Numerical solution of an optimal shape design problem with elastic solids (Q1205066)

An optimal design problem is studied for elastic bodies. We define this problem from a mathematical point of view by functional equations based on virtual works, analyzing later the existence of a solution and the necessary minimum conditions for the adopted cost functional (global deformation). Subsequently the finite element method is applied, obtaining a new problem: the approximate problem, from which the existence of its solution and the convergence of its solution to the original problem solution is proved.