Abordagem orientada a objetos para implementação computacional de elementos finitos de cascas planos

Abstract

One of the simplest ways of studying the behavior of a shell, using the Finite Element Method (FEM), is to approximate the geometry of its middle surface by plane finite elements obtained from the combination of plate and membrane elements. This master's thesis discusses the computational implementation of such elements using the bject-oriented programming methodology. The base of this implementation is the numerical core of INSANE (INteractive Structural ANalysis Environment), an object-oriented, modular, expansible and change-friendly computational system that is been developed by the Structural Engineering Department of Federal University of Minas Gerais. After the presentation of Reisnner-Mindlin and Kirchho shell theories and the corresponding FEM models, the implementation of these models is discussed in such a way that details the main changes performedin the numerical core of INSANE. Numerical simulations concerning Patch Tests, convergence study and application examples are presented. The obtained results are compared with analytic solutions and with numerical results from literature or from other computational systems.