High order sensitivity analysis in shape optimization problems (Q1116817)

A formulation for high order directional differentiation of functions defined through integration is presented. The formulation has been developed initially for sensitivity analysis in optimal shape design problems by the finite element method. However, its application range is much wider. Explicit analytical expressions are given for sequential directional derivatives. Special emphasis has been made in holding recurrence and simplicity of intermediate operations. The proposed scheme does not depend strongly on any particular form of the state equations, and its numerical implementation in finite elements method programs can be considered easy and efficient. As an example, up to second order sensitivity techniques are applied to the optimization of a concrete roof. Structural analysis has been performed in linear elastic conditions, with quadratic three-dimensional elements for the discretization of the roof.