无网格彼得洛夫伽辽金法在大变形问题中的应用

将无网格局部彼得洛夫伽辽金(MLPG)法推广应用于大变形问题。导出了非线性局部子域对称弱形式,通过对该弱形式进行线性化得到了用于非线性计算的MLPG格式,并对MLPG的计算速度进行了优化,使MLPG成为一种复杂度为O(N)的算法。几何非线性和几何与材料双重非线性的数值算例表明,相对有限元方法,MLPG在处理此类大变形问题时收敛性好,精度高,并能减小有限元分析中易遇到的网格畸变带来的困难。

APPLICATION OF MLPG METHOD IN LARGE DEFORMATION ANALYSIS

The meshless local Petrov-Galerkin method (MLPG) is extended for solving large deformation problems in this paper. A nonlinear local symmetric weak form is derived and linearized to obtain the nonlinear MLPG approach, and the optimization of the efficiency of MLPG is performed to make the MLPG method to be an algorithm of O(N). Some numerical examples on both geometrically nonlinear, and geometrically and material multiple nonlinear problems are given to verify that the MLPG handles such large deformation problems with good convergence and high accuracy as compared with the finite element method, and it can reduce the difficulty of mesh distortion, which usually encountered in the finite element analysis.