应力高梯度问题的无网格分析

Analysis of Problems with High Stress Gradient by Meshless Method

基于移动最小二乘法的无网格计算 ,采用线性基函数即可得到C1连续位移场 ,使得应力、应变场在整个求解域内保持连续 ;节点之间脱离了单元的约束 ,对求解域进行离散和加密节点时变得十分灵活 ,因此适合分析应力高梯度问题。本文简要介绍了无网格方法的基本原理 ,给出了确定节点影响域大小的方法 ,应用无网格方法对带有V型缺口的受拉方板及J2 3- 10曲柄压力机机身进行了受力分析 ,得到的应力集中部位的计算结果与实际值更为接近。

Because the approximation of displacement field is based on moving least squares (MLS) method, meshless computation has some advantages over traditional finite element method (FEM) in dealing with structural problem with high stress gradient. If only the weight function has C1 continuity, the displacement field possesses C1 continuity with linear basis, which makes meshles method free of post processing. No element connectivity makes h adaptive flexible. The basic principle of meshless method was illustrated in this paper and how to determine the modal compact support was discussed at the same time. Two numerical examples with high stress gradient, V shaped plate and body of J23-10 C frame press, were analyzed at the end of the paper. The numerical results have a high accuracy, which validates the efficiency of the method.