TIDE NUMERICAL SIMULATION OF BI-MATERIAL PROBLEMS USING MFSMFREE METHODS

Abstract

Meshless techniques over advantages over the classical Finite element method in situations where the geometry is changing and hence, the need for remeshing arises. Examples of such problems include crack growth and large-deformation analysis In the present work, element free Galerkin method (EFGM) has been applied to solve solid mechanics problems containing material discontinuities. The method is based on treatment of interface conditions at the variational level. Modifications are made in the EFGM to incorporate material discontinuities, which include the variational form of the governing differential equations. Another technique for incorporating discontinuities in derivatives into meshless methods is also presented. The technique enriches the approximation by adding special shape functions that contain discontinuities in derivatives known as Jump Function. The special shape functions have compact support which results in banded matrix equations. Two bi-material cantilever beam problems have been solved using EFGM, with two different interface conditions. Graphs are plotted across the interface for two different kind of problems, the plots shows the comparisons of EFGM with Lagrange multiplier approach and the EFGM with Jump Function with the FEM solution. From the plots it will be clear that the discontinuities are captured clearly across the interface after adding the Jump Function to the Existing EFGM approximation rather with the EFGM with Lagrange multiplier approach.