Elastic-plastic stress analysis of large axisymmetrically deflected shallow thin shells of revolution

Abstract

The elastic-plastic stress analysis of a large axisymmetrically deflected shallow thin shell of revolution uses equilibrium, strain-displacement and constitutive relationships. A shell with complex deflection constraints and boundary conditions can be analyzed by experimentally determining the strain history along the axis of revolution, the contour along the generatrix of the shell surface, and the elastic-plastic constitutive relationship. The stress history at the axis of revolution is easily derived from the strain history and takes the place of the boundary conditions in the solution of the equation set. The descriptive relationships reduce to three equations and one inequality in terms of location coordinates, radial and normal displacements, radial and tangential stresses, a functional of the second deviatoric-stress invariant, and constitutive constants.