华东师范大学学报（自然科学版） >

2016 , Vol. 2016 >Issue 3: 9 - 20

DOI: https://doi.org/2016.03.002

数学

构造高阶插值函数求解表面冲击碰撞问题

  • 冯云青 ,
  • 侯磊
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  • 1. 上海大学~~数学系, 上海\; 200444;
    2. 上海高校计算科学E-研究院, 上海
冯云青, 女, 硕士研究生, 研究方向为有限元软件应用.

收稿日期: 2015-05-06

  网络出版日期: 2016-09-22

基金资助

国家自然科学基金项目(11271247)

收起

High order interpolation function for surface contact problem

  • FENG Yun-Qing ,
  • HOU Lei
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Received date: 2015-05-06

  Online published: 2016-09-22

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摘要

本文主要采用Lagrange双三次形函数来构造插值函数,从而利用有限元方法求解表面冲击碰撞问题中的耦合方程组.为了避免龙格现象, 采用Lobatto点构造插值节点.本文不仅采用高阶的形函数, 也使用两种不同的数值积分方法, 结合这两点,从而提高数值解的精度. 根据以上的理论分析结果,本中使用Matlab编程模拟发生碰撞材料的形变和应力变化。

关键词： 有限元; Lagrange; 正交积分

本文引用格式

冯云青 , 侯磊 . 构造高阶插值函数求解表面冲击碰撞问题[J]. 华东师范大学学报（自然科学版）, 2016 , 2016(3) : 9 -20 . DOI: 2016.03.002

Abstract

This paper mainly adopts Lagrange bicubic shape function to construct interpolation function and uses finite element method to solve the coupling equations of surface contact. The Lobatto points are used to construct the interpolation nodes to avoid the Runge phenomenon. Higher shape functions and  two different numerical integration methods are adopted to improve the accuracy of the numerical solution. According to the above analysis, this article uses Matlab program to simulate the deformation and stress changes in surface contact problem.

Key words： finite element; Lagrange; ; orthogonal integration

参考文献

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