Estratégia de enriquecimento para métodos baseados na partição da unidade

Abstract

The hp-Cloud is a meshless method that present as its main feature the ability to enrich the shape functions of the approximated problem. Working similarly to the Generalized Finite Element Method, the hp-Cloud operates through of enrichment of the Partition of Unity, obtained by the Least Square Method, which is the basis of the Element-Free Galerkin Method. Appeal of the meshless methods is the mesh independence behavior, making them more efficient and more accurate in some specialsituations. Based on this concept, this work tackle aspects of the implementation of the enrichment strategy , using Object Oriented Programming, and valid for any Partition of Unity Method. Using INSANE platform and the existing implementation of the Element-Free Galerkin, it presented the main concepts relating to the hp-Cloud Method, as well as changes and extensions of INSANE, focusing in linear structural analysis.The work presents the numerical results for two-dimension Elasticity problems, evaluating their convergence and comparing them with other methods such as the Generalized Finite Element Method and Element-Free Galerkin. The study also checks the behavior of the method related to parameters like inuence domain size, degree of the polynomials basis, renementh,p and the strategy of applying theboundary conditions