Topology Optimization using a Topology Description Function Approach

During the last two decades, computational structural optimization methods have emerged, as computational power increased tremendously. Designers now have topological optimization routines at their disposal. These routines are able to generate the entire geometry of structures, provided only with information on loads, supports, and space to work in. The most common way to do this is to partition the available space in elements, and to determine the material content of each of the elements separately. This thesis presents a different approach, namely the \emph{Topological Description Function} (TDF) approach. The TDF is a function parametrized by design variables. The function determines a geometry using a level-set approach. A finite element representation of the geometry then is used to determine how well the geometry performs with respect to objective and constraints. This information is given to an optimization program, which has the purpose of finding an optimal combination of values for the design variables. This approach decouples the geometry description of the design from the evaluation, allowing the designer to tune the detailedness of the geometry and the computational grid separately as wished. In this thesis, the concept of a TDF is explained in detail. Using a genetic algorithm for the optimization turns out to be too computationally expensive, however, it shows the validity of the TDF as a geometry description method. A method based on an intuitive updating scheme shows that the TDF approach can be used to do topology optimization.