74N15 Analysis of microstructure
We study a mechanical equilibrium problem for a material consisting of two components with different densities, which allows to change the outer shape by changing the interface between the subdomains. We formulate the shape design problem of compensating unwanted workpiece
changes by controlling the interface, employ regularity results for transmission problems for a rigorous derivation of optimality conditions based on the speed method, and conclude with some numerical results based on a spline approximation of the interface.
A mechanical equilibrium problem for a material consisting of two components with dierent 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.