Finite element approximation of a shape optimization problem for von karman system

An optimal shape design problem of an elastic body described by a system of two nonlinear elliptic equations is considered. The problem is to find the boundary of the domain occupied by the body in such a way that the stiffnes of the system in the equilibrium state is minimized.

It is assumed that the volume of the body is constant. Moreover, the function describing the boundary of the domain and its gradient are bounded.