ENRICHED METHODS ALLIED TO MODIFIED LOCAL GREEN'S FUNCTION METHOD FOR ELASTO STATIC PROBLEMS

Marcelo Pinto da Silva¹; Roberto Dalledone Machado²; João Elias Abdalla Filho¹

¹ Pontifícia Universidade Católica do Paraná.; ² Universidade Federal do Paraná.

doi:10.20906/CPS/CILAMCE2017-0366

Resumo

The Modified Local Green's Function Method (MLGFM) has been extensively employed during last decades to solve a large number of solid mechanics problems. The MLGFM is an integral method that uses finite element approaches in the domain, to automatically generate fundamental solutions to be applied in a boundary system. It uses traditional Langrange shape functions to approximate the solution space. In this paper, the solution space is now enriched using, in this first attempt, a hierarchical approach with Lobatto shape functions. Once MLGFM uses domain and boundary meshes, the solution space can be enriched only in the domain, on the boundary or in both meshes at the same time. Some 2D elasto static problems are solved by this new approach showing excellent accuracy and convergence.

Palavras-chave: MLGFM.; Enriched Methods.; Hierarchical Finite Element.; Lobatto Shape Functions.