轴对称动力学问题的无网格自然邻接点Petrov-Galerkin法

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振动与冲击 ›› 2015, Vol. 34 ›› Issue (3) : 61-65.

论文

轴对称动力学问题的无网格自然邻接点Petrov-Galerkin法

陈莘莘李庆华刘永胜

作者信息 +

Meshless natural neighbour Petrov-Galerkin method for axisymmetric dynamic problems

CHEN Shen-shen, LI Qing-hua, LIU Yong-sheng

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文章历史 +

摘要

基于无网格自然邻接点Petrov-Galerkin法，提出了复杂轴对称动力学问题求解的一条新途径。几何形状和
边界条件的轴对称特点，将原来的空间问题转化为平面问题求解。计算时仅仅需要横截面上离散节点的信息，无论
积分还是插值都不需要网格。自然邻接点插值构造的试函数具有Kronecker delta函数性质，因此能够直接准确地
施加本质边界条件。有限元三节点三角形单元的形函数作为权函数，可以减少域积分中被积函数的阶次，提高了计
算效率。数值算例结果表明，本文提出的方法对求解轴对称动力学问题是行之有效的。

Abstract

A novel algorithm for solving complex axisymmetric dynamic problems is put forward on the basis of the meshless natural neighbour Petrov-Galerkin method. Axial symmetry of geometry and boundary conditions reduces the original three-dimensional (3D) problem into a two-dimensional (2D) problem. Only a set of scattered nodes over the cross section are needed and no meshes are required either for interpolation purposes or for integration purposes. The natural neighbour interpolation shape functions possess Kronecker delta property and therefore the essential boundary conditions can be directly imposed. The three-node triangular finite element method shape functions are taken as test functions, which reduces the orders of integrands involved in domain integrals and improves the computational efficiency. Numerical examples show that the proposed method for solving axisymmetric dynamic problems is effective.

导出引用

陈莘莘李庆华刘永胜. 轴对称动力学问题的无网格自然邻接点Petrov-Galerkin法[J]. 振动与冲击, 2015, 34(3): 61-65

CHEN Shen-shen;LI Qing-hua;LIU Yong-sheng. Meshless natural neighbour Petrov-Galerkin method for axisymmetric dynamic problems[J]. Journal of Vibration and Shock, 2015, 34(3): 61-65