2-D有限元网格优化新方法

网格质量在很大程度上影响着有限元数值分析的准确性和分析过程的可持续性．基于新的网格单元畸变度量体系，文中设计了一种新的关于节点位移的无约束最优化的目标函数，该函数有效客观地反映了有限元计算网格的畸变程度，且通过求偏导数(等于0)，可以得到问题求解的显式表达式，因此，该算法具有设计合理、实现简便、保持拓扑性等特点．此外，还可用于二维几乎所有形状的网格，具有非常强的通用性。

The new algorithm of 2-D mesh optimization in FEM

The singularity of FE mesh influences greatly the accuracy of result in FEM simulation. A new objective function for FE mesh optimization is guided from distortional potential in the paper. The objective function is reasonable to measure the element's distortion and through setting its partial ssrivative vanishing, one can obtain the explicit formulation to solve the problem. So the algorithm has the advantage of time-consuming and effectiveness. Moreover, it can be used to optimize any kind of 2-D mesh, including the triangle, tetragon, etc.