Topology optimization of plates

Abstract

In this report we propose a stabilization method for topology optimization of planes. The method can be classified in the category of continuation methods. The new continuation method is based on using continuous of design variables (DV) defined on a set meshes different from the one used for the finite element solution. The optimization procedure stars with using a coarse DV-mesh compared to finite element one. Once the convergence is obtained in the optimizations steps, a finer DV-mesh is nominated for further steps. With such a continuation method one can control the bounds of the gradients of the DV while simultaneously smooth the values in a more logical fashion, compared to what conventional filters perform. The DV-mesh refinement can be continued until the final mesh becomes similar to the finite element mesh. Depending on the formulation and elements used for the plate problems, e.g. with Kirchhoff or Mindlin-Reissner hypothesis, the refinement may further be continued so that the DV elements become smaller than the plate elements. Application of the method is shown over a wide range of plate problems. Linear and nonlinear plate behaviors formulated by Kirchhoff or Mindlin Reissner hypothesis, while using several forms of DV, are considered to show the performance of the proposed method. As one of the main DV, density is used in a power-law approach (or in an artificial material approach). This is performed in two forms, on in obtaining the topology of Thickness is also used as a realistic design variable in order to show the performance of the method in a rather well-posed optimization problem. We have also included results from a homogenization approach. Comparison in made with conventional element/nodal based approaches using filter. The results show excellent and robust performance of the proposed method. Due to the wide range of cases studied, some inserting side conclusions are also given in this report.