Optimization of multilaminated structures using higher-order deformation models

A refined shear deformation theory assuming a non-linear Variation for the displacement field is used to develop discrete models for the sensitivity analysis and optimization of thick and thin multilayered angle ply composite plate structures. The structural and sensitivity analysis formulation is developed for a family of C-0 Lagrangian elements, with eleven, nine and seven degrees of freedom per node using a single layer formulation. The design sensitivities of structural response for static, free vibrations and buckling situations for objective and/or constraint functions with respect to ply angles and ply thicknesses are developed. These different objectives and/or constraints can be generalized displacements at specified nodes, Hoffman's stress failure criterion, elastic strain energy, natural frequencies of chosen vibration modes, buckling load parameter or the volume of structural material. The design sensitivities are evaluated either analytically or semi-analytically. The accuracy and relative performance of the proposed discrete models are compared and discussed among the developed elements and with alternative models. A few illustrative test designs are discussed to show the applicability of the proposed models.