Modelagem numérica de problemas bidimensionais viscoelásticos utilizando métodos sem malha

Abstract

In engineering studies, most of the existing phenomena are modeled by differential and integral equations. The analysis of the behavior of these systems can be performed through analytical or numerical methods, the latter which presents an approximate approach to the results. Due to the complexity of the real-life structure models, the use of approximate solutions is increasing. Among these solutions, the meshless methods are the most recent and have as advantage over those without of mesh, making easy the refinement where existing more complexity of the behaviors variables. However, because they are relatively recent methods, the use of these solutions is still not enough to researche and to apply in real structures. Viscoelastic materials are defined as presenting a combination of elastic and viscous elements. A viscoelastic structure is represented by physical models that increase the number of elements as the complexity of the problem grows. Therefore, for more complex models, it is necessary to use numerical solutions. In this context, the purpose of this article is the application of the meshless methods of collocation, Modified Galerkin applied to strong formulation and Local Petrov-Galerkin to study two-dimensional viscoelastic structures, subjected to in-plane state, in order to perform an analysis of the effectiveness and convergence of each method evaluated, thus verifying its efficiency for these structures.