Minimization of the dynamic response of composite laminated doubly curved shells using design and control optimization

A design control optimization approach is used to determine optimal levels of ply thickness, fiber orientation angle and closed-loop control force for composite laminated doubly curved shells. The optimization objective is the minimization of the dynamic response of a shell subject to constraints on the thickness and control energy. A higher-order shell theory is used to formulate the control objective for various cases of boundary conditions. The dynamic response is expressed as the sum of the total elastic energy of the shell and a penalty functional of a closed-loop control force. Comparative examples are presented for symmetric (or antisymmetric) spherical and cylindrical shells with various cases of boundary conditions. The advantages of the present control optimization over some design and control approaches are examined. The effect of number of layers, aspect ratio and orthotropy ratio on the control process is demonstrated. The discrepancy between optimal results obtained using the classical, first-order and higher-order shell theories is studied.