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The optimal stacking sequence design for the maximum frequencies of the lowest three modes of symmetric variable stiffness composite laminated beams in air and in water is investigated for the first time using a layer-wise optimization method. Two fiber orientation angles in each layer are considered as design variables. The shifted path technique is used to construct the fiber paths. The  p -version of the finite element method is used in conjunction with the Euler–Bernoulli beam theory coupled with torsion to calculate the frequencies. The numerical results are validated by comparison with published results for a single-layer constant stiffness composite beam with rectilinear fibers in air and in water. Extensive results are presented, which may serve as a benchmark for future research. Furthermore, a parametric study is performed showing the effects of geometrical and mechanical parameters and boundary conditions on the optimal solutions.

A layer-wise optimization method for the optimal stacking sequence design of symmetric VSCL beams in air and in water