Topology Optimization with h-Adaptive Refinement Process in Thermoelastic Bidimensional Problem

Abstract

This work proposes a formulation for optimization of bidimensional (2D) structure layouts submitted to mechanic and thermal shipments and applied an h-adaptive filter process which conduced to computational low spend and high definition structural layouts. The main goal of the formulation is to minimize the structure mass submitted to an effective state of stress of von Mises, with stability and lateral constraint variants. A criterion of global measurement was used for intents a parametric condition of stress fields. To avoid singularity problems was considerate a release on the stress constraint. On the optimization was used a material approach where the homogenized constructive equation was function of the material relative density. The intermediary density effective properties were represented for a Solid Isotropic Microstructures with Penalization (SIMP) type artificial model. The problem was simplified by use of the method of finite elements of Galerkin using triangles with linear Lagrangian basis. On the solution of the optimization problem, was applied the augmented Lagrangian Method, that consists on minimum problem sequence solution with box-type constraints, resolved by a second order projection method which uses the method of the quasi-Newton without memory, during the problem process solution. This process reduces computational expends showing be more effective and solid. The results materialize more refined layouts with accurate topologic and shape of structure definitions. On the other hand formulation of mass minimization with global stress criterion provides to modeling "ready" structural layouts, with violation of the criterion of homogeneous distributed stress.