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.
Variational inequality formulation of an inverse elasticity problem / Manservisi S.; Gunzburger M.. - In: APPLIED NUMERICAL MATHEMATICS. - ISSN 0168-9274. - STAMPA. - 34:1(2000), pp. 99-126. [10.1016/S0168-9274(99)00042-2]
Variational inequality formulation of an inverse elasticity problem
Manservisi S.;
2000
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
