Topology optimization: perimeter restriction using total variation

Sammanfattning: Topology optimization is a method used to find optimal material distributions, within a specified domain, with respect to some performance measure. To avoid various artifacts to appear in the suggested design, the solution space is typically restricted, where some restriction methods allow different length scales to be controlled in the design. The suggested material distribution may result in complex designs that are difficult and costly to manufacture. By controlling the perimeter of the design, solutions with limited complexity can be found. In this thesis, two different methods of controlling the perimeter of the solution in topology optimization are investigated. First, a method is presented where a constraint on the total variation is added to the optimization problem. The method is evaluated by solving a 2-dimensional heat flow topology optimization problem, where two different penalization strategies are used. With the total variation constraint method, the perimeter cannot be fully controlled. However, some useful applications in engineering might still be found. For comparison, the topology optimization problem is also solved using a PDE-filter, which is modified for computational efficiency. Finally, a filter with total variation regularization is presented, without being successfully implemented.