10h-11h : Prof E. de Souza Neto, University of Swansea
The Method of Multiscale Virtual Power: A General Recipe for Multiscale Modelling
11h15-12h15 : Prof. E. Fancello, Universidade Federal de Santa Catarina (Florianopolis, Brésil)
Level set based topology optimization with local stress constraints: Hamilton-Jacobi and reaction-diffusion evolution equations.
Although the strain energy or total potential energy (compliance problem) has been the most widely used objective function in structural topology optimization due to their particularly convenient mathematical properties, the corresponding optimal designs are not validated against mechanical failure. Such designs need to be post processed and, after stress analysis verification, conveniently modified in order to satisfy some material failure criterion. With the aim to eliminate this necessary “rework”, and despite challenging mathematical and numerical difficulties, stress-constrained topology optimization problems have attracted the attention in structural problems.
This presentation will discuss the quite obvious structural topology optimization problem of mass minimization with local stress constraints. Among serveral alternatives, a level set based procedure that uses an Augmented Lagrange function to treat the local constraints is focused. A classical approach to control geometry in a level set based optimization problem is an upwind time integration of Hamilton-Jacobi equation. Despite satisfactory results were obtained, this technique does not allow the creation of new holes and level set reinitialization procedures are almost mandatory, generating undesirable noise in the solution near convergence. In order to overcome these drawbacks, the HJ procedure was replaced by reaction-diffusion evolution equation. This choice allowed the elimination of the reinitialization step and, most important, the possibility of creating new holes, leading the method truly “topological”. Technical details and numerical examples of both techniques will be presented.