Development of a refinement algorithm for tetrahedral finite elements

Abstract

Many of the engineering problems are analyzed using numerical methods such as the finite element (FEM) whose results provide a basis to make basic decisions regarding the design of many important works. It is commonly accepted that FEM computations are reliable; however, the results may be affected by the configuration of the finite element mesh to simulate the medium to be analyzed, this is particularly true when the internal and external boundaries are time dependent, as is the case of soil consolidation. Accordingly, a thorough investigation was carried out with the main purpose of eliminating this shortcoming. The main steps to carried out the development of the innovative geometric procedure to automatically refine finite element tetrahedra-type (3D) are described. This geometric algorithm is based on the theory of fractals and is a generalization of the algorithm for triangular element finite element meshes (2D) [1,2]. This paper presents the fundaments of this new algorithm and shows its great approximation using 3D close form solutions, and its versatility to adapt the original Finite Element Mesh when the load boundary conditions are modified (Neumann conditions).