Sensitivity analysis and optimization of thin laminated structures with a nonsmooth eigenvalue based criterion

This paper presents a discrete model for the design sensitivity analysis of thin laminated angle-ply composite structures using a plate shell element based on a Kirchhoff discrete theory for the bending effects. To overcome the nondifferentiability of multiple eigenvalues, which may occur during a structural optimization involving free vibrations or buckling design situations, a nonsmooth eigenvalue based criterion is implemented. Angle-ply design variables and vectorial distances from the laminated midle surface to the upper surface of each layer are considered as design variables. The design sensitivities and the directional derivatives are evaluated analytically. The efficiency and accuracy of the model developed is discussed with two illustrative cases which show the need to compute sensitivities of multiple eigenvalues as directional derivatives for laminated composite structures.