Abstract
In this paper we develop the material derivative method for the optimal shape design of contact problems described by variational inequalities. Since the method can be used for solving the optimal shape problem for systems described by partial differential equations, here we shall use it to solve it for differential inequalities by taking limits of the equations resulting from a penalized approximation. The computations are done by the finite-element method; the gradient of the criteria as a function of coordinates moving nodes is computed, and the performance criterion is then minimized by a material derivative (or speed) method (Zolesio (1981)).
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