The enriched modified local green's function method applied to elasto static problems

Abstract

The Modified Local Green's Function Method (MLGFM) has been applied to solve a large number of solid mechanics problems. It employs the finite element method (FEM) as an auxiliary tool to automatically develop the Green's functions projections (GFp) without knowing the fundamental solutions using conventional Lagrange shape functions to approximate the solution space. Also, improvements have been made in Finite Element Methods aiming to develop approximate solution capabilities of given problems by enriching their solution spaces. A good example of that is the hierarchical finite element approach. In this paper, the Modified Local Green's Function Method is enriched using a hierarchical approach based on Lobatto shape functions. Some standard set of elasto static problems are employed and compared with the MLFGM, classic FEM and analytical solutions.