Static analysis of anisotropic doubly-curved shells with arbitrary geometry and variable thickness resting on a Winkler-Pasternak support and subjected to general loads

Laminated doubly-curved shells constituted by innovative materials have become a standard application in several engineering fields. However, this requires a proper formulation of such structures, since several very complex issues affecting such applications must be kept in mind, among all, the curvature effect and the coupling issues between two adjacent layers. In the present work a generalized formulation based on Higher Order Theories is proposed for the linear static analysis of curved structures with completely anisotropic materials in each layer of the lamination scheme. The shell model is described according to the Equivalent Single Layer approach and a mapping procedure based on a Non-Uniform Rational Basis Spline (NURBS) description of the shell edges is applied for the geometric description. Different thickness variations have been considered in the analyses. The fundamental equations of the static problem are derived from the minimum potential energy principle directly in the strong form and the effect of the Winkler-Pasternak support has been accounted for. The external surface load has been applied in each principal direction and arbitrary actions have been enforced to the external edges of the structure. The proposed approach has been validated with respect to the outcomes of some 3D Finite Element models and very good agreement is found between such simulations. Shells characterized by very complex shapes have been accounted for and accurate results have been found with a reduced number of degrees of freedom.