Nonlinear Through-Thickness Behavior of a Toroidal Shell Using 2-D Finite Elements

Abstract

The use of two-dimensional shell finite elements is explored for finding the three-dimensional state of stress in a toroidal shell. The torus under study represents a 90-degree pipe elbow with a pressure load on a portion of its surface. Layer-wise polynomials are used to represent the transverse shear and normal stretch deformations in the shell. These functions are chosen such that displacements and stresses (but not strains) are continuous at the ply interfaces. Both isotropic and composite (cross-ply) versions of the shell are investigated, and the thicknesses of each are varied to see the effect on through-thickness behavior. Significant qualitative and quantitative differences in these behaviors are observed, particularly in the important direct through-thickness (peeling) stress. The contribution of the transverse deformations to strain energy is investigated and, in most of the shells studied, the thickness stretch component is found to be a greater contributor to strain energy than the transverse shear, though the transverse shear contribution is seen to vary more dramatically with changes in shell thickness.