Modified Fixed Grid Finite Element Method to Solve 3D Elasticity Problems of Functionally Graded Materials

Abstract

In the present paper, applicability of the modified fixed grid finite element method in solution of three dimensional elasticity problems of functionally graded materials is investigated. In the non-boundary-fitted meshes, the elements are not conforming to the domain boundaries and the boundary nodes which are used in the traditional finite element method for the application of boundary conditions no longer exist. Therefore, special techniques are needed for computation of the stiffness matrix of boundary intersecting elements and application of boundary conditions.The stiffness matrix of boundary intersecting elements are calculated via integration of strain energy over the internal parts of these elements. Essential boundary conditions are applied using penalty function method. To examine the effectiveness of the proposed method, some numerical examples are solved and results are compared with those obtained using the standard finite element method.