MATLAB上的有限元网格自动生成-《计算机技术与发展》

文章信息/Info

Author(s):: LIU Yao; TAN Jian-guo; National University of Defense Technology,Changsha 410073,China

摘要:: DistMesh是基于MATLAB的有限元网格自动生成程序,具有程序代码简短明晰、网格质量高、移植性好等突出特点.但是因为DistMesh用以筛选和优化节点的距离函数是解析表达式,用户无法实现对复杂模型的构造,限制了DistMesh的工程应用和推广.由于非均匀有理B样条(NURBS)是计算机辅助技术(CAD)中三维建模的通用和标准技术,故基于MATLAB中的NURBS工具箱,提出一种利用NUBRS曲线和曲面的方向来判断节点与曲线、曲面位置关系的方法,以完成对节点的筛选和移动.基于力的平衡原理的迭代循环,通过对比理想的与实际的网格长度,以不断调整网格边长,完成对网格的优化.将通用的NUBRS建模与DistMesh相结合,突破了DistMesh原来建模复杂的限制,既能生成高质量的网格,又提高了DistMesh的适用性.

Abstract:: DistMesh is an automatic generation program of finite element mesh based on MATLAB,with prominent features such as short and clear code,high-quality mesh and great portability. However,because the DistMesh’s distance function for filtering and optimizing nodes is an analytic expression,users are unable to construct complex models,which limits the application and promotion of DistMesh in engineering. Non-uniform rational B-spline (NURBS) is a general and standard technique for 3D modeling in computer-aided design (CAD),so based on the NURBS toolbox in MATLAB,we propose a method which determines the position relationship between nodes, curve and surface according to the direction of NUBRS curves and surfaces,so as to complete the selection and movement of nodes. Based on the iterative cycle of force balance principle,by comparing the ideal mesh length with the actual mesh length,the mesh edge length is adjusted constantly to complete the mesh optimization. The combination of general NUBRS modeling and DistMesh breaks through the limitations of DistMesh’s original complex modeling,which can not only generate high-quality grids,but also improve the applicability of DistMesh.