Introduction

Doubly curved shells are largely used in aeronautics and aerospace and are subjected to dynamic loads that can cause vibration amplitudes of the order of the shell thickness, giving rise to significant nonlinear phenomena. In order to reduce the weight, traditional materials are often substituted with laminated panels. This justifies the study of nonlinear vibrations of isotropic and laminated curved panels.

Nonlinear (large amplitude) forced vibrations of doubly curved shallow-shells are initially studied by using Donnell's theory retaining in-plane inertia and the Lagrange equations. The effect of the geometry and curvature are investigated for isotropic shells. Then, nonlinear free vibrations of laminated composite shells are studied by using both the Donnell and the first-order shear deformation theories in order to compare numerical results. It is observed that a shear deformation theory should be adopted for moderately thick laminated shells for which the ratio between the thickness and the largest of the in-plane curvilinear dimensions is equal or larger than 0.04.

The stability of a spherical shell under static normal load is discussed. Finally, the example of buckling analysis of the external tank of the NASA space shuttle, taking into account the effect of initial geometric imperfections, is performed following the study of Nemeth et al. (2002).

Literature review

Leissa and Kadi (1971) studied linear and nonlinear free vibrations of doubly curved shallow-shells with rectangular boundaries, simply supported at the four edges and without in-plane constraints. Donnell's nonlinear shallow-shell theory was used.