Incremental stresses in loaded orthotropic circular membrane tubes. I: Theory. II: Numerical solution (Q675517)

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, and shape of the boundary is changed or a slit is formed in the membrane. These changes are regarded as small perturbations imposed on the initial homogeneous state of stress. A numerical method is devised to solve the resulting elliptic sixth order system of equations, for tubes which contain no slits or holes. In this method, Fourier decomposition is used in the circumferential direction and finite element discretization is used in the longitudinal direction. Special finite elements with six degrees-of-freedom are employed. Using this numerical method, the solutions of several specific problems of membrane tubes are obtained, presented and discussed.