This thesis has focussed on structure - material interaction by studying the interplay of material tailoring variables, viz., fiber orientation, spacing, density, ply-thickness and lamination sequence, with certain structural parameters i.e. applied loading and boundary conditions, in the linear and nonlinear stability of laminated, rectangular and circular plate and cylindrical shell elements. The optimization of laminates for improving buckling strength has been widely studied in the literature, yet the effects of material tailoring on postbuckling response are still largely unknown and, therefore, the proposition of including postbuckling performance parameters in laminate optimization is rationally advanced in the context of composite materials. The investigation is biased toward explaining the basic mechanics of various issues related to creative laminate design, optimization, postcritical stiffness and imperfection sensitivity in simple, physical terms, with the aim of their pragmatic adaptation into structural engineering practice.

The presentation is divided into two major segments accounting for linear and nonlinear behaviour and the analytical component is largely based on the Rayleigh-Ritz energy method. Many interesting features of shape optimization of simply supported, isotropic plates are discussed which have led to improved, inhomogeneous laminate designs where fiber spacing in a lamina, not orientation, is treated as the design variable. The sensitivity of buckling loads to fiber orientation is greatly affected by stress gradient, anisotropic coupling and in-plane restraints. Moreover, laminates with negative Poisson's ratio exhibit fairly unusual pre and post buckling responses.

In the second section, deteriorating postbuckling behaviour of rectangular plates and cylindrical shells is reported when optimization of the buckling load is exercised;​ the circular plate is an exception to this general conclusion. It is seen that rectangular laminates, optimal in buckling, are most likely to exhibit inferior postbuckling behaviour due to reduced stiffness. The criteria for improving pre and post buckling of orthotropic circular plates, studied using an initial value formulation, are virtually synonymous. The postbuckling behaviour of circular, cylindrical shells is investigated using an approximate physical approach, known as the reduced stiffness method, where the imperfection sensitivity is estimated in terms of a reduced buckling load obtained by ignoring the nonlinear circumferential membrane energy in a linearized buckling analysis. The success of this treatment lies in its articulation of lamination parameters governing postbuckling behaviour, especially their variation during optimization of the buckling load.