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Conical differentiability for bone remodeling contact rod models
Figueiredo, Isabel N.; Leal, Carlos F.; Pinto, Cecília S.We prove the conical di erentiability of the solution to a bone remodeling contact rod model, for given data (applied loads and rigid obstacle), with respect to small perturbations of the cross section of the rod. The proof is based on the special structure of the model, composed of a variational inequality coupled with an ordinary di erential equation with respect to time. This structure enables the veri catio...
Shape analysis of an adaptive elastic rod model
Figueiredo, Isabel N.; Leal, Carlos F.; Pinto, Cecília S.We analyse the shape semiderivative of the solution to an asymptotic nonlinear adaptive elastic rod model, derived in Figueiredo and Trabucho [8], with respect to small perturbations of the cross section. Taking advantage of the special structure of this model, which is de ned by generalized Bernoulli-Navier elastic equilibrium equations coupled with an ordinary di erential equation with respect to time, using ...
Sensitivity Analysis of a Nonlinear Obstacle Plate Problem
Figueiredo, Isabel N.; Leal, Carlos F.We analyse the sensitivity of the solution of a nonlinear obstacle plate problem, with respect to small perturbations of the middle plane of the plate. This analysis, which generalizes the results of Rao and Sokolowski 1987, Rockafeller 1989 for the linear case, is done by application of an abstract variational result Levy 1999, where the sensitivity of parameterized variational inequalities in Banach spaces, w...
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