CN101241520A - Model state creation method based on characteristic suppression in finite element modeling - Google Patents

Abstract

The present invention provides a restraining model generating method based on the characteristics in finite element modeling, characterized in that the providing unreduced model by users; identifying reducible characteristics in the unreduced model; determining numbers of unreduced characteristics; acquiring sensitive value of the unreduced characteristics after being suppressed representing model lateral error by the sum of all suppressed characteristics sensitive values; evaluating unit amount of the model after being grid divided; selecting the model according to the lateral error of the model and the unit amounts Ne, acquiring simplified model code; a simplified model corresponding to the simplified model code generated by suppress characteristics method. The invention achieves that each characteristic changes in the model objectively evaluates the finite element result sensibility, establishes sensibility measurement system of results by choosing and changing of each element in the model, and gives an precise evaluating method of the model time consumption, generating model on the basis.

Description

The model state creation method that suppresses based on feature in the finite element modeling

Technical field

The present invention relates to the Computer Aided Modeling method, a kind of model state creation method that is applied in the finite element modeling of more specifically saying so.

Background technology

Social productive forces have been brought into play more and more important effect, particularly computer aided design cad to computing machine, ancillary works CAE, the auxiliary CAM of manufacturing are increasingly mature and universal in industry member for improving, and have greatly improved the efficient of industrial design and production.Adopt finite element analysis and, can improve the structural design of product, make product have rational structure under the situation of strength and stiffness satisfying based on the optimization process of finite element analysis.

Finite element analysis FEA as far back as the fifties at first in the continuum mechanics field, such as being applied in and the dynamic analysis static, be applied to analyze heat conduction, electromagnetic field and fluid mechanics equicontinuity problem subsequently very soon at aircaft configuration.

The physical substance of finite element analysis is to use non-individual body of assembly approximate substitution of being made up of limited unit that is connected at the node place, thereby the problem analysis of non-individual body is converted into the problem analysis of element analysis and unit combination.The combination of the powerful data-handling capacity of finite element analysis and computing machine, the analysis of some large and complex structures that can not carry out of making has over become conventional calculation task.

Carry out finite element analysis and at first will set up the geometric model of object to be analyzed.Realistic model is very complicated usually, is mainly reflected in feature kind and enormous amount that it comprises, except common hole, cavity feature, also contains a large amount of Interims.If modeling precision is too high, undoubtedly can be for calculating bring great burden, especially the existence of Interim can increase calculated amount greatly, therefore, need carry out feature reduction to realistic model.When being simplified, the feature in the realistic model relates to following two key problems: the one, and how tiny hole, groove and Interim are simplified the back influence that former result of calculation causes is estimated; The 2nd, how to estimate computing time of the required consumption of model after the simplification, to judge whether simplify the back model can promote counting yield.

At this problem, roll up on the 13 phase 925-934 pages or leaves in periodical " Computer-Aided Design ", calendar year 2001 33, in the article of A Sheffer. " Model Simplification for Meshing Using Face Clustering " (hereinafter to be referred as document 1), analyzed several frequently seen Interim to dividing the negative influence that grid causes; But do not handle at Interim, more do not estimate the influence that the result is caused behind the feature reduction and simplify after computing time of the required consumption of model.

On " Computer-Aided Design " 2002 34 volumes 22 phase 109-123 pages or leaves, H Zhu, the article " An Efficient Algorithm for Recognizing and SuppressingBlend Features " (hereinafter to be referred as document 3) of Cui Xiu sweet smell on 2004 the 5th phase 24-28 pages or leaves of another piece document of C H Menq " B-Rep Model Simplification by Automatic Fillet/Round Suppressing for EfficientAutomatic Feature Recognition " (hereinafter to be referred as document 2) and " Computer-Aided Design " though in comparatively perfect Blend Feature Recognition and short-cut method have been proposed, do not estimate yet Interim be suppressed the influence that the result is caused the back and simplify after computing time of the required consumption of model.

The article " Feature-based multiresolution techniques for product design " (hereinafter to be referred as document 4) of LEE Sang Hun has proposed during product is made the modeling method based on level of detail LOD on journal of Zhejiang university natural science edition 2006 the 7th volume the 9th phase 1535-1543 page or leaf, in this method, feature in the geometric model is divided into simply adds feature and subtract feature, determine by the user value of LOD decides whether each feature exists in the model, to reach the purpose that reduces calculated amount.But this method too relies on user experience; Whether owing to how much difference between model hierarchy are excessive, it is suitable also to need behind the preference pattern level to test repeatedly with verification model simultaneously, and process is too complicated, and does not provide the evaluated error of hierarchical model correspondence, the time that the model after also estimating to simplify need consume.

In 2005 master thesis of HeFei University of Technology " the polymorphic model pre-test of geometry in the science calculating " (hereinafter to be referred as document 5), with neutron transport program MCNP is research object, the key element that influences that adopts certain model attitude to replace the error of calculation of master pattern generation in the science calculating field has been done Primary Study, and, summed up the rule between the error of calculation and the feature volume based on experimental data.According to the rule of summing up, the method that adopts feature to suppress forms the model attitude.The corresponding evaluated error of each model attitude provides a good aided modeling function to the user.Its research method has certain property used for reference, but has the field limitation, and promptly the summary method of error key element is not considered the self-characteristic in finite element field, and the reliability of conclusion and versatility are not strong, and do not provide the method for estimation of model attitude counting yield.

In 2007 master thesis of HeFei University of Technology " selection of model attitude research in the finite element field " (hereinafter to be referred as document 6), based on experiment, from experimental data, summed up and adopted certain model attitude to replace the error of calculation rule that master pattern produces in the heat conduction field, and the factor that influences computing time has been carried out initial analysis and summary; On the basis of the formalization expression formula that provides computational accuracy and computing time, constructed the fitness function of genetic algorithm, selected the highest model attitude of fitness by the iterations of some; Suppress algorithm according to model attitude coding use characteristic at last master pattern transformation is obtained final geometric model.The concrete steps that the model attitude of being put down in writing in the paper generates are:

A, at the different application of finite element, set up and only comprise a naive model of waiting to simplify feature, the feature to be simplified here is modal groove in the processing parts, hole or cylinder Interim, sets up the model that comprises them, and structure steady state thermal conduction experiments scheme.

B, according to feature volumetric parameter and location parameter structure experimental program, promptly the groove of the distance D that contains some groups of different characteristic volume ratio V and feature and plane of load, the model of hole characteristic are carried out analytical calculation, according to the internal relation of result of calculation analytical error, its relation is carried out match than the distance D of EP, feature volume ratio V and feature and plane of load.

C, user utilize the Interim in self domain knowledge judgment models whether to have influence degree to the result, if certain Interim can be left in the basket to the influence degree of result of calculation, then the quality with grid dividing is a standard, Interim is determined the geometric attribute threshold value that it is deleted, occur unpredictable problem when avoiding calculating; The Interim that can not delete will be retained.

D, be defined as further improving the suppressible groove of counting yield, hole characteristic according to the distance D and the funtcional relationship between the error ratio EP of feature volume ratio V, feature and the plane of load of the groove that simulates, hole characteristic.

The expression formula P=1-∑ EP of e, structure reaction precision key element _iExpression formula with element of time $\stackrel{\‾}{V}=\frac{1}{n}\mathrm{\Σ}{V}_i$ , and based on this structure genetic algorithm fitness function $F=\left\{\begin{array}{cc}\mathrm{\α}\×\stackrel{\‾}{V}+(1-\mathrm{\α})\×P& \mathrm{EP}\≤{\mathrm{EP}}_{\max }\\ 0& \mathrm{EP}>{\mathrm{EP}}_{\max }\end{array}\right.$ , selected other parameters of genetic algorithm.Here EP _iBe that i feature is suppressed the error ratio that the back produces,

Be the average characteristics volume ratio, EP _MaxIt is the acceptable maximum error that the user imports.

F, geometric model is handled the model attitude of finally being selected according to coding.

In above-mentioned steps among the a-d, be to obtain funtcional relationship between the distance D of error ratio EP, feature volume ratio V, feature and plane of load by the match experimental data.But this mode has the deficiency of two aspects: at first, the relation between error ratio, feature volume ratio and feature and the plane of load distance only draws by the data of limited number of time experiment, has randomness; Secondly, can not guarantee to influence the comprehensive of error key element summary.In step (e), according to the average external volume ratio size of the feature that contains in the model attitude $\stackrel{\‾}{V}=\frac{1}{n}\mathrm{\Σ}{V}_i$ The time of coming the estimation model attitude to consume, obviously lack objectivity and accuracy.

Summary of the invention

The present invention is for avoiding above-mentioned existing in prior technology weak point, the model state creation method that suppresses based on feature in a kind of finite element modeling is provided, the factor that after comprehensive consideration model simplification result of finite element is influenced, thereby the variation of each feature is to the objective evaluation of result of finite element susceptibility in the implementation model, set up the choice and the sensitivity assessment system that changes result of calculation of each key element in the model, and provide the time consuming method of estimation of a kind of objective precise analytic model attitude, generation model attitude on this basis.

Technical solution problem of the present invention adopts following technical scheme:

The characteristics of the model state creation method that suppresses based on feature in the finite element modeling of the present invention are to carry out as follows:

A, provided by the user and to treat simplified model, the described simplified model for the treatment of has the load-up condition when carrying out finite element analysis, and the mesh generation condition, and described mesh generation condition is maximum mesh diameter h _MaxWith minimum grid diameter h _Min

B, the described feature for the treatment of in the simplified model simplified of identification, and deposit the feature chained list in;

C, in described feature chained list, select feature to be simplified, determine to wait to simplify feature quantity n; In any order selected n feature to be simplified is numbered, calculate obtain selected each wait to simplify the volume V of feature _iWith location parameter P _i

D, according to each selected volume V that waits to simplify feature _i, location parameter P _i, and each selectedly waits to simplify the grid diameter change amount of feature after it is suppressed, and obtains the corresponding sensitivity value E of feature after it is suppressed that wait to simplify _i=V _iP _iH _iBe suppressed the error level of the sensitivity value sum characterization model attitude of feature with all;

E, by model attitude grid cell is carried out the estimation of quantity, estimate the element number N after the model attitude is carried out grid dividing _e, described element number N _eWith model attitude stiffness matrix exponent number linear dependence, with described element number N _eThe reflection model required FEM (finite element) calculation time of attitude;

F, according to the error level and the element number N of model _e, adopt genetic algorithm to carry out the selection of model attitude, obtain the simplified model coding;

G, application characteristic inhibition method generate the simplified model corresponding to described simplified model coding.

The characteristics of the inventive method also are:

Simplify feature locations parameter P among the described step c _iObtain in the following way:

A, given each wait to simplify behind the feature reduction the weight of result of finite element influence, be made as q ₁, q ₂... q _n, q wherein _i∈ [0,1], (i=0,1 ... n), q _iI of=0 sign waited to simplify feature and whether existed not influence of result of finite element; q _i=1 characterizes i waits to simplify feature and whether exists and result of finite element is had the greatest impact q _iBig more the closer to 1 characteristic feature to the influence of result of finite element;

B, make i=1;

C, establish i wait to simplify feature to plane of load apart from d _i

D, i location parameter P that waits to simplify feature of calculating _i=q _i/ d _i

E, make i=i+1, repeating step c～d remains to be simplified the location parameter P of feature in model _iCalculating finishes.

Grid diameter change amount obtains as follows in the described steps d:

A, if wait to simplify feature and form by the plane, obtain the minimum length of side h that this waits to simplify feature _i, computing grid diameter change amount H _Temp=h _Max-min (h _Max, h _i), if H _Temp＞0, then adopt this kind feature reduction scheme, corresponding grid diameter change amount $H_{i,c_i}=H_{\mathrm{temp}},$ Otherwise commentaries on classics next step;

B, if wait to simplify and have curved surface in the feature, obtain the current mean-Gaussian curvature θ that waits to simplify all higher curvature curved surfaces that feature i comprises _Avgi, computing grid diameter change amount $H_{\mathrm{temp}}=h_{\max }-\min (h_{\max },\frac{\mathrm{\ϵ}}{{\mathrm{\θ}}_{\mathrm{avgi}}})$ , if H _Temp＞0, then adopt this kind feature reduction scheme, corresponding grid diameter change amount $H_{i,c_i}=H_{\mathrm{temp}}.$

The estimation of among the described step e model attitude grid cell being carried out quantity is to carry out as follows:

A, the maximum mesh diameter h that provides according to the user _Max, minimum grid diameter h _Min, get grid cell length of side h=(h _Max+ h _Min)/2;

B, in conjunction with the grid cell type and the grid cell length of side, calculate an actual volume ve that grid cell is shared, the volume calculation formula is different because of the unit;

C, calculate the actual volume v of model attitude, obtain the element number N that model meshes is divided _e=v/v _e

Adopting genetic algorithm to carry out the model attitude among the described step f selects to carry out as follows:

A, use binary coding representation model attitude, code length is a feature quantity, each feature is corresponding to the bit in the individuality; On behalf of certain feature, 0 do not exist in the model attitude, and on behalf of certain feature, 1 be present in the model attitude;

B, user import tolerable error level rank m, and m ∈ [1, n] forms the limits of error $E_{\max }=\frac{1}{n-m+1}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{E}_i$ , wherein n is a feature quantity;

C, generate individual amount at random and be $N=\left\{\begin{array}{cc}{2}^{N_F}& N_F\≤6\\ 100& N_F>6\end{array}\right.$ Population, N wherein _FBe feature quantity; Crossover probability P is set _c∈ [0.6,0.8], the variation probability P _m∈ [0.01,0.02], each individual fitness computing formula is $F=\left\{\begin{array}{cc}\mathrm{\α}\×N_e+(1-\mathrm{\α})\×\widehat{E_M}& E_M\≤E_{\max }\\ 0& E_M>E_{\max }\end{array}\right.$ , wherein $\widehat{E_M}=E_M\×{\lg }^{N/E_M},$ E _M=∑ E _i, i is to be 0 feature sequence number in the model attitude coding; α is a weight factor, and α is chosen for 0.3 here;

D, iterations are , every iteration once estimates the grid cell quantity of the corresponding model attitude of all individual codings in this generation, calculates fitness function based on this; If the bigger individual or arrival maximum iteration time of fitness does not appear in the three generations continuously, then the individuality of fitness maximum is the simplified model coding that is obtained in the population in last generation.

Compared with the prior art, beneficial effect of the present invention is embodied in:

1, the objectivity of error component analysis

The inventive method is analyzed at using certain model attitude to replace master pattern to calculate the generation reasons of error, has drawn the key element relevant with error: grid diameter change amount behind volume, feature locations parameter and the feature reduction; Abandoned from experience, data are sought the randomness of error relevant factor method by experiment.

2, the accuracy of calculation consumption time estimation

In the existent method, only in document 7, tentatively summed up to weigh and calculated key element consuming time, but it proposes the average characteristics volume in the model as calculating measurement parameter consuming time, accuracy deficiency.The inventive method can accurately reflect calculates key element consuming time, i.e. element number N behind the model division grid _eAs the element of time in the model attitude essential elements of evaluation, can reflect the computing time of model attitude correspondence exactly, be of value to choosing of optimization model attitude coding.

3, the rationality of genetic algorithm fitness function structure

The structure of fitness function has been considered the equilibrium relation between model attitude computing time and the computational accuracy fully, for the factor of influence of two key elements of balance, to error level E in the fitness function _MCarried out order of magnitude correction.

Description of drawings

Fig. 1 is the selection transition mathematical model synoptic diagram of model attitude in the inventive method.

Fig. 2 is grid vertex method schematic vector diagram outside the corresponding point on curved surface.

Fig. 3 is for concerning synoptic diagram between model surface curvature and the grid.

Fig. 4 is model attitude coding synoptic diagram.

Fig. 5 chooses synoptic diagram for the model attitude.

Fig. 6 is that the feature of groove, hole and fillet is formed the face synoptic diagram.Wherein, Fig. 6 (a1) is for containing the model of cavity feature; Fig. 6 (a2) is the face edge graph of Fig. 6 (a1) institute representation model correspondence; Fig. 6 (b1) is for containing the model of hole characteristic; Fig. 6 (b2) is the face edge graph of Fig. 6 (b1) institute representation model correspondence; Fig. 6 (c1) is for containing the model of Fillet Feature; The face edge graph of Fig. 6 (c2) Fig. 6 (c1) institute representation model correspondence.

Fig. 7 (a) is the model that contains a blind hole, a through hole and a cavity feature, and Fig. 7 (b) is Fig. 7 (a) characteristic of correspondence subgraph.

Fig. 8 (a), Fig. 8 (b), Fig. 8 (c), Fig. 8 (d) and Fig. 8 (e) are respectively the feature subgraph classification chart of square tube hole, square blind hole, round tube hole, circle blind hole and groove.

Fig. 9 is aspect of model tree synoptic diagram.

Figure 10 is realistic model synoptic diagram to be simplified in the inventive method.

Figure 11 is the simplified model synoptic diagram so that the inventive method was obtained.

Number in the figure: cylinder C, 5 interior six prismatic A, 6 interior eight prismatic A, 7 interior eight prismatic B, 8 interior six prismatic B, 9 groove A, 10 groove B, 11 groove C, 12 groove D, 13 groove E, 14 groove F, 15 fillet A, 16 fillet B, 17 fillet C, 18 fillet D in 1 pedestal, 2 interior cylinder A, the 3 interior cylinder B, 4.

Below pass through embodiment, and in conjunction with the accompanying drawings the present invention be further described:

Embodiment

Present embodiment provides the horizontal construction method of model error to carry out as follows:

1, provide model to be simplified by the user, model described to be simplified has the load-up condition when carrying out finite element analysis, and the mesh generation condition, and described mesh generation condition is maximum mesh diameter h _MaxWith minimum grid diameter h _Min

2, it is carried out feature identification, deposit the tagsort that identifies in the feature chained list; Traversal feature chained list calculates the volume V that obtains each feature _i, the location parameter P of each feature _i

Wherein, chained list is a kind of computer data structure of routine;

In this step, wait to simplify the volume V of feature _iCubature formula routinely calculates, the location parameter P of feature _iObtain in the following way:

A, given each wait to simplify behind the feature reduction the weight of result of finite element influence, be made as q ₁, q ₂... q _n, q wherein _i∈ [0,1], (i=0,1 ... n), q _iI of=0 sign waited to simplify feature and whether existed not influence of result of finite element; q _i=1 characterizes i waits to simplify feature and whether exists and result of finite element is had the greatest impact q _iBig more the closer to 1 characteristic feature to the influence of result of finite element;

B: make i=1;

C: ask for i and wait to simplify the feature bounding box centre of form,, then obtain the centre of form of load body if load is body load; Calculate i wait to simplify the feature centre of form to plane of load apart from d _iIf, body load, then calculate i wait to simplify the feature centre of form to the load bodily form heart apart from d _iWait to simplify the distance of the feature centre of form if there are a plurality of plane of loads then to calculate i, get its mean value again to each load;

D: calculate i location parameter P that waits to simplify feature _i=q _i/ d _i

E: make i=i+1, repeating step c～d remains to be simplified the location parameter P of feature in model _iCalculating finishes;

3, calculate acquisition and remain to be simplified the maximum Gaussian curvature θ that all features of feature are formed faces _Max

4, according to grid diameter change amount computing method, calculated characteristics is simplified the change amount H of back grid diameter _i

According to maximum curvature θ _Max, maximum mesh diameter h _MaxWith minimum grid diameter h _MinObtain grid diameter change amount as follows;

A, make i=1, calculate ε=θ _Maxh _MinIf feature composition face is the plane, then obtain the minimum length of side h that this waits to simplify feature _i, computing grid diameter change amount H _Temp=h _Max-min (h _Max, h _i), if H _Temp＞0, corresponding grid diameter change amount H _i=H _Temp, otherwise change next step;

B, if having curved surface in the feature composition face, then obtain the current mean-Gaussian curvature θ that waits to simplify all curved surfaces that feature i comprises _Avgi, computing grid diameter change amount $H_{\mathrm{temp}}=h_{\max }-\min (h_{\max },\frac{\mathrm{\ϵ}}{{\mathrm{\θ}}_{\mathrm{avgi}}})$ , if H _Temp＞0, Dui Ying grid diameter change amount H then _i=H _Temp, otherwise change next step;

C, make i=i+1, repeating step a, b remain to be simplified feature and the corresponding grid diameter of its simplified way change amount H in model _i, i=1,2 ..., n, calculating finishes;

5, by error level estimation formulas E _i=V _iP _iH _iEstimate the sensitivity value after this feature is suppressed, and be suppressed the error level of the sensitivity value sum characterization model attitude of feature with all;

6, the structure genetic algorithm each parameter and carry out the selection of model attitude;

The construction step of genetic algorithm is as follows:

A, the conventional binary coding representation model attitude of use, code length is a feature quantity, each feature is corresponding to the bit in the individuality; On behalf of certain feature, 0 do not exist in the model attitude, and on behalf of certain feature, 1 be present in the model attitude;

B, user import tolerable error level rank m, and m ∈ [1, n] forms the limits of error $E_{\max }=\frac{1}{n-\mathrm{<figure-callout\; id="1"\; label="m\; +"\; filenames="S2008100205612E00011.png,S2008100205612E00041.png"\; state="\{\{state\}\}">m</figure-callout>}+1}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{E}_i$ , wherein n is a feature quantity;

C, generate individual amount at random and be $N=\left\{\begin{array}{cc}{2}^{N_F}& N_F\&le;6\\ 100& N_F>6\end{array}\right.$ Population, N wherein _FBe feature quantity; Crossover probability P is set _c∈ [0.6,0.8], the variation probability P _m∈ [0.01,0.02], each individual fitness computing formula is $F=\left\{\begin{array}{cc}\mathrm{\&alpha;}\&times;N_e+(1-\mathrm{\&alpha;})\&times;\widehat{E_M}& E_M\&le;E_{\max }\\ 0& E_M>E_{\max }\end{array}\right.$ , wherein $\widehat{E_M}=E_M\&times;{\lg }^{N/E_M},$ E _M=∑ E _i, i is to be 0 feature sequence number in the model attitude coding; α is a weight factor, and α is chosen for 0.3 here;

D, iterations are

, every iteration once estimates the grid cell quantity of the corresponding model attitude of all individual codings in this generation, calculates fitness function based on this; If the three generations does not have more outstanding individual or arrival maximum iteration time to occur continuously, then genetic algorithm finishes, and obtains optimization model attitude coding;

In this step, the grid cell quantity of the corresponding model attitude of all individual codings of certain generation obtains in the following way in the population:

(1), the maximum mesh diameter h that imports according to the user _Max, minimum grid diameter h _Min, get unit length of side h=(h _Max+ h _Min)/2;

(2), combining unit type element type and the unit length of side, calculate the actual volume v that a unit takies according to geometric knowledge _e, the volume calculation formula is different because of the unit;

(3), in the usual way calculate the actual volume v of model attitude, obtain the element number N that model meshes is divided _e=v/v _e

7, according to optimization model attitude coding, traversal feature chained list, use characteristic inhibition technology obtains the corresponding geometric model of coding.

The principle of the model state creation method institute foundation that suppresses based on feature in the finite element of the present invention field comprises:

The polymorphic model theory of institute of the present invention foundation is that the model from the angle of systematology is calculated science is analyzed and researched, and as a system, the feature that is comprised in the model is as the key element of construction system with model.The changeability of key element itself is that each key element all has polymorphic characteristic, and the variation of the constituted mode between the key element simultaneously can cause system state to change, and when therefore model being considered as a system, itself presents polymorphic characteristic.By research to the characteristic element that polymorphic model comprised and the mode of composition thereof, for realistic model is set up corresponding system, with the element of feature as system, study the susceptibility of various features, set up the quantitatively evaluating standard of feature sensitivity, seek the attitude of model and the regularity that in its change procedure, is contained, set up polymorphic theoretical system and explain the various states that complex model produces owing to the variation of model accuracy, computing time, computational accuracy.The core concept of polymorphic theoretical system is the transition of attitude, and promptly the grand master pattern kenel arrives the dynamic process of object module attitude: as shown in Figure 1, the system model attitude is designated as M, can be described as M{f ₁, f ₂..., f _n, f wherein _i(i=1,2 ... n) for the feature that it comprised, be designated as for simplicity $M=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{f}_i$ 。If $M_0=\underset{i=1}{\overset{m_0}{\mathrm{\&Sigma;}}}{f}_{0i}$ Be the grand master pattern kenel, $M_j=\underset{i=1}{\overset{m_j}{\mathrm{\&Sigma;}}}{f}_{\mathrm{ji}},(j=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;n)$ Be the transition model attitude.Remember that each attitude calculation cost (for example computing time) is C _c(M _j), (j=0,1,2 ..., n).If model attitude M _iTo model attitude M _j(i, j=0,1 ... n, i ≠ j) have conversion pathway (path may be not unique) establishes the conversion pathway set and is P _Ij, model attitude M _iAlong path p (p ∈ P _Ij) be converted into model attitude M _jConversion cost (for example error of result of calculation) be designated as

, model attitude M then _iTo model attitude M _jMinimum transform cost and be designated as According to given conversion cost threshold value c _ε, can get and satisfy the model attitude set T that transforms the cost threshold value surely _Minct={ M _j| C _Tmin(M ₀→ M _j)＜c _ε, again according to T _MinctGet the model attitude M that satisfies the minimum of computation cost surely _f, i.e. M _fSatisfy condition $C_c\left(M_f\right)=\underset{M_j\&Element;T_{\min \mathrm{ct}}}{\min }\left\{C_c\left(M_j\right)\right\}.$

The attitude that uses a model in the inventive method replaces master pattern to calculate and produces the principle of the error level estimation foundation of error:

When limited cell type and interpolation method were determined, feature only need be considered three factors to the sensitivity value of simplifying in the computation model: Δ T, Δ H and Δ U

Wherein, Δ T is the key element that reflection is estimated in zone that feature reduction exerts an influence to mesh generation.

Δ H is the key element of grid diameter change amount reflection behind the feature reduction.

The key element of the semi-norm reflection of field function in the Δ U zone that to be feature reduction exert an influence to mesh generation.

Need calculate three key element Δ T, Δ H and Δ U when each feature is to the sensitivity value simplified in computation model; But the exact value of key element Δ T and Δ H need just may be known behind mesh generation, the exact value of key element Δ U need just may be known after FEM (finite element) calculation, if it is difficult will obtaining their exact value before FEM (finite element) calculation, and the accurate Calculation required time to them may be greater than the computing time of saving after the model simplification, consider to carry out accurate Calculation from cost, therefore need to seek a kind of method they are carried out valuation.Tangible fact is that the key element Δ T that reflection is estimated in zone that feature reduction exerts an influence to mesh generation is directly proportional with aspect of model volume, so available feature volume V replaces key element Δ T.Replace key element Δ T with feature volume V in the methods of the invention, replace key element Δ U, so error estimation formula computing method are: E with feature locations parameter P _i=V _iP _iH _i, E wherein _i, V _i, P _i, H _iThe simplification error, feature volume, location parameter and the grid diameter change amount that in i, produce under the simplified way of representation feature respectively.

The principle of grid diameter change amount computing method institute foundation in the inventive method:

Known situation is; the model that CAD system is set up can comprise some complex characteristic usually; as tiny characteristics and higher curvature feature etc., and finite element analysis can strengthen mesh generation density when carrying out mesh generation at these complex characteristic places, thereby the grid diameter at these complex characteristic places is smaller.Deletion or be in order to reduce the mesh-density at these feature places, also promptly to strengthen the grid diameter at these feature places with the purpose that simple feature is replaced complex characteristic.In error estimation formula computing method principle, be effect characteristics to one of factor of simplifying responsive value with the change amount of pointing out grid diameter before and after the feature reduction, the inventive method uses replacement and deletion dual mode that feature is simplified, and different simplified ways to grid diameter change amount computing method is respectively:

1, do not contain the computing method that higher curvature is formed the feature deletion back grid diameter change amount of face

Do not form face if do not contain the higher curvature feature in the feature, then finite element analysis is when carrying out mesh generation, grid diameter on the feature will depend on the maximum mesh diameter that the user can tolerate and meet the minimum value of this feature geometries attribute grid diameter, and the grid diameter that meets this feature geometries attribute minimum length of side in the feature composition face for this reason.After the feature deletion, this feature does not exist in the model, should carry out subdivision by the specified maximum mesh diameter of user when then mesh generation is carried out in finite element analysis, i.e. the h of user's input _Max, the feature deletion back grid diameter change amount that does not therefore contain higher curvature composition face should be h _Max-min (h _Max, h), the h minimum length of side in the feature composition face of feature for this reason wherein.

2, contain the computing method that higher curvature is formed the feature deletion back grid diameter change amount of face

Form face if contain the higher curvature feature in the feature, then should at first estimate to form the grid diameter at face place in the higher curvature feature.At first set forth grid diameter how to estimate higher curvature feature place.

In the finite element grid generative process, the density control of grid comprises two kinds: a kind of is the priori control of carrying out grid density according to the geometric properties and the physical characteristics of analytic target, another kind is the result of calculation according to current grid, strengthens mesh generation density and changes the posteriority control that mild place reduces mesh generation density at computational data in the zone that computational data changes greatly.This method at before finite element analysis to the pre-service of model, the therefore priori of considering gridding density control.Geometric properties according to analytic target carries out grid control, mainly is meant according to the size of grid to the fitting degree decision grid diameter of model surface.Grid to the fitting degree available grids summit of model surface on curved surface outside the corresponding point angle of method vector be similar to.As shown in Figure 2, a certain surface of model uses a triangular element to come match, and the angle of the outer method vector finger tip of vertex of a triangle correspondence has determined the fitting degree of unit to model surface.For given allowable error η, then require each external method vector all to satisfy (1-N to the model surface fitting degree _iN _j)≤η, i ≠ j and i, j ∈ (1,2,3).

When a certain regional area Δ of model surface S being carried out subdivision with the mesh generation algorithm, consideration be its method of average curvature, be made as ρ, the curvature radius of a ball is r, can be at the grid diameter of considering on the sphere that with r is radius on the Δ S.If △ ABC is a triangle gridding, because of normal curvature is identical on the sphere everywhere,, be without loss of generality so △ ABC is an equilateral triangle, the length of side of △ ABC is discussed with limit AB.

As shown in Figure 3, be located among the coordinate system XOY, A, the B coordinate is respectively (x ₁, y ₁, z ₁), (x ₂, y ₂, z ₂), when model surface fitting degree allowable error ε one timing, following equation is arranged:

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

$x_1^2+{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="S2008100205612E00011.png,S2008100205612E00041.png"\; state="\{\{state\}\}">y</figure-callout>}}_1^2+{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="S2008100205612E00011.png,S2008100205612E00041.png"\; state="\{\{state\}\}">z</figure-callout>}}_1^2={\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="S2008100205612E00011.png"\; state="\{\{state\}\}">r</figure-callout>}}^2$

$x_2^2+{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="S2008100205612E00011.png"\; state="\{\{state\}\}">y</figure-callout>}}_2^2+{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="S2008100205612E00011.png"\; state="\{\{state\}\}">z</figure-callout>}}_2^2={\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="S2008100205612E00011.png"\; state="\{\{state\}\}">r</figure-callout>}}^2$

$\frac{x_1{x}_2+y_1{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="S2008100205612E00011.png"\; state="\{\{state\}\}">y</figure-callout>}}_2+z_1{z}_2}{\sqrt{x_1^2+{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="S2008100205612E00011.png,S2008100205612E00041.png"\; state="\{\{state\}\}">y</figure-callout>}}_1^2+{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="S2008100205612E00011.png,S2008100205612E00041.png"\; state="\{\{state\}\}">z</figure-callout>}}_1^2}\sqrt{x_2^2+{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="S2008100205612E00011.png"\; state="\{\{state\}\}">y</figure-callout>}}_2^2+{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="S2008100205612E00011.png"\; state="\{\{state\}\}">z</figure-callout>}}_2^2}}\&GreaterEqual;1-\mathrm{\&eta;}$

ρ＝1/r

Thereby have

$\mathrm{\&rho;h}\&le;\sqrt{2\mathrm{\&eta;}}---\left(2.1\right)$

In a single day during finite element analysis subdivision grid, when detecting $\mathrm{\&rho;h}\&le;\sqrt{2\mathrm{\&eta;}}$ Promptly stop tessellated mesh, therefore can think $\mathrm{\&rho;h}=\sqrt{2\mathrm{\&eta;}}$ 。If remaining to be simplified the feature of feature in the model, to form the maximum curvature of face be ρ _Max, minimum grid diameter h then should be arranged on this feature _Min, therefore $\sqrt{2\mathrm{\&eta;}}={\mathrm{\&rho;}}_{\max }{h}_{\min }$ , the mean curvature of forming face when the feature of waiting to simplify feature is ρ _AvgThe time, this grid diameter of waiting to simplify on the feature should be estimated as $\frac{\sqrt{2\mathrm{\&eta;}}}{{\mathrm{\&rho;}}_{\mathrm{avgi}}}=\frac{{\mathrm{\&rho;}}_{\max }\&CenterDot;h_{\min }}{{\mathrm{\&rho;}}_{\mathrm{avgi}}}.$

Equally, after this category feature deletion, this feature does not exist in the model, should carry out subdivision by the specified maximum mesh diameter of user when then finite element software carries out mesh generation, i.e. the h of user's input _Max, the feature deletion back grid diameter change amount that does not therefore contain higher curvature composition face should be $h_{\max }-\min (h_{\max },\frac{{\mathrm{\&rho;}}_{\max }\&CenterDot;h_{\min }}{{\mathrm{\&rho;}}_{\mathrm{avgi}}}).$

3, contain higher curvature and form the computing method that the feature of face is replaced back grid diameter change amount

For this type feature to be simplified, the grid diameter method of estimation on the feature is identical with method of estimation in the last type, and the feature of this type that different is will have multiple reduction procedure.For mean curvature is ρ _AvgCurved surface, its surperficial grid diameter is $\frac{{\mathrm{\&rho;}}_{\max }\&CenterDot;h_{\min }}{{\mathrm{\&rho;}}_{\mathrm{avgi}}}$ , replace back grid diameter with positive k distortion and should be $\frac{2}{{\mathrm{\&rho;}}_{\mathrm{avgi}}}\sin \frac{\mathrm{\&pi;}}{j}$ , so grid diameter change amount 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 computing method foundation of feature in the inventive method:

Described in the principle of error estimation formula computing method institute foundation, the zone that function on the scene is violent, one of three key elements of simplification error Δ U also can be bigger, as if being simplified, features in these zones can cause bigger error, therefore the feature that can be simplified in the model must be confined to field function and changes mild zone, also is that to change severe degree be to the key factor of result of finite element influence degree behind the feature reduction for the field function of feature affiliated area in model.Before the FEM (finite element) calculation of reality, can obtain the severe degree that feature affiliated area field function changes in the model by following two kinds of methods.

1, according to experience

By the severe degree that the given aspect of model affiliated area of user field function changes, this is a very important reference value.In finite element analysis, the physical attribute of feature, be the attribute that plus load and boundary condition are given feature---the severe degree that feature regional field function of living in changes, with feature geometry identical significant effects is arranged, and these physical attributes can't obtain exact value before FEM (finite element) calculation, can provide the ordering of feature physical property values according to analysis experience in the past, influence has important reference role to result of finite element to simplify the back for analytical characteristic.

2, the effect of distance

According to St. Venant principle, in balanced system of force, the far field function is mild more more from load, thus the inventive method with feature to the distance of load as one of factor of the severe degree of reflection field function variation, with the weight product of distance and expert's appointment estimated value as Δ U.

According to conventional theoretical, feature is inversely proportional to, is directly proportional with the weights of user's appointment with distance the sensitivity value of simplifying, so take the weights of family appointment and feature to the ratio of the distance of load location parameter, reflect the severe degree that feature affiliated area field function u changes with this as feature.

Choose model and divide element number behind the grid as the principle of element of time institute foundation

In the finite element field, the solution procedure of each problem all is identical, and step is as follows:

A, subdivision is carried out in the zone of finding the solution of problem, the result of subdivision is the unit, finds the solution the set that discrete region is the unit.

B, structure tentative function space.

C, computing unit stiffness matrix and unit load vector.

D, calculated population stiffness matrix and gross load vector.

E, processing constraint condition are also found the solution.

With the one-dimensional finite element problem is example, will find the solution in the zone [a, b], and be [a, b] subdivision n part at first, establish node x ₀, x ₁..., x _nSatisfy a=x ₀＜x ₁＜...＜x _n=b, the sub-range e that obtains like this _i=[x _I-1, x _i] (i=1,2 ..., n), i.e. unit.Unit e _iLength h _i=x _i-x _I-1Consider the basis function v that structure is fairly simple _h, it satisfies: goes up continuously at [a, b], and at each e _iOn be linear function, all functions that satisfy these conditions constitute the tentative function space.Computing unit stiffness matrix again $K_{e_i}={\&Integral;}_{x_{i-1}}^{x_i}(p{B}^{T}B+q{N}^{T}N)\mathrm{dx}=\left[\begin{array}{cc}{k}_{i-1,i-1}^{e_i}& k_{i-1,i}^{e_i}\\ k_{i,i-1}^{e_i}& k_{i,i}^{e_i}\end{array}\right]$ With the unit load vector $F_{e_i}={\&Integral;}_{x_{i-1}}^{x_i}{N}^T\mathrm{fdx}=\left[\begin{array}{c}{f}_{i-1}^{e_i}\\ F_i^{e_i}\end{array}\right].$ With element stiffness matrix k _EiExpand to (n+1) rank matrix $\stackrel{\&OverBar;}{K_{e_i}}={\left[\begin{array}{cccccccc}& & & \&CenterDot;& \&CenterDot;& & & \\ & & & \&CenterDot;& \&CenterDot;& & & \\ & & & \&CenterDot;& \&CenterDot;& & & \\ \&CenterDot;& \&CenterDot;& \&CenterDot;& k_{i-1,i-1}^{e_i}& k_{i-1,i}^{e_i}& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& k_{i,i-1}^{e_i}& k_{i,i}^{e_i}& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ & & & \&CenterDot;& \&CenterDot;& & & \\ & & & \&CenterDot;& \&CenterDot;& & & \\ & & & \&CenterDot;& \&CenterDot;& & & \end{array}\right]}_{(n+1)\&times;(n+1)}$ Promptly k _EiFour element correspondences be placed on (n+1) rank matrix

(i-1) row and the capable 2 rank diagonal blocks of i in, and other elements are 0.In like manner, can be with unit load vector F _EiBe expanded into the vector on (n+1) rank ${\stackrel{\&OverBar;}{F_{e_i}}=\left[\begin{array}{c}\&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ F_{i-1}^{e_i}\\ F_i^{e_i}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\end{array}\right]}_{(n+1)}$ , global stiffness matrix so $K=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{K_{e_i}}$ , the gross load vector $F=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{F_{e_i}}$ , separate Algebraic Equation set v under the prerequisite of consideration constraint condition ^T(Ku-F)=0, can obtain Finite-Element Solution.If think that this approximate solution is accurate inadequately, can be so that subdivision be thinner, promptly node get more.From whole solution procedure as can be seen, finite element solving is separated an Algebraic Equation set exactly, obviously, in this Algebraic Equation set equation how much determined find the solution the needed time, and the quantity of equation is exactly the exponent number of global stiffness matrix K, i.e. the number of nodes that obtains of Problem Areas subdivision.Though number of nodes and needed time of calculating are not necessarily linear, it is can reflect the parameter of required computing time.And element number and number of nodes behind the model division grid are linear, so thereby estimating element number by algorithm reflects the model attitude calculation consumption time.

Use the principle of genetic algorithm preference pattern attitude foundation in the inventive method:

In the inventive method, as the key element of distinguishing the model attitude, the expression mode of model attitude is M{f with feature ₁, f ₂..., f _n.By the principle of permutation and combination as can be known, the model that contains n feature has 2 ⁿIndividual possible model attitude.If the feature quantity that contains in the model is too many, selection course will expend the plenty of time.

On the process nature of selection generation model attitude is to be guide with the cost function, in the best or almost best problem of separating of possible solution space search.Therefore, the key problem of polymorphic model theory is exactly how to find the problem of optimum solution in so big solution space fast.Searching algorithm commonly used has greedy algorithm, simulated annealing and genetic algorithm etc.Though there is the problem that easily is absorbed in suboptimization in preceding two kinds of algorithm fast convergence rates; And genetic algorithm has the big advantage in search volume, but speed of convergence is slower.

Genetic algorithm is a kind of biological heredity and evolutionary process and a kind of adaptive global optimization probabilistic search algorithm of forming in physical environment of simulating, and it has simple general-purpose, strong robustness, is suitable for the characteristics of parallel processing.It is modeled to individual living environment with the feasible solution in the practical problems, and objective function is modeled to individual viability, is chromosome with the coding simulation of feasible solution.Like this, from any initial population, through selection, intersect, three kinds of computings of variation produce population of new generation, through after the iteration repeatedly, make it converge on globally optimal solution or suboptimum is separated.

The flow process of genetic algorithm is: target setting and fitness function, through after the iteration of certain number of times, find the individuality of fitness maximum.Wherein, the model attitude generating mode of characteristics that the binary coding mode of chromosome structure is had in the algorithm and feature inhibition has good consistance and harmony.Coded system as shown in Figure 4, the length of coding is exactly the quantity of feature, the existence of the corresponding feature of each coding, 0 certain feature of expression is not present in this model attitude, the opposite meaning of 1 expression.By this code construction fitness function being come the quality of evaluation model attitude.The present invention is directed to the independent characteristic in the master pattern, in conjunction with the characteristics of finite element analysis, is point of penetration with hot analysis field, proposes a model attitude of considering computing time and computational accuracy simultaneously and selects the generation standard.Adopt genetic algorithm as searching algorithm, by search for the best or almost the best model attitude set up suitable computation model.As shown in Figure 5, generate the initial population of some at random, select, intersection and mutation operation carry out iteration, obtains the coding of optimization model attitude at last according to individual lengths.

The essential elements of evaluation of model attitude is the element number N after model meshes is divided _eWith error level E _iN _EBig more, calculate consuming time many more; E _iBig more, precision is low more.So N of model attitude correspondence _EAnd E _iMore little, its quality is high more.In most cases, the relation of mutual restriction is arranged between these 2 key elements, promptly concerning same model, N _EGet over the bright E of novel _iMay be higher, so this is a binocular mark optimization problem.

Traditional Multipurpose Optimal Method is the single goal function that each sub-goal is aggregated into a band positive coefficient, and (Decision Maker, DM) perhaps adjusted by the optimization method self-adaptation by decision by the decision maker for coefficient.Wherein, weighted method is a kind of common classical approach, is to convert the MOP problem to the SOP problem by the linear combination to objective function.

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

ω _iBe called weight, usually weight makes ∑ ω after can regularization _i=1, the optimization problem of finding the solution above-mentioned different weights then can be exported one group and separate.

Based on the weighting solution of classic multi-objective problem, based on N _EAnd E _MThe structure fitness function $F=\left\{\begin{array}{cc}\mathrm{\&alpha;}\&times;N_e+(1-\mathrm{\&alpha;})\&times;\widehat{E_M}& E_M\&le;E_{\max }\\ 0& E_M>E_{\max }\end{array}\right.$ 。In definition, the value of α has material impact to the model attitude quality of choosing, and adopts the optimal value of trying to achieve α based on the mode of experiment statistics.The method of exhaustion can all be enumerated all possible model attitude out, therefrom chooses optimum solution, i.e. global optimum's model attitude, and the therefore model attitude quality of selecting by more different α values is selected the optimum value of α according to statistical law.

The principle of feature identification of the present invention and inhibition algorithm foundation:

In the inventive method, adopt the method for attribute adjacent map to carry out feature identification.Feature is made up of face, and promptly feature is specific face collection.

As shown in Figure 6, in a square phantom type, contain groove, hole and Interim respectively.Wherein cavity feature is made up of three planes, and hole characteristic is made up of a face of cylinder and Interim is made up of 1/4 face of cylinder.In face-edge graph in computer graphics, as node, if adjacency between face and the face, then representing has line segment to link to each other between the node of face with face.In containing the square phantom type of groove, hole and Interim respectively, there are three nodes, a node and a node to represent individual features respectively.Square phantom type in Fig. 7 contains 1 grooved features, 1 round blind hole feature and 1 round tube hole feature, supposes all faces in the model are numbered, and the face of cavity feature correspondence is numbered 2,3, and 4; The face numbering of circle blind hole feature correspondence is 11,12; The face of round tube hole feature correspondence numbering is 13, so in its corresponding face-edge graph, is numbered three nodes of 2,3,4 and comprises that all coupled limits have constituted the subgraph of this feature correspondence; In like manner, be numbered 11,12 node has constituted round blind hole feature together with all coupled limits subgraph; Be numbered 13 node and constituted the subgraph of round tube hole feature, as shown in Figure 8 together with all coupled limits.The subgraph of different feature correspondences has different characteristics, in Fig. 9, according to the different characteristics of groove, hole, Interim subgraph, the feature in the model can be divided into hole, groove, Interim is discerned and deposit chained list in, so that feature suppresses.

In document 6, the technology of feature identification and inhibition is described in detail.Step is as follows:

1, judges the concavity and convexity on every limit, the AAG figure of generation model.

2, traversal AAG finds out all convex surfaces, constitutes face collection fvex, fvex is analyzed find out the single type feature, concrete classification:

(1) round tube hole feature: convex surface, type is a cylinder, and has only two limits.

(2) Fillet Feature: convex surface, type comprise anchor ring, cylinder, sphere, spline surface.

3, delete fvex from AAG figure, obtain subgraph, wherein all nodes constitute face collection fcav.Find out all connected components of this subgraph, each connected component is a feature subgraph.Each feature subgraph is discerned according to the characteristic of division of above-mentioned feature subgraph, judged concrete characteristic type.

4, justify the blind hole feature: two faces have one to be leaf node.Article two, adjacent limit, acquiescence leaf node correspondence is the plane, another face is the face of cylinder.

5, square blind hole feature: have a face, all adjacent sides all are concave edge.Contain a loop among the figure, the node corresponding surface in the loop all belongs to this feature.

6, square tube hole characteristic: contain a loop among the figure, the node corresponding surface in the loop all belongs to this feature.Each face all has four adjacent edges, and to satisfy two be chimb, and two is concave edge.

7, groove: three faces, two concave edges.

8, according to the characteristic type that identifies, generate the characteristic of correspondence object, the record characteristic of correspondence is formed face.

9, generation model characteristic of correspondence tree is used for subsequent treatment.

Embodiment:

1, provide by the user and to treat simplified model, model to be simplified has the load-up condition when carrying out finite element analysis, and mesh generation condition, as shown in figure 10, treat that it is (0 that simplified model has a centre coordinate, 0,0), the length of side is the square pedestal 1 of 10 units, deducting the center of circle, a bottom surface is (2,-2,0), radius is 0.8 unit, height is the interior cylinder A2 of 10 units, and deducting the center of circle, a bottom surface again is (1,-1,3.5), radius is 0.8 unit, height is the interior cylinder B3 of 3 units, and deducting the center of circle, a bottom surface again is (3.5,1,0), radius is 0.5 unit, height is the interior cylinder C4 of 10 units, deduct a centre coordinate again and be (2,0,0), the length of side is 0.8 unit, height is interior six prismatic A5 of 10 units, deducting a centre coordinate again is (2.5,2 ,-2.5), the length of side is 0.5 unit, height is interior eight prismatic A6 of 5 units, and deducting a centre coordinate again is (1,2,0), the length of side is 0.8 unit, height is interior eight prismatic B7 of 10 units, and deducting a centre coordinate again is (1,2,3.5), height is interior six prismatic B8 of 3 units, deduct again angular vertex is (2,4 ,-5) and (3,5,5) groove A9, deducting angular vertex again is (1,4,-5) and (0.5,5,5) groove B10, deducting angular vertex again is (3,3,-5) and the groove C 11 of (2,5,5), deducting angular vertex again is (2,-4 ,-5) and (3 ,-5,5) groove D12, deduct again angular vertex is (1 ,-4 ,-5) and (0.5,-5,5) groove E13, deducting angular vertex again is (3 ,-3,-5) and (2,-5,5) groove F14 carries out the corners operation that radius is 0.8 unit to the four edges of cubical right flank, obtain fillet A15, fillet B16, fillet C17, fillet D 18, plane of load is cubical left surface, and the mesh generation condition is maximum mesh diameter h _Max=2 and minimum grid diameter h _Min=1;

2, set up the feature chained list

The load condition of model, finite element cell attribute and mesh generation condition are as shown in table 1.The user uses business modeling software to set up the 3D geometric model of form as .SAT, model file is imported and carries out feature identification, deposits the tagsort that identifies in the feature chained list; Travel through the feature chained list once more, at each feature, according to D _iCalculate the location parameter P of this feature _iObtain location parameter P in the following way _i:

A, given each wait to simplify that the weight to the result of finite element influence is q behind the feature reduction ₁=q ₂=...=q ₈=0.5;

B: make i=1;

C: establish i and wait to simplify the feature bounding box centre of form, centre of form coordinate is (x _i, y _i, z _i), calculate i wait to simplify the feature centre of form to plane of load apart from d _i, d _i=x _i

D: calculate i location parameter P that waits to simplify feature _i=q _i/ d _i

E: make i=i+1, repeating step c～d remains to be simplified the location parameter P of feature in model _iCalculating finishes;

Obtain the selected maximum Gaussian curvature θ that all features of feature are formed face that waits to simplify _Max=0.25;

2, according to each selected volume V that waits to simplify feature _i, location parameter P _i, each selectedly waits to simplify the grid diameter change amount of feature under its corresponding reduction procedure by computing formula E _i=V _iP _iH _iObtain the sensitivity value E of this feature under its corresponding reduction procedure _i, as shown in table 1;

Grid diameter change amount obtains as follows in the present embodiment:

A, calculating ε=θ _Maxh _Min=0.25, make i=1;

B, make i=1, calculate ε=θ _Maxh _MinIf feature composition face is the plane, then obtain the minimum length of side h that this waits to simplify feature _i, computing grid diameter change amount H _Temp=h _Max-min (h _Max, h _i), if H _Temp＞0, corresponding grid diameter change amount H _i=H _Temp, otherwise change next step;

C, if having curved surface in the feature composition face, then obtain the current mean-Gaussian curvature θ that waits to simplify all curved surfaces that feature i comprises _Avgi, computing grid diameter change amount $H_{\mathrm{temp}}=h_{\max }-\min (h_{\max },\frac{\mathrm{\&epsiv;}}{{\mathrm{\&theta;}}_{\mathrm{avgi}}})$ , if H _Temp＞0, Dui Ying grid diameter change amount H then _i=H _Temp, otherwise change next step;

D, make i=i+1, repeating step b, c remain to be simplified feature and the corresponding grid diameter of its simplified way change amount H in model _i, i=1,2 ..., n, calculating finishes, and obtains table 1;

Responsive value is long-pending for the grid diameter change amount under the volume of character pair, location parameter and the corresponding simplified way in the present embodiment, counts: E _i=V _iP _iH _i, i=1,2 ..., n obtains table 1;

The tabulation of table 1 characteristic attribute

Numbering	The feature kind	V i	D i	α	P i	H i	E i
								1	Round tube hole	7.85	8.50	0.01	0.085	0.88	0.58
2	Round tube hole	20.11	7.00	0.01	0.07	0.92	1.30
								3	The circle blind hole	6.03	4.00	1.00	4.00	0.90	21.71
4	The square tube hole	16.63	7.00	0.85	5.95	0.35	34.63
								5	The square tube hole	18.10	6.00	0.50	3.00	0.15	8.15
6	Side's blind hole	4.99	4.00	0.90	3.60	0.60	10.24
								7	Side's 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, finite elements is chosen and is used for thermoanalytical Solid Tet 10node Unit 87 in the present embodiment, i.e. 10 node units, and mesh generation adopts the division density of acquiescence.Because the average length of side is 1.5 units, so the average external volume of unit is 3.375, and the volume of model attitude is v, then its corresponding element number N _E=v/3.375;

5, use binary coding representation model attitude, code length is a feature quantity, in hot analysis field, rule of thumb Fillet Feature is very big and can ignore the influence of result of calculation to the negative effect of grid dividing as can be known for the user, 4 Fillet Feature of this model are suppressed in advance, so feature coding is 13, corresponding to may exist 2 ¹³Individual model attitude, in the model order of feature with the table in the feature sequence number consistent.Wherein the introductory die kenel is encoded to 1111111111111.

6, user's error originated from input rank is 1, calculates tolerable quantization error E _Max=11.55.

7, generate the population that individual amount is N=100 at random; Crossover probability P _c=0.8, the variation probability P _m=0.02, get α=0.3, each individual fitness computing formula is so $F=\left\{\begin{array}{cc}0.3\&times;v/3.375+0.7\&times;\widehat{E_M}& E_M\&le;11.55\\ 0& E_M>11.55\end{array}\right.,,$

Wherein $\widehat{E_M}=E_M\&times;{\lg }^{(0.3\&times;v)/(3.375\&times;E_M)},.$

8, iterations is

, every iteration once uses the mesh generation algorithm to estimate the stiffness matrix exponent number of the corresponding model attitude of all individual codings in this generation, calculates fitness function again.The final mask attitude be encoded to 0011010011011, suppress through feature, geometric configuration as shown in figure 13, remaining square pedestal 1, circle blind hole feature 3, regular hexahedron through hole 5, regular hexahedron blind hole 8, groove 10,11,14.

Claims (5)

1, the model state creation method that suppresses based on feature in the finite element modeling is characterized in that carrying out as follows:

A, provided by the user and to treat simplified model, the described simplified model for the treatment of has the load-up condition when carrying out finite element analysis, and the mesh generation condition, and described mesh generation condition is maximum mesh diameter h _MaxWith minimum grid diameter h _Min

B, the described feature for the treatment of in the simplified model simplified of identification, and deposit the feature chained list in;

C, in described feature chained list, select feature to be simplified, determine to wait to simplify feature quantity n; In any order selected n feature to be simplified is numbered, calculate obtain selected each wait to simplify the volume V of feature _iWith location parameter P _i

D, according to each selected volume V that waits to simplify feature _i, location parameter P _i, and each selectedly waits to simplify the grid diameter change amount of feature after it is suppressed, and obtains the corresponding sensitivity value E of feature after it is suppressed that wait to simplify _i=V _iP _iH _iBe suppressed the error level of the sensitivity value sum characterization model attitude of feature with all;

E, by model attitude grid cell is carried out the estimation of quantity, estimate the element number N after the model attitude is carried out grid dividing _e, described element number N _eWith model attitude stiffness matrix exponent number linear dependence, with described element number N _eThe reflection model required FEM (finite element) calculation time of attitude;

F, according to the error level and the element number N of model _e, adopt genetic algorithm to carry out the selection of model attitude, obtain the simplified model coding;

G, application characteristic inhibition method generate the simplified model corresponding to described simplified model coding.

2, the model state creation method that suppresses based on feature in the finite element modeling according to claim 1 is characterized in that simplifying among the described step c feature locations parameter P _iObtain in the following way:

A, given each wait to simplify behind the feature reduction the weight of result of finite element influence, be made as q ₁, q ₂... q _n, q wherein _i∈ [0,1], (i=0,1 ... n), q _iI of=0 sign waited to simplify feature and whether existed not influence of result of finite element; q _i=1 characterizes i waits to simplify feature and whether exists and result of finite element is had the greatest impact q _iBig more the closer to 1 characteristic feature to the influence of result of finite element;

B, make i=1;

C, establish i wait to simplify feature to plane of load apart from d _i

D, i location parameter P that waits to simplify feature of calculating _i=q _i/ d _i

E, make i=i+1, repeating step c～d remains to be simplified the location parameter P of feature in model _iCalculating finishes.

3, the model state creation method that suppresses based on feature in the finite element modeling according to claim 1 is characterized in that grid diameter change amount obtains as follows in the described steps d:

A, if wait to simplify feature and form by the plane, obtain the minimum length of side h that this waits to simplify feature _i, computing grid diameter change amount H _Temp=h _Max-min (h _Max, h _i), if H _Temp＞0, then adopt this kind feature reduction scheme, corresponding grid diameter change amount $H_{i,c_i}=H_{\mathrm{temp}},$ Otherwise commentaries on classics next step;

B, if wait to simplify and have curved surface in the feature, obtain the current mean-Gaussian curvature θ that waits to simplify all higher curvature curved surfaces that feature i comprises _Avgi, computing grid diameter change amount $H_{\mathrm{temp}}=h_{\max }-\min (h_{\max },\frac{\mathrm{\&epsiv;}}{{\mathrm{\&theta;}}_{\mathrm{avgi}}})$ , if H _Temp＞0, then adopt this kind feature reduction scheme, corresponding grid diameter change amount $H_{i,c_i}=H_{\mathrm{temp}}.$

4, the model state creation method that suppresses based on feature in the finite element modeling according to claim 1, the estimation that it is characterized in that among the described step e model attitude grid cell is carried out quantity is to carry out as follows:

A, the maximum mesh diameter h that provides according to the user _Max, minimum grid diameter h _Min, get grid cell length of side h=(h _Max+ h _Min)/2;

B, in conjunction with the grid cell type and the grid cell length of side, calculate an actual volume v that grid cell is shared _e, the volume calculation formula is different because of the unit;

C, calculate the actual volume v of model attitude, obtain the element number N that model meshes is divided _e=v/v _e

5, the model state creation method that suppresses based on feature in the finite element modeling according to claim 1 is characterized in that adopting among the described step f genetic algorithm to carry out the model attitude and selects to carry out as follows:

A, use binary coding representation model attitude, code length is a feature quantity, each feature is corresponding to the bit in the individuality; On behalf of certain feature, 0 do not exist in the model attitude, and on behalf of certain feature, 1 be present in the model attitude;

B, user import tolerable error level rank m, and m ∈ [1, n] forms the limits of error $E_{\max }=\frac{1}{n-m+1}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{E}_i$ , wherein n is a feature quantity;

C, generate individual amount at random and be $N=\left\{\begin{array}{cc}{2}^{N_F}& N_F\&le;6\\ 100& N_F>6\end{array}\right.$ Population, N wherein _FBe feature quantity; Crossover probability P is set _c∈ [0.6,0.8], the variation probability P _m∈ [0.01,0.02], each individual fitness computing formula is $F=\left\{\begin{array}{cc}\mathrm{\&alpha;}\&times;N_e+(1-\mathrm{\&alpha;})\&times;\widehat{E_M}& E_M\&le;E_{\max }\\ 0& E_M>E_{\max }\end{array}\right.$ , wherein $\widehat{E_M}=E_M\&times;{\lg }^{N/E_M}$ , E _M=∑ E _i, i is to be 0 feature sequence number in the model attitude coding; α is a weight factor, and α is chosen for 0.3 here;

D, iterations are

, every iteration once estimates the grid cell quantity of the corresponding model attitude of all individual codings in this generation, calculates fitness function based on this; If the bigger individual or arrival maximum iteration time of fitness does not appear in the three generations continuously, then the individuality of fitness maximum is the simplified model coding that is obtained in the population in last generation.

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