Analytical sensitivity analysis of eigenvalues and lightweight design of composite laminated beams

The paper describes an optimisation technique for the lightweight design of composite laminated beams with a big ratio of span to thickness. The optimisation model for the lightweight design is to find the fibre volume fractions to minimise the mass of the composite laminated beams under the eigenvalue (or frequency) constraints. The analytical sensitivity of the eigenvalues, with respect to the fibre volume fractions, is formulated using the Euler–Bernoulli beam theory. The analytical formulae for sensitivity analysis are suitable for the different boundary conditions (pinned–pinned, fixed–fixed, fixed–free and fixed–pinned). The eigenvalues are linearised using Taylor’s series so that optimisation model is converted to a linear programming problem. The iterative computational procedure is proposed to solve the optimisation model and eliminate the Taylor’s series approximation since the current design point maybe not near the optimum design. Finally, the lightweight designs of the composite laminated beams with different boundary conditions are performed. The merits of the proposed method and lightweight designs obtained by proposed method are discussed.