Incremental stresses in loaded orthotropic circular membrane tubes—I. Theory

Abstract

Starting from the equations of general elastic nonlinear membrane theory in intrinsic form, the equations governing the incremental state of stress in an orthotropic circular membrane tube are derived and discussed. The tube is initially subjected to uniform internal pressure and to longitudinal extension, which lead to large homogeneous deformation. Then some changes in loading and/or geometry are considered, e.g. an additional load is applied, the shape of the boundary is changed or a slit is formed in the membrane. These changes are regarded as small perturbations on the initial homogeneous state of stress. The general form as well as some simplified forms of the equations are presented, leading finally to a set of two equations in terms of two scalar potential functions. Two different variational formulations for the problem are also presented, each of which may serve as a basis for numerical treatment.