Snap-through-type nonlinear creep-buckling of a shallow sinusoidal shell

摘要

This paper is concerned with creep and creep-buckling of the snap-through-type of a shallow, thin-walled, sinusoidalshell subjected to transverse (vertical) pressure. The material is governed by Odqvist's law of nonlinear viscoelasticity. Theshell wall is modelled as a sandwich type to which any actual wall may be reduced and which has been described in detail byHoff and others. The basic equations are formulated, and for a simply supported shell, approximate, analytic solutions areobtained describing the evolution in time of the deflection, i.e., the downward displacement of the initial rise. Instability isassumed to occur when the time rate of this deflection grows beyond all bounds. The time lapse after which instability occursis called the 'critical time' (lifetime) of the shell. It is of finite value for any loading, however small, as long as compressivestresses are created within the shell. If the shell exhibits nonlinear creep only, without elasticity as deformation mechanism,instability occurs when the shell traverses the horizontal plane. The effect of elasticity on the instability process results in aconsiderable reduction of the critical time. Here, instability occurs before the shell has reached the horizontal plane, as asnap-through phenomenon, as soon as the time rate of the deflection grows beyond all bounds.