Sistema computacional para análise dinâmica geometricamente não-linear através do método dos elementos finitos

Abstract

This masters thesis refers to the computational implementation, according to the object-oriented programming, of dynamic geometrically non-linear solution of Finite Element Method models. Some ways of considering damping in dynamic analysis are discussed. Many methods of dynamic solution are presented, not only those based on modal superposition, but also those based on direct integration. The Total Lagrangean and Updated Lagrangean formulations for non-linear analysis are discussed. Methods for solution of non-linear equations are also presented. The implementation is done in the numerical nucleus of INSANE computational system, which is developed in the Structural Department of UFMG. The object-oriented project of this system is presented, as well as the necessary modifications to add the proposed solution. Many numerical simulations are presented to validate the implementation, comparing the results obtained by the implementation with analytical and numerical results found in literature.