Multiobjective design and control optimization for minimum thermal postbuckling dynamic response and maximum buckling temperature of composite laminates

Design and control optimization is presented to minimize the thermal postbuckling dynamic response and to maximize the buckling temperature level of composite laminated plates subjected to thermal distribution varying linearly through the thickness and arbitrarily with respect to the in-plane coordinates. The total elastic energy of the laminates is taken as a measure of the dynamic response. The optimization control problem is solved under constraints on the laminate thickness and the control energy produced by a transverse dynamic load distributed over the upper surface of the laminate. The constrained control objective is expressed as the sum of the total elastic energy and penalty term involving the control force, which may be considered as a measure of the control energy. The thickness of layers and the fibers orientation angles are taken as optimization design variables. The design and control objectives are formulated based on shear deformation theory accounting for the von-Karman nonlinearity. The displacements are chosen as the sum of time-independent displacements due to the static thermal load and time-dependent displacements due to the initial disturbances and the applied control force. Liapunov–Bellman theory is used to obtain the optimal control force, buckled deflections and controlled elastic energy. Numerical examples are presented for angle-ply antisymmetric laminates with simply supported edges. Graphical studies are carried out to show the advantages of the present design and control procedures.