轴对称结构动力弹塑性分析的无网格自然邻接点Petrov-Galerkin法

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振动与冲击 ›› 2021, Vol. 40 ›› Issue (10) : 204-208.

论文

陈莘莘1，肖树聪1，周书涛2

作者信息 +

Dynamic elastoplastic analysis of axisymmetric structures by the meshless natural neighbour Petrov-Galerkin method

CHEN Shenshen1,XIAO Shucong1 ,ZHOU Shutao2

Author information +

文章历史 +

摘要

将无网格自然邻接点Petrov-Galerkin法与预校正形式的Newmark法相结合，建立了一种轴对称结构动力弹塑性分析的新方法。由于几何形状和边界条件的轴对称特点，三维的轴对称问题可转化为二维问题。此外，计算时仅需要轴对称面上的一组离散节点，有效地避免了复杂的网格划分和网格畸变的影响。在轴对称面上的局部多边形子域上采用局部加权余量法推导了轴对称结构动力弹塑性分析的离散化控制方程，并采用预校正形式的Newmark法在时间域上进行求解。为了克服本质边界条件不能直接施加的缺点，试函数采用自然邻接点插值进行构造。数值算例结果表明，该研究所提出的轴对称结构动力弹塑性分析方法是行之有效的。

Abstract

A novel numerical method was developed to solve the dynamic elastoplastic problem of axisymmetric structures by means of the meshless natural neighbour Petrov-Galerkin method combined with the predictor-corrector form of the Newmark algorithm.The axial symmetry of geometry and boundary conditions helps to transform the three-dimensional (3D) axisymmetric problem into a two-dimensional (2D) problem, and it is only necessary to generate an array of scattered nodes on the cross section, therefore, complex meshing and disadvantage of mesh distortion are effectively avoided.The discretized governing equations for the axisymmetric dynamic elastoplastic analysis were derived by using the local weighted residual method over local polygonal sub-domain on the cross section and the predictor-corrector form of the Newmark algorithm was utilized to solve the discretized governing equations.In order to overcome the shortcoming that the essential boundary conditions cannot be directly imposed, the natural neighbour interpolation was utilized to construct trial functions.Numerical examples demonstrate that the proposed method for the dynamic elastoplastic analysis of axisymmetric structures is effective.

导出引用

陈莘莘1，肖树聪1，周书涛2. 轴对称结构动力弹塑性分析的无网格自然邻接点Petrov-Galerkin法[J]. 振动与冲击, 2021, 40(10): 204-208

CHEN Shenshen1,XIAO Shucong1,ZHOU Shutao2. Dynamic elastoplastic analysis of axisymmetric structures by the meshless natural neighbour Petrov-Galerkin method[J]. Journal of Vibration and Shock, 2021, 40(10): 204-208

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