Layerwise optimisation for maximising the fundamental frequencies of point-supported rectangular laminated composite plates

The layerwise optimisation (LO) approach is extended in this work to point-supported, symmetrically laminated rectangular plates. The plates considered rest on some elastic or rigid point supports distributed in different arrangements. The LO approach provides a simple design procedure for composite structural optimisation which may be used to maximise the fundamental frequencies of the plates. The design variables are taken for a set of fibre orientation angles in the symmetric layers. The vibration problem is solved by the Ritz method with consideration of strain energy stored in the elastic supports or of the Lagrange multiplier for rigid supports. In numerical results, the symmetric 8-layer plates with eight different sets of support positions are considered and the applicability of the LO approach to the problem is demonstrated by comparing the present optimum solutions with reference frequencies of laminated plates with typical lay-ups. The relation of the support location and the optimum fibre orientation angles is discussed.