High Performance FEM On Complex Contact Interface And Its Data Post Processing

In this article, non-linear coupled PDEs:Cauchy conservation equation and P-T/T equation, are used to describe the deformation and stress distribution of complex contact interface. The initial boundary conditions of PDEs are set in accordance with experimen-tal data. The semi-discrete FEM method is used to solve the coupled PDEs:the space domain is discretized by finite element method, while the time domain is discretized by finite difference scheme. Two finite element shape functions are used in the discretiza-tion of space domain:9-points biquadratic Lagrange shape function and4-points bicubic Hermite shape function. Three time difference schemes are used in the discretization of time domain:Euler scheme, semi-implicit Crank-Nicolson scheme and explicit two-steps Adams scheme. Two finite element schemes and three time difference schemes together form6fully discrete schemes. Using Matlab, the numerical results of6fully discrete schemes are calculated.The convergence of fully discrete scheme depends on both finite element shape function and finite difference scheme. An equivalent problem, of which the analytical expression of exact solution is known, is introduced to help study the convergence of fully discrete scheme applied on coupled PDEs. The error estimate between numerical solution and exact solution of the equivalent problem is obtained. Furthermore, using6fully discrete schemes, the numerical solution of the equivalent problem is calculated, therefore, the real error between numerical solution and exact solution is obtained.The program implementation is elaborately discussed, among which the calcu-lation of element stiff matrix is focused. Using specialized modules,6fully discrete schemes are integrated in main function. The whole program is encapsulated using Matlab graphic user interface (GUI). The data structure of3-dimention cells may reduce the traversal upon elements.