A Refined Higher Order Theory for Statics and Dynamics of Doubly Curved Shells

Abstract

A complete formulation of static and dynamic analysis is presented using higher order shear and normal deformation theory (HOSNT) with twelve middle surface displacement parameters for doubly curved shells. Mathematical difficulty of obtaining a three dimensional (3D) solution for problems of plates and shells steered the development of two dimensional (2D) theories. Present model considers transverse shear strains and normal strains thus also incorporating rotary inertia and subsequent higher order expression in dynamic terms. A variational principle based on minimization of energy is used to derive the set of governing differential equations and associated boundary conditions. The theory presented here also uses extended thickness criteria where square of thickness to radius of curvature is considered less than unity instead of the classical assumption of taking thickness to radius of curvature less than unity. Problem of isotropic open cylindrical shell is solved and results are compared with available 3D solutions.