Creep buckling of shell structures

Abstract

The present article contains a review of the literatures on the creep buckling of shell structures published from late 1950's to recent years. In this article, the creep buckling studies on circular cylindrical shells, spherical shells, partial cylindrical shells and other shells are reviewed in addition to creep buckling criteria. Creep buckling is categorized into two types. One is the creep buckling due to quasi-static instability, in which the critical time for creep buckling is determined by tracing a creep deformation versus time curve. The other is the creep buckling due to kinetic instability, in which the critical time can be determined by examining the shape of total potential energy in the vicinity of a quasi-static equilibrium state. Bifurcation buckling and snap-through buckling during creep deformation belong to this type of creep buckling. A few detailed descriptions are given to the bifurcation and snap-through type of creep buckling based on the present authors' works.

Delayed buckling of spherical shells due to viscoelastic knockdown of the critical load

“…While a limited number of experimental contributions have come about since, to our knowledge our experiments on full spheres are novel to the existing creep buckling literature. Furthermore, we have demonstrated that some concepts central to general creep buckling theories, which previously were mostly tested on metallic, mono-resin materials, and reinforced concrete [49], are indeed applicable to soft, rubbery materials. We expect that the concepts we have studied can be extended to other geometries, other loading methods, and similar polymers.…”

“…Traditional analytical approaches to capture the critical time and/or the associated critical deflection (that is, the deflection at the onset of instability) for creep buckling involve incorporating calculated quantities for stress and strain into the constitutive model (in our case equation (2.2)). Instability may be identified by solving the eigenvalue problem of the governing differential equations, or by the quasi-static ‘critical strain approach’ [48] wherein the strain state at the point of buckling must be known or assumed a priori , and the corresponding time is directly solved for [49]. These methods require precise representations of the stresses and strains throughout deformation, and have met moderate success in capturing experimental behaviour for simple structures like columns [50,51], trusses and arches [52], plates and even cylinders [48].…”

“…These methods require precise representations of the stresses and strains throughout deformation, and have met moderate success in capturing experimental behaviour for simple structures like columns [50,51], trusses and arches [52], plates and even cylinders [48]. (See [49] for a review of the relatively recent work on creep buckling of shell structures, or [46] for an earlier review on creep buckling of plates and shells.) A clear problem with these approaches is that it is generally assumed that a shell undergoing creep will lose stability at the same strain as its elastic counterpart [53,54].…”

Delayed buckling of spherical shells due to viscoelastic knockdown of the critical load

“…3). Instability may be identified by solving the eigenvalue problem of the governing differential equations, or by the quasi-static "critical strain approach" [48] wherein the critical strain must be known or assumed a priori, and the corresponding time is directly solved for [49]. These methods require precise representations of the stresses and strains throughout deformation, and have met moderate 3.…”

“…(See Ref. [49] for a review of the relatively recent work on creep buckling of shell structures, or Ref. [46] for an earlier review on creep buckling of plates and shells.…”