A two-dimensional model to analyze the static and dynamic mechanical behavior of multilayered shell structures

Abstract

A new exact two-dimensional model is derived to analyze the mechanical behavior of multilayered shells in this work. Particularly, this model is used to investigate the static and transient responses of doubly-curved cross-ply laminated shells. The new laminate constitutive equations (LCE) used in this model was developed through the use of Kirchhoff-Love(K-L) based kinematic equations. This LCE accounts extensional-twisting-shear, extensional-Gauss bending-shearing, Gauss bending-shearing mechanical couplings which do not exist in some other models available in literature. The proposed exact model is more general than those used in several papers. Shear stresses across the thickness are also computed. Our model has been used to develop analytical solutions of simply supported, cross-ply laminated shells based on the Navier’s approach using Hamilton’s principle. This model could also be used without major conceptual modifications to handle stiffened multilayered shells which in fact cannot be considered uniformly as shallow shell. Several examples were carried out to validate and prove the accuracy and efficiency of the present model while taking into account different lamination scheme and some ratios. We showed that the above mechanical couplings influence the static and dynamic mechanical behavior of anisotropic shells when the thickness ratio χ=h2R becomes greater. The current work improves some General anisotropic doubly-curved shell theories proposed and studied in some recent work in literature by introducing a novel LCE.