基于滑动Kriging插值的MLPG法求解结构非耦合热应力问题

A Meshless Local Petrov-Galerkin Method Based on the Moving Kriging Interpolation for Structural Uncoupled Thermal Stress Analysis

将基于滑动Kriging插值的无网格局部Petrov-Galerkin(MLPG)法用来求解二维结构非耦合热应力问题,首先进行瞬态热传导的求解,然后再通过顺序耦合法将不同时刻节点温度作为附加体力项施加到应力分析中.瞬态温度场和非耦合热应力分析通过加权余量法来离散,同时用Heaviside分段函数作为局部弱形式的权函数.由于滑动Kriging插值构造的形函数满足Kroneckerδ函数的性质,因此方便了本质边界条件的施加.刚度矩阵形成过程中只涉及到边界积分而没有涉及到区域积分,因此可以减少计算工作量,最后通过两个数值算例来验证本文方法的有效性.

A meshless local Petrov-Galerkin（ MLPG） method based on the moving Kriging interpolation was employed for the solution of 2D structural uncoupled thermal stress problems. The transient heat conduction problem was solved firstly and then the thermal solutions were imposed as body loads with the sequential coupled-field method in the stress analysis. The local weak forms were developed with the weighted residual method locally from the partial differential equations of transient heat conduction and structural dynamics,where the Heaviside step function was used as the weighted function in each subdomain.The essential boundary conditions can be implemented directly since the shape functions constructed from the moving Kriging interpolation possess the Kronecker δ property. This method does not involve the subdomain integral during generation of the global stiffness matrix except for the boundary integral,so the computational costs are reduced largely. The results of 2 numerical examples show the effectiveness of this method.