Sistema computacional orientado a objetos para análise termomecânica fisicamente não-linear em regime transiente via método dos elementos finitos

Abstract

This master’s thesis refers to the implementations of tools in the free computational environment INSANE (INteractive Structural ANalysis Environment), written accordingly with the object-oriented programming paradigm, for the solution of physically non-linear thermomechanical problems in the time-dependent regime. The spatial discretization follows the parametric formulation of the Finite Element Method (FEM), and the temporal discretization follows an expansion in Finite Differences (FD). The scope is limited to situations where the temperature variation occur in a quasi-static regime. In this regime, both the temperature variation and the mechanical actions change slowly, allowing neglect the heat produced during the deformation process, as well as the heat produced by dissipative phenomena. Removing these terms we obtain a set of decoupled partial differential equations, enabling the solution of the thermal problem independently of the mechanical problem. However, to solve the mechanical problem, the thermal solution should be known in advance, since the temperature variation contributes to the strain field in the body. To manage the solution process, we introduced a new entity in the object-oriented design of the software’s numerical core, named SimulationManager. The analysis of problems whose analytical solution is previously known validated the new classes, as well as all other modifications made in the source code.