Distortion compensation as a shape optimization problem for a sharp interface model
Please always quote using this URN:urn:nbn:de:0296-matheon-13004
- A mechanical equilibrium problem for a material consisting of two components with di� erent densities is considered. Due to the heterogeneous material densities, the outer shape of the underlying workpiece can be changed by shifting the interface between the subdomains. In this paper, the problem is modeled as a shape design problem for optimally compensating unwanted workpiece changes. The associated control variable is the interface. Regularity results for transmission problems are employed for a rigorous derivation of suitable � first-order optimality conditions based on the speed method. The paper concludes with several numerical results based on a spline approximation of the interface.