基于对流粒子域插值物质点法的壳结构分析

Shell Structure Analysis Based on the ConvectedParticle Domain Interpolation

物质点法(material point method,MPM)采用Lagrange质点和Euler网格双重描述,适合处理大变形和接触问题.该文基于对流粒子域插值物质点法(CPDI2)框架分析了薄壳结构的大变形问题:使用四边形网格来离散壳体结构,通过物质点到壳单元节点再到背景网格节点的双重映射计算基函数,在背景网格上求解动量方程,基于BT壳单元理论更新物质点的内力.数值算例将受大变形的壳结构与参考解进行了比较,验证了该文方法的准确性.

The material point method(MPM)adopts the dual description of Lagrangian particles and Euler grids,so it can deal with large deformation and contact problems conveniently.The large deformation problem of thin shell structures was analyzed based on the framework of the convected particle domain interpolation ma-terial point method(CPDIMPM).The quadrilateral mesh was used to discretize the shell structure.The basis function was calculated by the double mapping from the material point to the shell element node and then to the background grid node.The momentum equation was solved on the background grid,and the internal force of the material point was updated based on the Belytschko-Tsay(BT)shell element theory.In the numerical ex-ample,the comparison of large deformations of the shell structure with reference solutions verifies the accuracy of the proposed method.