Layup optimization of symmetrically laminated thick plates for fundamental frequencies using lamination parameters

This paper examines the optimum laminate configurations for maximizing the fundamental frequencies of symmetrically laminated thick plates. The transverse shear effect is taken into consideration in the free vibration analysis of symmetrically laminated thick plates on the basis of the first-order shear deformation theory. Layup optimization is performed by introducing four out-of-plane and two in-plane lamination parameters that characterize the out-of-plane and the transverse shear stiffnesses, respectively. A variational approach is applied to find the boundary of the feasible region in the design space of the six lamination parameters. Using the information of the boundary of the feasible region, the optimum lamination parameters that give the maximum fundamental frequency are obtained for the cases of simply supported and clamped boundary conditions. The laminate configurations intended to realize the optimum lamination parameters are also obtained by using a mathematical programming method. The transverse shear effect on the optimum results is discussed in comparison with the optimum results obtained for classical laminated plate theory.