Three-dimensional nonlinear analysis of laminated cylindrical shells under cylindrical bending

On the basis of three-dimensional (3D) nonlinear elasticity, asymptotic solutions for the laminated cylindrical shells under cylindrical bending are presented. The basic 3D nonlinear equations such as the relations between finite strains (Green strains) and displacements, the nonlinear stress equilibrium equations in terms of the Kirchhoff stress components and the generalized Hooke's law for a monoclinic elastic material are considered in the present formulation. After introduction of a set of nondimensionalized field variables, asymptotic expansion, consideration of the effects of shear deformations at the leading order problem and then successive integration, we obtain the recursive sets of governing equations for various orders. The von Karman-type first-order shear deformation theory (FSDT) is derived as a first-order approximation to the 3D nonlinear theory. The admissible edge conditions for various orders are derived in the form of generalized force and moment resultants by means of the variational principles for finite deformations. With a set of appropriate edge conditions, the asymptotic solutions of laminated cylindrical shells under cylindrical bending at each order level can be obtained. Since the differential operators for various order problems remain identical, it is shown that the solution procedure can be repeatedly applied to various order problems.