Stability of shells in creep

Abstract

We consider a thin homogeneous shell subjected to an arbitrary load causing loss of stability. We assume that the shell has some initial irregularities in its middle surface which can be described in terms of certain initial displacements. When the load is applied, these initial irregularities begin to develop due to creep and cause a redistribution of stresses over both the thickness and the entire area of the shell. This process of stress redistribution may be so considerable that at a certain moment the equilibrium state of the shell may become unstable in Euler's sense, i.e., at a certain moment several modes of equilibrium may be possible, transition to any one of these being instantaneous. We shall call this moment the “critical moment” of loss of stability of the shell.

The deviation of the subcritical stress and strain state of an actual shell from the basic state corresponding to a perfectly smooth shell can be described by a system of equations in the stress and deflection functions, assuming that the quantities characterizing these deviations satisfy linearlized creep relations analogous to the relations for viscoelastic bodies. This system of equations must be combined with a system of stability equations which takes into account the stresses and strains defined by the system of equations of the subcritical state.