Limit Analysis for Combined Edge and Pressure Loading on a Cylindrical Shell

Abstract

Equations describing the stress field and velocity field occurring in a circular cylindrical shell at plastic collapse are derived corresponding to stress states lying on each face of a yield surface for a uniform shell of material obeying the Tresca yield condition. They are then applied to the case of a shell under combined axisymmetric loadings (moment, shear force, and axial force) at one end and uniform internal or external pressure on the lateral surface. For a sufficiently long shell, complete solutions are obtained for a fixed far end, and for a certain range of values of axial force and pressure, they are obtained for a free far end. All the solutions are represented by either closed form or by quadratures. It is shown that in many cases the radial velocity field is proportional to the shear force.