Transverse shear and normal stresses in nonlinear shell theory

Abstract

Failure in composite shells often occurs at the interface between material layers due to inter-laminar shear or transverse normal stresses. To understand these failures, it is important to accurately predict the transverse direction stresses that develop due to arbitrary loading on curved shells undergoing large deformations. This work solves the nonlinear, three-dimensional equilibrium equations for through thickness shear and normal stresses in single-director shell theory assuming slowly varying shell curvature and surface tractions and small thickness to radius of curvature ratio. For linear plate theory, the transverse shear stress distribution reduces to the usual parabolic distribution without resorting to uni-directional, pure bending assumptions. It is shown that the equilibrium-determined stresses match well with finite element predictions.