Multi-objective optimal design of hybrid composite laminates for minimum cost and maximum fundamental frequency and frequency gaps

The design of hybrid composite laminates made of high-stiffness skin and low-stiffness core layers is presented. By considering vibration characteristics, the objective is the simultaneous maximization of fundamental frequency (or the gap between two consecutive frequencies) and minimization of cost by seeking the optimal stacking sequences of both skin and core layers. By introducing the concept of ground structure in laminate design, an initial stacking sequence consisting of high-stiffness skin and low-stiffness core layers is firstly given, and the design problem is then formulated with mixed discrete and continuous variables by defining a weighted min-max objective function and determining the minimum, where discrete variables represent the existence of each ply in the initial stacking sequence, and continuous variables are used for ply thicknesses. The problem is made explicit with branched multipoint approximate functions, and genetic algorithm (GA) is adopted to optimize discrete variables so that necessary/unnecessary layers from the initial stacking sequence are retained/suppressed. For fitness calculation in GA, a second-level approximation is built with the convex linearization to optimize continuous ply thicknesses of the retained layers. Using that approach, optimal stacking sequences are found for hybrid graphite/epoxy-glass/epoxy laminated plates with different aspect ratios, by considering free vibration.