NUMERICAL MODELING OF VISCOELASTIC BIDIMENSIONAL PROBLEMS USING MESHLESS LOCAL PETROV-GALERKIN METHOD

Resumo

In engineering studies, most of the existing phenomena are modeled by differential and in-
tegral 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 com-
plexity 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, be-
cause they are relatively recent methods, the use of these solutions is not still enough to research 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 paper is the application of the Meshless Local
Petrov-Galerkin 01 (MLPG-01) and MLPG-02 or Local Collocation Method 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.