Application of a new tailoring optimization technique to laminated and sandwich plates and to spherical panels

A tailoring optimization technique recently developed for improving structural response and energy absorption of composites is applied to laminated and sandwich plates and to sandwich spherical panels. The in-plane variation of the stiffness properties of plies and the through-the thickness variation of the core properties are determined solving the Euler–Lagrange equations of an extremal problem in which the strain energy due to out-of-plane strains and stresses is minimized, while that due to their in-plane counterparts is maximized. The zig-zag model with hierarchic representation of displacements recently developed by the authors is used as structural model. It accurately describes the strain energy and the interlaminar stresses directly from the constitutive equations. It a priori fulfils the displacement and stress contact conditions at the interfaces and considers a hierarchic representation that adapts itself to the variation of solutions. Refinement of the solution does not imply an increase of the number of functional degrees of freedom, which are the traditional mid-plane displacements and the shear rotations. As shown by the numerical applications, the critical interlaminar stress concentrations at the interfaces are sensibly reduced without any bending stiffness loss and the strength to debonding of faces from the core is improved.