基于 Jacobian 矩阵的三维有限元网格质量优化

Jacobian Matrix Based 3D Finite Element Mesh Optimization

对Ｊａｃｏｂｉａｎ矩阵变换后得到一个新的目标函数，该目标函数有效地反映了有限元单元的拉压变形和剪切变形，且具有易于求导，便于采用优化算法求解等优点．该函数和单元的尺寸无关，并能适用于绝大多数类型的有限元网格（包括平面和三维网格）．利用该函数实现了对复杂形状的有限元网格的质量优化．

A new objective function for FE mesh optimization is guided from Jacobian matrix. The objective function is sensitive to combined stretching and shearing of the element. It is indepedent of the element size and is suited to work for many types of elements(including 2D and 3D meshes). The function can be easily solved by an optimization algorithm. A complicated FE mesh is optimized by using the function.