Topology Optimization using the Topology Description Function Approach

摘要

Topology Optimization is the process of finding the optimal shape and layout for a certain (mechanical) problem. The approach of meshing the available space and determining the content of the elements generally yields an ill-posed problem. This can be overcome by methods that restrict the design space, imposing a limit on the optimality, or by methods that extend the design space, thus relaxing the problem. In general the content of each element is described by a number of design variables, causing a strong coupling between the design variables and the Finite Element (FE) description used. In the Topology Description Function (TDF) approach the design variables and the FE description are fully decoupled. The design variables in the TDF approach are parameters that determine a function on the reference domain. This function determines unambiguously a geometry using a cut-off level. The number of parameters used controls the amount of detail of this geometry. To evaluate the performance of this design a FE model is used. The TDF approach is shown to work using iterative adaptation of the design parameters. For a more effective optimization method design sensitivities are required. The first results of the design sensitivity analysis are presented, and their accuracy is studied.