Abstract
In this paper we discuss the problem of computing and analyzing the static equilibrium of a nonrigid water tank. Specifically, we fix the amount of water contained in the tank, modelled as a membrane. In addition, there are rigid obstacles that constrain the deformation. This amounts to a nonconvex variational problem. We derive the optimality system and its interpretation in terms of equilibrium of forces. A second-order sensitivity analysis, allowing to compute derivatives of solutions and a second-order Taylor expansion of the cost function, is performed, in spite of the fact that the cost function is not twice differentiable. We also study the finite elements discretization, introduce a decomposition algorithm for the numerical computation of the solution, and display numerical results.
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