Aplicação orientada a objetos para análise físicamente não-linear com modelos reticulados de seções transversais compostas

Abstract

This masters thesis refers to the computational implementation, according to objectoriented paradigm, of material nonlinear solution of finite element models of framed structures with composed and geometrically arbitrary cross sections. These sections are represented by decomposition in smaller areas, in which the materials nonlinear stress-strain relations are monitored. In such way, it is possible to determine the constitutive equation of each section, the stiness matrix and the internal eorts of the finite element. Then, the equilibrium paths for certain degrees of freedom of the model are obtained through an incremental-iterative procedure. The mathematical and discrete models formulations, based on Timoshenko and Euler-Bernoulli bending theories, are presented, considering the most general framed structuralmodel, the space frame. The nonlinear solution of equilibrium equations is discussed briefly. Through the use of various software development solutions, the related implementation takes place with the progressive rearrangement and extension of the numerical nucleus of INSANE (INteractive Structural ANalysis Environment), a computational environment segmented and friendly to changes. The numerical nucleus conception and the set of segments that represent the necessary abstractions to a numerical resolution of a finite element model are discussed. Some numerical simulations are presented to validate the implementation and to show the application modeling potential.