Higher order semi-analytical solution for bending of angle-ply composite laminated cylindrical shells based on three-dimensional theory of elasticity

摘要

This paper develops a high-performance semi-analytical numerical model to analyze the bending responses of the angle-ply composite laminated cylindrical shells with the fiber reinforced layers using the scaled boundary finite element method (SBFEM). As the thin-walled structures, the angle-ply composite laminated shells are assumed to be made of orthotropic materials in the cylindrical coordinate system. Both the geometric and basic variables are discretized by utilizing the two-dimensional (2D) high order spectral elements in the curved surface domain of the shells. According to the exact three-dimensional (3D) theory of elasticity rather than the approximate shell theories, the weak form of the partial differential governing equations for each layer of the composite laminated cylindrical shells in the cylindrical coordinate system are transformed into ordinary differential equations using the SBFEM. In the circumstances, there are no variables about the curved surface of shell in the SBFEM governing equations for each lamina, so that it can be analytically solved on the basis of the dual variable approach and the precise integration technique (PIT). Employing the interface continuity conditions of displacement between the layers, the complete SBFEM model with respect to the global stiffness matrix of the composite laminated cylindrical shell can be obtained. Unlike the general layer wise theories, which supposes that the basic variables varied linearly with the thickness coordinate, the through-thickness distributions of the displacement field in each discrete layer is assumed to be a quadratic polynomial with respect to the radial coordinate in this paper, thus the through-thickness stress field can be described more accurate. Numerical examples for solving the bending problem of composite laminated cylindrical shells are presented. As a result, the numerical efficiency, accuracy and applicability of the proposed formulations are confirmed by the comparison of the published results involving the distributions of the displacements and stresses through the thickness and along the circumferential direction for different staking configurations, geometric properties and boundary conditions.