Design of the elastic properties of laminates with a minimum number of plies

The design of laminates with a minimum number of layers for obtaining the given elastic properties is addressed in the paper. The problem is treated and solved in the general case — no simplifying hypotheses are made about the type of their stacking sequence. The problem is stated as a nonlinear programming problem, where a unique objective function includes all the requirements to be satisfied by the solutions. The optimum solutions are found within the framework of the polar-genetic approach, since the objective function is written in terms of polar parameters of the laminates, while a nonclassical genetic algorithm is used as the optimization scheme. The optimization variables include the number of layers, layer orientations and layer thicknesses. In order to include the number of plies among the design variables, certain modifications of the genetic algorithm have been done, and new genetic operators have been developed. Some examples and numerical results concerning the design of laminates with a minimum number of layers for obtaining some prescribed elastic symmetries, bending-extension uncoupling, and quasi-homogeneity are shown in the paper.