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