Otimização topológica 3D sob restrição de tensão

Abstract

The Topology Optimization Problem consists in the total mass minimization of a structure. In order to solve three-dimensional stress problem, the Galerkin Finite Element Method was applied. It considers a four nodes tetrahedron finite element which interpolates not only the displacement fields, but also the relative density field. This work proposes to combine a stabilized element to avoid checkerboard problems, with a selective integration scheme to avoid volumetric locking. The optimal objective function is to minimize the mass, subjected to: a stress criterion (failed function); side and stability constraints to avoid checkerboard instability problems. Moreover, the design variables are given by the nodal relative densities of the finite element mesh using the SIMP material. With the proposed considerations it was obtained a layout that characterizes the structural topology of problems 3D, assisting the solution of problem in a competitive way. The formulation was shown promising for the implementation of adaptivity resources