INCREMENTAL STRESSES IN LOADED ORTHOTROPIC CIRCULAR MEMBRANE TUBES .1. THEORY

Starting from the equations of general elastic nonlinear membrane theo ry in intrinsic form, the equations governing the incremental slate of stress in an orthotropic circular membrane tube are derived and discu ssed. The tube is initially subjected to uniform internal pressure and to longitudinal extension, which lead to large homogeneous deformatio n. Then some changes in loading and/or geometry are considered, e.g. a n 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 poten tial functions. Two different variational formulations for the problem are also presented, each of which may serve as a basis for numerical treatment.