Static and dynamic analysis of 2D and 3D elastic solids using the modified FGFEM

In this paper, a modification on the fixed grid finite element method (FGFEM) is presented and used for the static and dynamic analysis of 2D and 3D elastic solids. In this study, fixed non-boundary-fitted meshes are used to solve elasticity problems. A new approach for computing stiffness matrix of boundary intersecting elements is presented. Natural boundary conditions applied via numerical integration of traction forces and essential boundary conditions applied using a technique based on penalty function on the non-conforming boundaries. The proposed method is applied to some 2D and 3D problems in linear elasticity and the results show good agreement with analytic solutions. This method is also used for the natural frequency analysis of elastic solids and the results show good agreement with those obtained using the finite element method.