Imperfection sensitivity in cylindrical shells under uniform bending

Abstract

Efforts are ongoing to characterise a comprehensive resistance function for cylindrical shells under uniform bending, a ubiquitous structural system that finds application in load-bearing circular hollow sections, tubes, piles, pipelines, wind turbine support towers, chimneys and silos. A recent computational study by Rotter et al. (2014) demonstrated that nonlinear buckling of perfect elastic cylinders under bending is governed by four length-dependent domains-'short', 'medium', 'transitional' and 'long'-depending on the relative influence of end boundary conditions and cross-section ovalisation. The study additionally transformed its resistance predictions into compact algebraic relationships for use as design equations within the recently-developed framework of Reference Resistance Design (RRD). This paper extends on the above to present a detailed computational investigation into the imperfection sensitivity of thin elastic cylindrical shells across the most important length domains, using automation to carry out the vast number of necessary finite element analyses. Geometric imperfections in three forms-the classical linear buckling eigenmode, an imposed cross-section ovalisation, and a realistic manufacturing 'weld depression' defectare applied to demonstrate that imperfection sensitivity is strongly length-dependent but significantly less severe than for the closely-related load case of cylinders under uniform axial compression. The axisymmetric weld depression almost always controls as the most deleterious imperfection. The data is processed computationally to offer an accurate yet conservative lower-bound algebraic design characterisation of imperfection sensitivity for use within the RRD framework. The outcomes are relevant to researchers and designers of large metal shells under bending and will appeal to computational enthusiasts who are encouraged to adopt the automation methodology described herein to explore other structural systems.

Pure bending of pipe-in-pipe systems

“…A similar trend is known to exist in the bifurcation buckling of very short single cylinders and, is related to the effect of boundary conditions on development of membrane stresses [19]. In the vicinity of boundaries, larger moments are required to cause a finite segment of the shell to reach its critical membrane stress [16,21].…”

“…Previous studies [16,19] have shown that the linear elastic buckling moments and shape and number of the wrinkles at the onset of buckling of the tubes, are significantly influenced by their lengths. Using Eigen-buckling analysis in ANSYS [33], and assuming isotropic linear material definition with parameters shown in Table 2 In very short PIP, where the length of the system is of the order of the bending half wave length of the outer pipe, the critical buckling moment is significantly higher than the classical buckling moment of the system proposed in Eq.…”

“…Other researchers examined Brazier's moment theory [16,19,21,25,26,36], and found that the Brazier moment is unachievable because premature bifurcation buckling occurs at a moment which is almost 5% below Br M (Eq. 3).…”

“…2 and 3 suggests that the critical buckling moment of an infinitely long tube is about half of the critical buckling moment of the short tube. The effect of length on the buckling moment of tubes under bending action has been studied by many researchers [16,18,19,21,36]. One of the significant studies conducted by Rotter et al [19] investigated the bending response of cylindrical shells with D/t ≥ 40 (r/t ≥ 20) under geometrically nonlinear but elastic analyses.…”

“…The structural response of a single cylinder under bending has been extensively studied in the past, most notably are the work done by [16][17][18][19][20][21]36]. Previous studies have shown that, thin cylinders (large D/t) subjected to bending may exercise wrinkling and shell-type buckling which eventually results in a localised collapse [19].…”