基于边界面法的CAE与CAD一体化研究

发布时间：2019-06-19 13:06

【摘要】：CAD与CAE一体化已成为工程及科学计算领域中的一大研究热点。目前商业CAE分析软件普遍采用有限单元法,其分析模型是通过网格生成模块对CAD模型离散而获得的。CAD与CAE对应模型表达方式不同,前者是连续的参数模型,后者为近似的离散网格模型。因此,虽然很多CAD软件中添加了CAE分析功能,但还不能从根本上实现两者的无缝集成。基于边界积分方程的边界面法具有许多优点,例如一般只需要离散问题域的表面且可采用不连续单元。在边界面法中,对边界的数值积分和场变量的插值都是在几何模型边界曲面的二维参数空间里进行的。其几何数据直接由参数曲面计算得到,而不是通过分段多项式插值近似,从而能够避免几何误差,有利于实现CAD\CAE的一体化。本文基于边界面法,在CAD\CAE一体化的程序设计实现和理论方面做出一系列的探索。主要完成了以下研究工作:(1)为实现对复杂三维实体的表面网格自动生成,本文利用C++语言构建了一个实体表面网格自动生成框架。该框架分为公共几何接口模块、拓扑修复、网格尺寸场、曲线离散、网格数据管理和网格生成方法六个部分。本文设计了一个统一的网格数据管理器,以便于程序的调整、维护及扩充。在该框架中可方便地添加和实现各种二维网格生成方法,可将所得的网格单元转换为计算单元,且可导出到其他模块(比如体网格生成模块)。(2)为实现对复杂三维实体的表面三角形网格自动生成,本文提出了一种将推进波前法与Delaunay方法相结合的方式来生成网格。该方法利用推进波前法生成面内点,之后采用Delaunay内核插点算法将该点加入到网格中。本文添加了对前沿的识别,将前沿分为活动前沿及非活动前沿,只对满足要求的活动前沿插入新点。创建了基于曲面邻近特征的自适应尺寸场,并将其作为背景网格,使得所生成的网格能较好地反映曲面邻近特征。该方法能够生成较高质量的表面网格,且可以保证网格生成的收敛。同时,实现了栅格法,使得对于几类曲面特征的网格生成规模大大降低。(3)为实现对具有焊缝的钢架结构的曲面网格生成,鉴于边界面法的特点,本文首先直接基于连续曲面模型,完成了短边、窄面和不光滑边界等3类曲面缺陷几何特征的拓扑修复。拓扑修复中涉及的所有操作皆为虚操作,不改变原有模型的几何定义。并且提出了基于栅格法的混合网格生成方式,对不同的子区域采用不同的网格生成方法,最后将子区域上的网格合并得到最终的曲面网格。与传统的网格生成方式对比,大大降低了网格规模。(4)为求解边界积分方程中的弱奇异及近奇异积分,提出了一种通用的自适应单元细分方法。该算法通过一系列以源点为球心且半径不断减小的球与单元相交来细分单元,能够对靠近源点的积分片进行自动加密细分,并在生成积分片的过程中额外添加点的迁移算法来保证每个积分片具有较“好”的形状及大小。该算法适用于任意形状的单元,而且源点可以在任意位置。使用本文的方法所获得的计算精度有显著的提高。而且,在要求获得相同数量级计算精度的情况下,该算法需要少得多的高斯积分点,因而大大提高了计算效率。(5)在多域边界面法实现中,提出了一个域编号序列优化算法来减小总体组装矩阵的带宽。由于矩阵的稀疏结构与未知量在整体方程组系统中的顺序直接相关,因此采用了一种排序策略来获得最佳的块结构。该域序号优化算法的优点是使得矩阵中非零块尽可能地靠近主对角线。在该算法中,首先通过考虑域的自由度及连通性产生一个或者多个层次结构。其次,对于每个连续的层次结构,分别计算这些层次结构的带宽。最后,根据具有最小带宽的层次结构对域进行重新排序。数值算例表明采用该算法对整体矩阵进行LU分解的时间显著减少,同时内存开销也显著降低。
[Abstract]:The integration of CAD and CAE has become a hot topic in engineering and scientific computing. At present, the finite element method is widely used in commercial CAE analysis software, and the analysis model is obtained by the discrete of the grid generation module to the CAD model. The former is a continuous parameter model, and the latter is the approximate discrete grid model. Therefore, although the CAE analysis function is added to many CAD software, it is not possible to fundamentally realize the seamless integration of the two. The boundary surface method based on the boundary integral equation has many advantages, for example, it generally requires only the surface of the discrete problem domain and may employ discrete units. In the boundary surface method, the numerical integration of the boundary and the interpolation of the field variable are carried out in the two-dimensional parameter space of the boundary surface of the geometric model. The geometric data is directly calculated by the parametric surface, rather than the piecewise polynomial interpolation approximation, so that the geometric error can be avoided, and the integration of the CADCAE can be facilitated. In this paper, based on the boundary surface method, a series of exploration is made in the design and theory of the integration of CAD and CAE. The following research work is mainly done: (1) In order to realize the automatic generation of the surface mesh of the complex three-dimensional entity, this paper constructs a solid surface mesh automatic generation framework using the C ++ language. The framework is divided into six parts: common geometric interface module, topology repair, mesh size field, curve dispersion, grid data management and grid generation method. In this paper, a unified grid data manager is designed to facilitate the adjustment, maintenance and expansion of the program. In the framework, various two-dimensional grid generation methods can be conveniently added and implemented, and the obtained grid cells can be converted into a calculation unit and can be exported to other modules (such as a body grid generation module). (2) In order to realize the automatic generation of the surface triangle mesh of the complex three-dimensional entity, this paper presents a method of combining the advance wave front method and the Delaunay method to generate the grid. The method uses the advance wave front method to generate the inner point of the plane, and then the point is added into the grid by using the delaunay kernel interpolation point algorithm. In this paper, the recognition of the leading edge is added, the leading edge is divided into the front of the active and the non-active front, and the new point is only inserted into the leading edge of the activity. The adaptive dimension field based on the adjacent feature of the surface is created and used as the background mesh, so that the generated mesh can better reflect the adjacent features of the curved surface. The method can generate a high-quality surface mesh, and can ensure the convergence of grid generation. At the same time, the grid method is realized, so that the grid generation scale for several types of surface features is greatly reduced. (3) In order to realize the surface mesh generation of the steel frame structure with the welding seam, in view of the characteristics of the boundary surface method, the topological repair of three surface defect geometric features such as the short side, the narrow surface and the non-smooth boundary is completed directly based on the continuous surface model. All operations involved in the topology repair are virtual operations and do not change the geometry of the original model. And a hybrid mesh generation method based on the grid method is proposed, different grid generation methods are adopted for different sub-regions, and finally, the mesh in the sub-region is combined to obtain a final curved surface mesh. Compared with the traditional grid generation method, the grid scale is greatly reduced. (4) In order to solve the weak singular and near singular integral in the boundary integral equation, a general adaptive unit subdivision method is proposed. The method comprises the following steps of: dividing a unit by a series of balls with a source point as a ball center and a constant radius, and enabling the integration piece close to the source point to be automatically encrypted and subdivided, And the migration algorithm of the additional points is added in the process of generating the integral piece to ensure that each integral piece has a higher "-Okay." shape and size. The algorithm is suitable for any shape of cell and the source point can be in any position. The accuracy of the calculation obtained by using the method provided by the method is remarkably improved. Moreover, in the case where the calculation accuracy of the same order of magnitude is required, a much less Gaussian integration point is required for the algorithm, and thus the calculation efficiency is greatly improved. (5) In the multi-domain boundary surface method, a domain number sequence optimization algorithm is proposed to reduce the bandwidth of the overall assembly matrix. Since the sparse structure of the matrix is directly related to the order of unknowns in the system of the integral equations, a sort of sort strategy is used to obtain the best block structure. The advantage of the domain sequence number optimization algorithm is that the non-zero blocks in the matrix are as close as possible to the main diagonal. In this algorithm, one or more hierarchies are first generated by considering the degree of freedom and connectivity of the domain. Second, for each successive hierarchy, calculate the bandwidth for these hierarchies, respectively. Finally, the domain is re-ordered according to the hierarchy with the minimum bandwidth. The numerical example shows that the time of LU decomposition of the whole matrix is significantly reduced by using the algorithm, and the memory overhead is also significantly reduced.
【学位授予单位】：湖南大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP391.7

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