NONLINEAR POSITIONAL FORMULATION APPLIED FOR DYNAMIC 2D SOLIDS ANALYSIS CONSIDERING DIFFERENT TEMPORAL INTEGRATION METHODS

Resumo

The analytical resolution for dynamic problems employs partial derivarives regarding time
and space. However, sereral methods of temporal integration replace the resolution of it. Thus, this paper
aims to analyze the dynamic response of two dimensional structural solids through different methods of
temporal integration for both implicit and explicit cases. In this sense, methods of Newmark, Houbolt
and Wilson-θ are used as the implicit one. In addition, methods of Central Differences, Souza and Moura
and Chung and Lee correspond to the explicit case. The analysis of 2D solids under dynamic response
considers both geometric and material nonlinearities. In order to regard nonlinear geometric effect, the
positional Finite Element Method (FEM) formulation wich uses node coordinates as variables instead
of displacements is taken into account. Therefore, the development of each computational routines for
the proposed formulation induces numerical results that are discussed and compared with examples from
the specialized literature.