Shape Derivative for Some Eigenvalue Functionals in Elasticity Theory

This work is the second part of a previous paper which was devoted to scalar problems. Here we study shape derivative eigenvalue problems elasticity theory for various kinds boundary conditions, that Dirichlet, Neumann, Robin, and Wentzell conditions. We also case composite materials, having in mind applications sensitivity analysis mechanical devices manufactured by additive printing. The main idea, rests on computation minimum with respect parameter, successfully applied first this here extended more interesting situations vectorial (linear elasticity), manufacturing. These computations eigenvalues problem generalized conditions elastic structures constitute novelty paper. results obtained show efficiency method such calculations whereas methods used previously even classical clamped or transmission are lengthy based simplifying assumptions, as simplicity existence derivative.