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RESEARCH PRODUCT

Sensitivity analysis for discretized unilateral plane elasticity problem

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Abstract Numerical realization of optimal shape design problems requires gradient information which is used in minimization procedures. There are several possibilities for obtaining this information. Here we present a method, based on the use of the material derivative approach, applied to the finite element discretization of the problem. The advantage of this approach is that is gives the exact values of gradient and it can be very easily implemented on computers. We apply this method in the case of contact problems, where the situation is more involved compared with the case of elasticity problems with classical boundary conditions. We concentrate on a special choice of the cost functional, given by the total potential energy evaluated at the equilibrium state. This cost functional plays an important role also in grid optimization.