中文摘要：

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编程模拟发生碰撞时材料的形变和应力变化.

英文摘要：

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.