An optimal control approach to an inverse nonlinear elastic shell problem applied to car windscreen design Original Research Article

A numerical procedure to optimise the sag bending process for car windscreens is proposed. In particular a simplified elastic model with geometric nonlinearities is considered. The optimisation approach is based on the numerical resolution of an optimal control problem in nonlinear elasticity. The objective of the optimisation is to match a desired shape by controlling the temperature distribution and minimising a quadratic functional. Also, we define and analyse the finite element approximation of the optimality system and a gradient method for the solution of the resulting discrete variational inequality. Finally, numerical experiments for the simulation of the simplified model are discussed.