Topology optimization using a Topology Description function

The topology description function (TDF) approach is a method for describing geometries in a discrete fashion, i.e. without intermediate densities. Hence, the TDF approach may be used to carry out topology optimization, i.e. to solve the material distribution problem. However, the material distribution problem may be ill-posed. This ill-posedness can be avoided by limiting the complexity of the design, which is accomplished automatically by limiting the number of design parameters used for the TDF. An important feature is that the TDF design description is entirely decoupled from a finite element (FE) model. The basic idea of the TDF approach is as follows. In the TDF approach, the design variables are parameters that determine a function on the so-called reference domain. Using a cut-off level, this function unambiguously determines a geometry. Then, the performance of this geometry is determined by a FE analysis. Several optimization techniques are applied to the TDF approach to carry out topology optimization. First, a genetic algorithm is applied, with (too) large computational costs. The TDF approach is shown to work using a heuristic iterative adaptation of the design parameters. For more effective and sound optimization methods, design sensitivities are required. The first results on design sensitivity analysis are presented, and their accuracy is studied. Numerical examples are provided for illustration.