Control and Cybernetics Radial Basis Function Level Set Method for Structural Optimization *

Abstract: This paper is concerned with simultaneous topology and shape optimization of elastic contact problems. The structural optimization problem for an elastic contact problem consists in finding such topology as well as such shape of the boundary of the domain occupied by the body that the normal contact stress is minimized. Shape and topological derivatives formulae of the cost functional obtained using material derivative and asymptotic expansion methods, respectively, are recalled. These derivatives are employed to formulate the necessary optimality condition and to calculate a descent direction in a numerical algorithm. Level set based method is employed in numerical algorithm for tracking the evolution of the domain boundary on a fixed mesh and finding an optimal domain. In order to increase the efficiency of the level set based numerical algorithm, the radial basis function approach is used to solve the equation governing domain boundary evolution. Numerical examples are provided and discussed.