Shape analysis of an adaptive elastic rod model

Abstract

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 the properties of the forms and data de ning the model, and the regularity of its solution, we compute and completely identify, in an appropriate functional space involving time, the weak shape semiderivative.