A Critical Strain Approach to Creep Buckling of Plates and Shells

Abstract

A creep buckling hypothesis presented previously suggested that the known solutions for short-time buckling can be used in terms of critical strain to estimate creep buckling.The major portion of the paper is concerned with a creep buckling investigation of aluminum cylinders under compressive and torsional loads. The test techniques and equipment are described in some detail. The results of the experiments are correlated with the critical strain approach, and good agreement is obtained both in terms of critical strain and critical time. Some preliminary data on creep buckling of cylinders under cyolid load conditions are also presented.An examination of test data on creep of long flat plates under compressive loads indicates that the theory may be adequate for plates of small width-thickness ratio. Plates of large widththickness ratio which can buckle upon the initial application of load require an analysis of the post-buckled state under creep conditions. SYMBOLS b = plate width, in. E = modulus of elasticity, psi E s = secant modulus, psi G = shear modulus, psi h = plate thickness, in. L -length, in. R = radius, in. t = time, hours 7 = shear strain, in./in. e = strain, in./in. v = Poisson's ratio a a = applied creep stress, psi r a = applied creep shear stress, psi r cr = critical shear stress, psi(1) INTRODUCTION I N REFERENCE 1, an hypothesis was advanced for estimating the critical time for creep buckling of columns, plates, and shells. This hypothesis suggested that, as an engineering approximation, creep buckling occurred when the critical strain determined from elastic and plastic stability considerations was reached in the creep process.

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

“…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].…”

“…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]. (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.)…”

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.…”

“…success in capturing experimental behavior for simple structures like columns [50,51], trusses and arches [52], plates and even cylinders [48]. (See Ref.…”

Creep buckling of shell structures

“…Earlier works (Gerard, 1958;Bozajior, 1958;Hoff, 1959) on the creep buckling of circular cylindrical shells under axial compression were based on the analogy of elastic and plastic instability called critical strain approach. In this approach, creep buckling is assumed to occur when the critical strain determined from elastic and plastic instability considerations is reached in creep process.…”