Research On Key Technologies Of Automatic CAE Analysis Based On Dual Interpolation Boundary Face Method

The dual interpolation boundary face method(Di BFM)based on the boundary integral equation is a combination of the dual interpolation method and the boundary face method(BFM).The boundary face method uses the boundary representation(B-rep)data structure in CAD packages to analyze CAE directly in CAD geometry,thereby naturally integrating CAE and CAD.In addition,the boundary face method inherits the advantages of BEM:dimension reduction,trial function does not require C~0 continuity to allow mesh discontinuity and the BEM is suitable for solving infinite domain problems.The dual interpolation method unifies the continuous and discontinuous elements in the BEM.Not olny the accuracy of interpolation is improved,but also the discontinuous characteristic of the trial function of the boundary integral equation is maximized,which makes the mesh generation more flexible and free.The Di BFM does not require geometric repair operations for the‘dirty'geometry model,because it ensures the accuracy of the calculation and greatly reduces the requirements of mesh quality and continuity.Due to the discontinuous grids allow to the existence of hanging points,discontinuous grids are more freedom for discretizing“dirty”geometry without geometry repair than continuous grids.This paper focuses on the key technologies of CAE automatic analysis based on the dual interpolation boundary face method,including the improvement of boundary curve discrete algorithm in the process of continuous mesh generation,the realization of discontinuous mesh generation algorithm,the treatment of singular integral problem in the Di BFM and extending the dual interpolation boundary face method to three-dimensional case and so on.The specific research works of this paper are as follows:(1)In the boundary representation(B-Rep)data structure of the CAD solid modeling system,a face is defined as the area surrounded by the loop.The inner loop and the outer loop are the basis for determining the side of the area,and also provide the basis for the subsequent determination of the direction of the mesh on the face.Therefore,it is very important to determine the inner loop and outer loop.Based on the fact that a non-closed face is a closed area in the parameter plane and closed surface has periodicity,this paper proposes two methods for determining the inner and outer loops of the closed and non-closed faces respectively.In addition,combining with a bisection algorithm of boundary curves,an algorithm is proposed to judge the position of a target point relative to any loop in a plane.(2)Advance Front Method and Delaunay triangulation are two common and stable methods for continuous mesh generation.However,the initial step of these two methods is to discretize the boundary curve.Gauss integration is involved in the discretization of boundary curve by direct method,which requires a lot of calculation.This paper proposes an iterative method,which avoids the Gaussian integral through the approximate calculation of definite integrals,and greatly improves the efficiency compared to the direct method.(3)Automatic grid generation is still the major obstacle and technical bottleneck of CAE automation.Compared with continuous grid,discontinuous grid allows the existence of hanging points,so it is easier to discretize“dirty”geometry without geometry repair than continuous grids.In order to realize the automation of mesh generation for any complex models,this paper proposes a binary-tree mesh generation algorithm.It can adaptively generate the meshes based on the curvature of the curve and surface,making the mesh density control more flexible and free.This method can choose the subdivision direction to subdivide the elements,so that the anisotropic mesh generation is more simple and natural.Numerical examples show the practicability of this algorithm for closed and unclosed faces.(4)In order to evaluate the singular integrals involved in the Di BFM accurately and effectively,this paper proposes a binary-tree subdivision method based on the binary-tree meshing method.Compared with the conventional element subdivision method,even if the shape of the element is very irregular,the binary-tree subdivision method can evaluate singular integral accurately and efficiently for cases of arbitrary element shape and arbitrary location of the source point.Compared with the spherical subdivision method,this method is simple and stable.The binary-tree subdivision method can guarantee that the computational error comes from integration will be restricted to a very low level,and hence,significantly improve the stability for numerical simulation.(5)In this paper,the Di BFM is extended from two-dimensional case to three-dimensional case,and applied to solve three-dimensional elastic problems.For the three-dimensional elastic problem,the general formula of the Di BFM is derived in detail.In three-dimensional elastic problems,the small features of the geometric model will cause significant stress concentration.The numerical examples prove the accuracy and efficiency of the method in three dimensions case,as well as the ability to solve the problem of the practical engineering structure and structure with small features.In this paper,the related research on the key technology of automatic CAE analysis based on the Di BFM,which will actively promote the realization of CAE automatic analysis.The Di BFM does not require the continuity of the mesh,which frees the mesh generation from the restrained cage.The research on discontinuous mesh generation algorithm makes it possible to automatically mesh the geometric model without geometric repair.