A finite element-difference computational model for stress analysis of layered composite cylindrical shells

Abstract

A C⁰ finite element space discretization procedure is employed in a general fibre-reinforced composite cylindrical shell theory based on a higher-order displacement model. The displacement model incorporates non-linear variation of tangential displacement components through the thickness of the shell. The use of a shear correction coefficient thus becomes redundant. The discrete element chosen is a nine-noded Lagrangian quadrilateral with seven degrees of freedom per node. Two formulations, one in which (h/R) « 1 and another in which (h/R)² « 1, are derived. After the nodal displacements are obtained from the global finite element analysis, the secondary quantities are determined element-wise. The planar lamina stresses are computed through the constitutive relations while the transverse shear stresses are estimated by making use of the equilibrium equations. A special finite difference scheme is developed to integrate the equilibrium equations with a view to estimate transverse/interlaminar stresses across the shell thickness. The transverse/interlaminar stresses computed by the above technique do maintain the continuity at the interface of two layers. The results obtained are compared with available elasticity, closed-form and other finite element solutions.