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 struc- tures using a plate shell element based on a Kirchhoff discrete the- ory for the bending effects. To overcome the nondifferentiability of multiple eigenvalues, which may occur during a structural opti- mization involving free vibrations or buckling design situations, a nonsmooth eigenvalue based criterion is implemented. Angle-ply design variables and vectorial distances from the laminated mid- dle surface to the upper surface of each layer are considered as de- sign variables. The design sensitivities and the directional deriva- tives 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. eigenvalue problem is not discussed. From the above surveys one can find the need for and great interest in the develop- ment of efficient techniques to study sensitivities of response of composite plate-shells structures for general purpose ap- plications. It is evident from the surveys that the number of publications related to structural optimization of composite structures is very small when compared with isotropic struc- tures and specially when the problem of multiple eigenvalues is considered.