Creep analysis of orthotropic shells of revolution under asymmetrical loading

The paper describes the numerical analysis of creep problems of orthotropic shells of revolution under asymmetrical loads with application to a cylindrical shell. In this paper the authors study the creep problem of rotationally axisymmetrical shells made of a homogeneous and orthotropic material under asymmetrical load. The equations of equilibrium and the relations between the strains and the displacements are derived from the Sanders theory for thin shells. In the theory of creep it is assumed that in a given increment of time the total strain increments are composed of an elastic part and a part due to creep. The elastic strains are proportional to the stress by Hooke's law for orthotropic materials. The constitutive equations in the creep range are based on the orthotropic creep theory derived from the orthotropic plastic theory by Hill, and the effective creep strain is related to the effective stress by Norton-Vailey equation. The basic differential equations for the incremental values with respect to time are numerically solved by a finite difference method and the solutions at any time are obtained by summation of the incremental values. Resultant forces and resultant moments are given from numerical integration by Simpson's 1/3 rule. As a numerical example the creep deformation of simply supported cylindrical shell subject to asymmetrical, locally distributed load is treated. The numerical computations have been carried out for four cases of anisotropy. The effect of anisotropy has been studied. It is observed that the stress resultant and the displacement distributions are significantly affected by the anisotropy of the material. The analysis of shells in steady creep becomes a subcase of the more general transient creep process described here. (orig./HP)