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Abstract
We present some systematic approaches to the mathematical formulation and numerical resolution of an optimal control problem in linear elasticity. The objective of the optimization is to match a desired displacement by controlling the Young's modulus so as to minimize a quadratic functional. Theoretical results are presented in the general framework of linear elastic theory which lead to a variational inequality. Also, we define and analyze a finite element approximation of the optimality system and a gradient method for the solution of the discrete variational inequality. Finally, numerical experiments for the simulation of a simplified model for the “sag bending process” in the manufacturing of automobile windscreens are discussed.
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