A hybrid numerical method for trade-off optimal relation between mass and fundamental natural frequency of moderately thick laminated composite beams

Trade-off optimal relation between total mass and fundamental natural frequency of moderately thick symmetric laminated composite beams is found by employing a hybrid numerical method. The governing equations of the problem are obtained from the first-order shear deformation theory of beams and are discretized by applying the differential quadrature method to find frequencies of the beam. Fiber volume fraction, thickness and fiber orientation of each layer of the beam are considered as design variables of the problem. Then, the non-dominated genetic algorithm II and the differential quadrature method are coupled to investigate the trade-off relation. Accuracy, convergence and robustness of the proposed method are investigated and its applicability for solving the problem is demonstrated through the different optimization scenarios.