Shape Analysis of an Adaptive Elastic Rod Model

We analyze the shape semiderivative of the solution to an asymptotic nonlinear adaptive elastic rod model, derived in Figueiredo and Trabucho [Math. Mech. Solids, 9 (2004), pp. 331–354], with respect to small perturbations of the cross section. The rod model is defined by generalized Bernoulli–Navier elastic equilibrium equations and an ordinary differential equation with respect to time. Taking advantage of the model’s special structure and the regularity of its solution, we compute and completely identify, in an appropriate functional space involving time, the weak shape semiderivative.