An optimal design for the maximum fundamental frequency of laminated shallow shells

An optimal design is presented to determine the stacking condition that maximizes the lowest frequency of a laminated composite shallow shell with rectangular planform. The shallow shell considered has a symmetric laminate and is supported by shear diaphragms along the four edges. An analytical solution for natural frequencies is derived by discarding the cross-elasticity terms and then solving the governing equations of motion. In the optimization, fiber orientation angles in the layers are introduced as design variables, and a set of differential equations are presented which satisfy the Kuhn Tucker optimality conditions. Formulas are then derived to give the possible optimal fiber orientation angles. Using numerical examples, the effects of various shell curvatures upon the optimal fiber orientation angles are discussed for a wide range of shallow shell configurations. © 1998 Elsevier Science Ltd. All rights reserved