SENSITIVITY ANALYSIS AND OPTIMIZATION OF THIN LAMINATED STRUCTURES WITH A NONSMOOTH EIGENVALUE BASED CRITERION

This paper presents a discrete model for the design sensitivity analys is of thin laminated angle-ply composite structures using a plate shel l 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 o r buckling design situations, a nonsmooth eigenvalue based criterion i s implemented. Angle-ply design variables and vectorial distances from the laminated middle surface to the upper surface of each layer are c onsidered as design variables. The design sensitivities and the direct ional derivatives are evaluated analytically. The efficiency and accur acy of the model developed is discussed with two illustrative cases wh ich show the need to compute sensitivities of multiple eigenvalues as directional derivatives for laminated composite structures.