An extension of the polar method to the First-order Shear Deformation Theory of laminates

In this paper the Verchery’s polar method is extended to the conceptual framework of the First-order Shear Deformation Theory (FSDT) of laminates. It will be proved that the number of independent tensor invariants characterising the laminate constitutive behaviour remains unchanged when passing from the context of the Classical Laminate Theory (CLT) to that of the FSDT. Moreover, it will also be shown that, depending on the considered formulation, the elastic symmetries of the laminate shear stiffness matrix depend upon those of membrane and bending stiffness matrices. As a consequence of these results a unified formulation for the problem of designing the laminate elastic symmetries in the context of the FSDT is proposed. The optimum solutions are found within the framework of the polar-genetic approach, since the objective function is written in terms of the laminate polar parameters, while a genetic algorithm is used as a numerical tool for the solution search. In order to support the theoretical results, and also to prove the effectiveness of the proposed approach, some novel and meaningful numerical examples are discussed in the paper.