Contact shape optimization based on the reciprocal variational formulation. (Q1775169)

Optimal shape design for a unilateral frictionless contact of an anisotropic elastic body with a rigid obstacle is studied first theoretically, showing existence of the optimal shape. Then, an approximation scheme is proposed, together with its convergence analysis. Moreover, a sensitivity analysis necessary to get a gradient information, need usually for optimization procedures, is performed. The problem is posed in terms of small displacements, and the reciprocal formulation is used to obtain directly the contact stress which is involved in the cost functional of the optimization problem.