Sensitivity analysis and optimal design of geometrically non-linear laminated plates and shells

A high order shear deformation theory is used to develop a discrete model for the sensitivity analysis and optimization of laminated plate and shell structures in non-linear response. The geometrically non-linear analysis is based on an updated Lagrangian formulation associated with the Newton–Raphson iterative technique, which incorporates an automatic arc-length procedure. Fiber orientation angles and vectorial distances from middle surface to the upper surface of each layer are considered as the design variables. Different objectives, such as generalized displacements at specified nodes, volume of structural material, and limit load, and constraints of displacement and stress failure criterion are considered. The design sensitivities are evaluated analytically and are compared with sensitivities evaluated by the global finite difference. Numerical examples are given to show the accuracy of the proposed model in the non-linear response and the corresponding design sensitivity analysis, and to show the applicability in the optimal design.