& k_{i-1,i}^{e_i}& \&CenterDot;& \&Center\; Dot;& \&Center\; Dot;\\ \&Center\; Dot;& \&Center\; Dot;& \&Center\; Dot;& k_{i,i-1}^{e_i}& k_{i,i}^{e_i}& \&Center\; Dot;& \&Center\; Dot;& \&Center\; Dot;\\ & & & \&Center\; Dot;& \&Center\; Dot;& & & \\ & & & \&Center\; Dot;& \&Center\; Dot;& & & \\ & & & \&Center\; Dot;& \&Center\; Dot;& & & \end{array}\right]}_{(\mathrm{no}+1)\&times;(\mathrm{no}+1)}$ That is, put the four elements of k _ei in a (n+1) order matrix

In the (i-1)th row and the second-order diagonal block of the i row, the other elements are all 0. Similarly, the unit load vector F _ei can be expanded into a (n+1) order vector ${\stackrel{\&OverBar;}{f_{e_i}}=\left[\begin{array}{c}\&Center\; Dot;\\ \&Center\; Dot;\\ \&Center\; Dot;\\ f_{i-1}^{e_i}\\ f_i^{e_i}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\end{array}\right]}_{(\mathrm{no}+1)}$ , then the overall stiffness matrix $K=\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{K_{e_i}}$ , the total load vector $f=\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{f_{e_i}}$ , and consider the constraints under the premise of solving the algebraic equations v ^T (Ku-F) = 0, the finite element solution can be obtained. If you think this approximate solution is not accurate enough, you can make the subdivision finer, that is, take more nodes. It can be seen from the entire solution process that the finite element solution is to solve an algebraic equation system. Obviously, the number of equations in this algebraic equation system determines the time required for the solution, and the number of equations is the order of the overall stiffness matrix K, namely The number of nodes obtained by subdividing the problem domain. Although the number of nodes and the time required for calculation are not necessarily linear, it is the parameter that best reflects the time required for calculation. However, the number of units after the model is meshed is linearly related to the number of nodes, so the number of units is estimated by the algorithm to reflect the time consumed by the model state calculation.

The principle of using genetic algorithm to select model state basis in the inventive method:

In the method of the present invention, features are used as elements for distinguishing model states, and the representation of model states is M{f ₁ , f ₂ , . . . , f _n }. According to the principle of permutation and combination, a model with n features has 2 ⁿ possible model states. If the number of features contained in the model is too large, the selection process will consume a lot of time.

The process of selecting and generating model states is essentially a problem of searching for the best or almost optimal solution in the possible solution space with the cost function as a guide. Therefore, the core problem of polymorphic model theory is how to quickly find the optimal solution in such a large solution space. Commonly used search algorithms include greedy algorithm, simulated annealing algorithm and genetic algorithm. Although the former two algorithms have fast convergence speed, they are easy to fall into the problem of local optimization; while the genetic algorithm has the advantage of large search space, but the convergence speed is slow.

Genetic Algorithm is an adaptive global optimization probability search algorithm formed by simulating the genetic and evolution process of organisms in the natural environment. It is simple, versatile, robust and suitable for parallel processing. It simulates the possible solutions in practical problems as the living environment of the individual, the objective function as the survival ability of the individual, and the coding of the possible solutions as the chromosome. In this way, starting from any initial population, a new generation of population is generated through three operations of selection, crossover, and mutation, and after many iterations, it converges to the global optimal solution or suboptimal solution.

The process of genetic algorithm is: set the goal and fitness function, after a certain number of iterations, find the individual with the highest fitness. Among them, the characteristics of the binary coding method of the chromosome structure in the algorithm and the model state generation method of feature suppression have good consistency and coordination. The encoding method is shown in Figure 4. The length of the encoding is the number of features. Each encoding corresponds to the existence state of a feature. 0 means that a certain feature does not exist in this model state, and 1 means the opposite meaning. The quality of the model state is evaluated by constructing a fitness function for this code. Aiming at the independent features in the original model, combined with the characteristics of finite element analysis, the invention takes the field of thermal analysis as an entry point, and proposes a model state selection generation standard that considers both calculation time and calculation accuracy. The genetic algorithm is used as a search algorithm to establish a suitable calculation model by searching for the best or almost best model state. As shown in Figure 5, a certain number of initial populations are randomly generated according to the individual length, and the selection, crossover and mutation operations are iterated, and finally the code of the optimal model state is obtained.

The evaluation elements of the model state are the number of elements N _e and the error level E _i after the model grid is divided. The larger N _E is, the more time-consuming the calculation is; the larger E _i is, the lower the accuracy. Therefore, the smaller the _NE and E _i corresponding to the model state, the higher its quality. In most cases, there is a mutual restrictive relationship between these two elements, that is, for the same model, the smaller the N _E , the higher the E _i may be, so this is a dual-objective optimization problem.

The traditional multi-objective optimization method is to aggregate each sub-objective into a single objective function with positive coefficients. The coefficients are determined by the decision maker (DM) or adaptively adjusted by the optimization method. Among them, the weighting method is a common classical method, which converts the MOP problem into an SOP problem through the linear combination of the objective function.

y=f(x)=ω ₁ f ₁ (x)+ω ₂ f ₂ (x)+…+ω _k f _k (x)

ω _i is called a weight, and usually the weight can be regularized so that ∑ω _i = 1, and a set of solutions can be output by solving the above optimization problems with different weights.

Based on the weighted solution of classical multi-objective problems, the fitness function is constructed based on N _E and E _M $f=\left\{\begin{array}{cc}\mathrm{\&alpha;}\&times;N_e+(1-\mathrm{\&alpha;})\&times;\widehat{{\mathrm{E.}}_m}& {\mathrm{E.}}_m\&le;{\mathrm{<figure-callout\; id="0"\; label="E.\; max"\; filenames="S2008100205612E00011.png"\; state="\{\{state\}\}">E.</figure-callout>}}_{\max }\\ 0& {\mathrm{E.}}_m>{\mathrm{E.}}_{\max }\end{array}\right.$ . In the definition, the value of α has an important influence on the quality of the selected model state, and the optimal value of α is obtained by means of experimental statistics. The exhaustive method can list all possible model states, and select the optimal solution, that is, the global optimal model state. Therefore, by comparing the quality of the model states selected with different α values, the best value of α can be selected according to statistical laws .

The principle of feature recognition and suppression algorithm basis of the present invention:

In the method of the present invention, the method of attribute adjacency graph is used for feature recognition. A feature is composed of faces, that is, a feature is a specific set of faces.

As shown in Figure 6, in a cube model, there are slots, holes and transition features respectively. Among them, the groove feature is composed of three planes, the hole feature is composed of a cylindrical surface and the transition feature is composed of a 1/4 cylindrical surface. In the face-edge graph in computer graphics, faces are used as nodes, and if the faces are adjacent to each other, it means that the nodes on the faces are connected by line segments. In a box model that contains slot, hole, and transition features, respectively, there are three nodes, one node, and one node representing the corresponding features. The cube model in Figure 7 contains 1 slot feature, 1 round blind hole feature and 1 round through hole feature, assuming that all faces in the model are numbered, and the face numbers corresponding to the slot feature are 2, 3, 4 ; The surface numbers corresponding to the circular blind hole feature are 11, 12; the surface number corresponding to the circular through hole feature is 13, then in the corresponding surface-edge graph, the three nodes numbered 2, 3, 4 include the connection All the edges of the feature constitute the subgraph corresponding to this feature; similarly, the nodes numbered 11 and 12 together with all the edges connected to them constitute the subgraph of the circular blind hole feature; the nodes numbered 13 together with all the edges connected to them constitute The subgraph of the circular through hole feature is shown in Figure 8. The subgraphs corresponding to different features have different characteristics. In Figure 9, according to the different characteristics of the slot, hole, and transition feature subgraphs, the features in the model can be divided into holes, slots, and transition features for identification and stored in the linked list. , for feature suppression.

In Document 6, the technology of feature recognition and suppression is described in detail. Proceed as follows:

1. Determine the concave-convexity of each edge and generate the AAG graph of the model.

2. Traverse the AAG to find all the convex surfaces to form a face set fvex, analyze the fvex to find out the single-type features, specific classification:

(1) Round through hole features: convex, cylindrical, and only two sides.

(2) Fillet features: convex surface, types include torus, cylinder, sphere, spline surface.

3. Delete fvex from the AAG graph to obtain a subgraph in which all nodes form the face set fcav. Find all connected components of this subgraph, and each connected component is a feature subgraph. Each feature sub-graph is identified according to the classification features of the above-mentioned feature sub-graph, and the specific feature type is judged.

4. Round blind hole features: two faces, one of which is a leaf node. For two adjacent edges, the default leaf node corresponds to a plane, and the other side is a cylindrical surface.

5. Square blind hole feature: There is one surface, and all adjacent sides are concave. The graph contains a loop, and the corresponding surfaces of the nodes in the loop belong to this feature.

6. Square through hole feature: There is a loop in the figure, and the corresponding surfaces of the nodes in the loop belong to this feature. Each face has four adjacent edges, two of which are convex and two of which are concave.

7. Groove: three sides, two concave sides.

8. According to the identified feature type, generate the corresponding feature object, and record the corresponding feature composition surface.

9. Generate the feature tree corresponding to the model for subsequent processing.

Example:

1. The model to be simplified is provided by the user. The model to be simplified has the load conditions and grid division conditions during finite element analysis. As shown in Figure 10, the model to be simplified has a center coordinate of (0, 0, 0), cube base 1 with a side length of 10 units, minus an inner cylinder A2 with a bottom center of (2, -2, 0), a radius of 0.8 units, and a height of 10 units, and then subtract one Inner cylinder B3 whose bottom center is (-1, -1, 3.5), radius is 0.8 units, and height is 3 units, minus one inner cylinder whose bottom center is (3.5, 1, 0), radius is 0.5 units, Inner cylinder C4 with a height of 10 units, subtract an inner hexagonal prism A5 with a center coordinate of (2, 0, 0), a side length of 0.8 units, and a height of 10 units, and then subtract a center coordinate of (2.5, 2, -2.5), an inner octagonal prism A6 with a side length of 0.5 units and a height of 5 units, minus a center coordinate of (1, 2, 0), a side length of 0.8 units, and a height It is an inner octagonal prism B7 of 10 units, then subtract an inner hexagonal prism B8 whose center coordinates are (-1, 2, 3.5) and a height of 3 units, and then subtract the diagonal vertices to be (2, 4, - 5) and (3, 5, 5) slot A9, then subtract the slot B10 whose diagonal vertices are (-1, 4, -5) and (0.5, 5, 5), and then subtract the diagonal vertices as ( Slot C 11 for -3, 3, -5) and (-2, 5, 5), minus slot D12 with diagonal vertices (2, -4, -5) and (3, -5, 5) , then subtract the slot E13 whose diagonal vertices are (-1, -4, -5) and (0.5, -5, 5), and then subtract the diagonal vertices as (-3, -3, -5) and ( Slot F14 of -2, -5, 5), perform a rounding operation on the four sides of the right side of the cube with a radius of 0.8 units, and obtain rounded corners A15, rounded corners B16, rounded corners C17, and rounded corners D 18 , the load surface is the left side of the cube, and the grid division conditions are the maximum grid diameter h _max =2 and the minimum grid diameter h _min =1;

2. Create a feature list

The load conditions of the model, the properties of the finite element element and the grid division conditions are shown in Table 1. The user uses commercial modeling software to create a 3D geometric model in the format of .SAT, imports the model file and performs feature recognition, and stores the identified features into the feature list; traverses the feature list again, and calculates according to D _i for each feature. Get the position parameter P _i of this feature; obtain the position parameter P _i by the following method:

a. Given that the weight of each feature to be simplified on the finite element calculation result after simplification is q ₁ =q ₂ =...=q ₈ =0.5;

b: let i=1;

c: Set the centroid of the enclosing box of the i-th feature to be simplified, and the centroid coordinates are (x _i , y _i , zi ₎ , calculate the distance d _i from the centroid of the i-th feature to be simplified to the load surface, d _i = x _i ;

d: Calculate the position parameter P _i =q _i /d _i of the i-th feature to be simplified;

e: set i=i+1, repeat steps c~d until the position parameter P _i of all features to be simplified in the model is calculated;

Obtain the maximum Gaussian curvature θ _max = 0.25 of the surface composed of all features of the selected feature to be simplified;

2. According to the volume V _i of each selected feature to be simplified, the position parameter P _i , and the mesh diameter change amount of each selected feature to be simplified under its corresponding simplification scheme, according to the calculation formula E _i =V _i P _i H _i obtains the sensitive value E _i of this feature under its corresponding simplified scheme, as shown in Table 1;

In this embodiment, the mesh diameter change amount is obtained according to the following steps:

a. Calculate ε=θ _max h _min =0.25, let i=1;

b. Set i=1, calculate ε=θ _max h _min ; if the feature composition surfaces are all planes, then obtain the minimum side length h _i of the feature to be simplified, and calculate the grid diameter change H _temp =h _max -min( h _max , h _i ), if H _temp >0, the corresponding mesh diameter change H _i =H _temp , otherwise go to the next step;

c. If there is a curved surface in the feature composition surface, obtain the average Gaussian curvature θ _avgi of all the surfaces contained in the feature i currently to be simplified, and calculate the mesh diameter change $h_{\mathrm{temp}}=h_{\max }-\min (h_{\max },\frac{\mathrm{\&epsiv;}}{{\mathrm{\&theta;}}_{\mathrm{avgi}}})$ , if H _temp >0, then the corresponding mesh diameter change amount H _i =H _temp , otherwise go to the next step;

d. Let i=i+1, repeat steps b and c, until all the features to be simplified in the model and the grid diameter change amount H i corresponding to the simplification method, _i =1, 2,..., n, the calculation is completed, and the table is obtained 1;

In this embodiment, the sensitivity value is the product of the volume of the corresponding feature, the position parameter and the mesh diameter change under the corresponding simplified method, calculated as: E _i = V _i P _i H _i , i = 1, 2, ..., n, get Table 1;

Table 1 Feature attribute list

serial number Feature Type V _i D _i α P _{i Hi} E _i 1 Circular through hole 7.85 8.50 0.01 0.085 0.88 0.58 2 Circular through hole 20.11 7.00 0.01 0.07 0.92 1.30 3 Circular blind hole 6.03 4.00 1.00 4.00 0.90 21.71 4 Square through hole 16.63 7.00 0.85 5.95 0.35 34.63 5 Square through hole 18.10 6.00 0.50 3.00 0.15 8.15 6 square blind hole 4.99 4.00 0.90 3.60 0.60 10.24 7 square blind hole 3.54 7.50 0.30 2.25 0.40 7.97 8 groove 10.00 7.50 0.25 1.88 0.30 5.63 9 groove 15.00 5.75 0.88 5.06 0.46 34.91 10 groove 20.00 2.50 0.95 2.38 0.37 17.58 11 groove 10.00 7.50 0.23 1.73 0.25 4.31 12 groove 15.00 5.75 0.90 5.18 0.45 34.93 13 groove 20.00 2.50 0.90 2.25 0.30 13.50 14 fillet 5.03 9.20 0.008 0.074 0.95 0.35 15 Fillet 5.03 9.20 0.005 0.046 0.95 0.22 16 fillet 5.03 9.20 0.003 0.028 0.95 0.13 17 fillet 5.03 9.20 0.006 0.055 0.95 0.26

4. In this embodiment, the Solid Tet 10node 87 element used for thermal analysis is selected as the finite element, that is, the 10-node element, and the default division density is used for grid division. Since the average side length is 1.5 units, the average volume of the unit is 3.375, and the volume of the model state is v, then the corresponding unit number N _E =v/3.375;

5. Use binary coding to represent the model state, and the coding length is the number of features. In the field of thermal analysis, users know from experience that rounded corner features have a great negative impact on mesh division and the impact on calculation results can be ignored. The model's The four rounded corner features are suppressed first, so the feature encoding is 13 bits, corresponding to ²¹³ possible model states, and the order of the features in the model is consistent with the feature numbers in the table. The initial model state code is 1111111111111.

6. The user inputs an error level of 1, and calculates a tolerable quantization error E _max =11.55.

7. Randomly generate a population with the number of individuals N=100; crossover probability P _c =0.8, mutation probability P _m =0.02, take α=0.3, then the fitness calculation formula of each individual is $f=\left\{\begin{array}{cc}0.3\&times;v/3.375+0.7\&times;\widehat{{\mathrm{E.}}_m}& {\mathrm{E.}}_m\&le;11.55\\ 0& {\mathrm{E.}}_m>11.55\end{array}\right.,,$

in $\widehat{{\mathrm{E.}}_m}={\mathrm{E.}}_m\&times;{\lg }^{(0.3\&times;v)/(3.375\&times;{\mathrm{E.}}_m)},.$

，每迭代一次，使用网格剖分算法估计出这代中所有个体编码对应模型态的刚度矩阵阶数，再计算适应度函数。最终模型态的编码为0011010011011，经过特征抑制，几何形状如图13所示，剩下正方体基座1、圆盲孔特征3、正六面体通孔5、正六面体盲孔8、槽10、11、14。8. The number of iterations is

, each iteration, use the grid subdivision algorithm to estimate the order of the stiffness matrix corresponding to the model state of all individual codes in this generation, and then calculate the fitness function. The code of the final model state is 0011010011011. After feature suppression, the geometric shape is shown in Figure 13, and the remaining cube base 1, circular blind hole feature 3, regular hexahedral through hole 5, regular hexahedral blind hole 8, slots 10, 11, 14.

Claims (5)

1. The model state generation method based on feature suppression in finite element modeling is characterized by the following steps: a. The model to be simplified is provided by the user, and the model to be simplified has load conditions during finite element analysis and meshing conditions, and the meshing conditions are the maximum mesh diameter h _max and the minimum mesh diameter _hmin ; b. Identify the simplification features in the model to be simplified, and store them in the feature list; c. Select the feature to be simplified in the feature linked list, determine the number of features to be simplified n; number the selected n features to be simplified in any order, and calculate and obtain the volume V _i of each selected feature to be simplified positional parameter P _i ; d. According to the volume V _i of each selected feature to be simplified, the position parameter P _i , and the mesh diameter change of each selected feature to be simplified after it is suppressed, obtain the corresponding feature to be simplified in its The suppressed sensitive value E _i =V _i P _i H _i ; the error level of the model state is represented by the sum of the sensitive values of all suppressed features; e. By estimating the number _of grid cells in the model state, it is estimated that the number of cells in the model state after grid division _Ne is linearly related to the order of the stiffness matrix in the model state. N _e reflects the finite element calculation time required for the model state; f. According to the error level of the model and the number of units N _e , the genetic algorithm is used to select the model state to obtain the simplified model code; g. Applying feature suppression to generate a simplified model corresponding to said simplified model code. 2. The model state generation method based on feature suppression in the finite element modeling according to claim 1, characterized in that the simplified feature position parameter _Pi is obtained in the following manner in the step c: a. Given the weight of the influence of each feature to be simplified on the finite element calculation result after simplification, set it as q ₁ , q ₂ , ... q _n , where q _i ∈ [0, 1], (i=0, 1, ... n), q _i =0 indicates that the presence or absence of the i-th feature to be simplified has no effect on the finite element calculation results; q _i =1 indicates that the existence or non-existence of the ith feature to be simplified has the greatest impact on the finite element calculation results _, The closer to 1, the greater the influence of the characteristic features on the finite element calculation results; b. Let i=1; c. Set the distance d _i from the i-th feature to be simplified to the load surface; d. Calculate the position parameter P _i =q _i /d _i of the i-th feature to be simplified; e. Set i=i+1, repeat steps c-d until the calculation of position parameters P _i of all features to be simplified in the model is completed. 3. The model state generation method based on feature suppression in the finite element modeling according to claim 1, characterized in that the mesh diameter change amount is obtained in the following steps in the step d: a. If the features to be simplified are all composed of planes, obtain the minimum side length h _i of the features to be simplified, and calculate the mesh diameter change H _temp = h _max -min(h _max , h _i ), if H _temp >0, Then adopt this feature simplification scheme, the corresponding mesh diameter change $h_{i,c_i}=h_{\mathrm{temp}},$ Otherwise, go to the next step; b. If there is a curved surface in the feature to be simplified, obtain the average Gaussian curvature θ _avgi of all high-curvature surfaces contained in the current feature i to be simplified, and calculate the mesh diameter change $h_{\mathrm{temp}}=h_{\max }-\min (h_{\max },\frac{\mathrm{\&epsiv;}}{{\mathrm{\&theta;}}_{\mathrm{avgi}}})$ , if H _temp >0, then adopt this feature simplification scheme, the corresponding mesh diameter change $h_{i,c_i}=h_{\mathrm{temp}}.$ 4. The method for generating model states based on feature suppression in the finite element modeling according to claim 1, characterized in that the estimation of the number of model state grid cells in the step e is carried out as follows: a. According to the maximum grid diameter h _max and the minimum grid diameter h _min provided by the user, take the grid unit side length h=(h _max +h _min )/2; b. Combining the type of grid unit and the side length of the grid unit, calculate the actual volume v _e occupied by a grid unit, and the volume calculation formula varies from unit to unit; c. Calculate the actual volume v of the model state, and obtain the number of units _Ne = v/v _e of the model mesh; 5. The method for generating model states based on feature suppression in the finite element modeling according to claim 1 is characterized in that in the step f, genetic algorithm is used to carry out model state selection according to the following steps: a. Use binary code to represent the model state, the code length is the number of features, and each feature corresponds to a binary bit in the individual; 0 means that a certain feature does not exist in the model state, and 1 means that a certain feature exists in the model state; b. The user inputs the tolerable error level level m, m∈[1,n], forming the maximum allowable error ${\mathrm{E.}}_{\max }=\frac{1}{\mathrm{no}-m+1}\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}{\mathrm{E.}}_i$ , where n is the number of features; c. The number of randomly generated individuals is $N=\left\{\begin{array}{cc}{2}^{N_f}& N_f\&le;6\\ 100& N_f>6\end{array}\right.$ , where _NF is the number of features; set the crossover probability P _c ∈ [0.6, 0.8], the mutation probability P _m ∈ [0.01, 0.02], the fitness calculation formula of each individual is $f=\left\{\begin{array}{cc}\mathrm{\&alpha;}\&times;N_e+(1-\mathrm{\&alpha;})\&times;\widehat{{\mathrm{E.}}_m}& {\mathrm{E.}}_m\&le;{\mathrm{E.}}_{\max }\\ 0& {\mathrm{E.}}_m>{\mathrm{E.}}_{\max }\end{array}\right.$ ,in $\widehat{{\mathrm{E.}}_m}={\mathrm{E.}}_m\&times;{\lg }^{N/{\mathrm{E.}}_m}$ , E _M ＝∑E _i , i is the feature serial number of 0 in the model state code; α is the weight factor, here α is selected as 0.3; d. The number of iterations is

, each iteration, estimate the number of grid cells corresponding to the model state for all individuals in this generation, and calculate the fitness function on this basis; The individual with the greatest fitness in the first generation population is the obtained simplified model code.

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