Layerwise optimization for the maximum fundamental frequency of laminated composite plates

A new concept of a layerwise optimization approach (LOA) is proposed to optimize vibration behavior for the maximum natural frequency of laminated composite plates. Design variables are taken to be the fiber orientation angles in all N layers. This usually causes a rapid increase in computation time due to the search for optimum solutions in the N-dimensional space. The LOA makes possible this multi-dimensional optimization into only N times repetition in a one-dimensional search. The idea is based on the physical consideration that the outer layer has more stiffening effect than the inner layer in the bending of plates and is more influential in determining the natural frequency. In numerical examples, a Ritz method is employed to calculate the natural frequencies of laminated rectangular plates under any combination of the three classical edge conditions. Results are corroborated by comparing with other optimum solutions available in the literature.