Solid or shell finite elements to model thick cylindrical tubes and shells under global bending

Adam J. Sadowski*, J. Michael Rotter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper explores the use of solid continuum finite elements and shell finite elements in the modelling of the nonlinear plastic buckling behaviour of cylindrical metal tubes and shells under global bending. The assumptions of shell analysis become increasingly uncertain as the ratio of the radius of curvature to the thickness becomes smaller, but the classical literature does not draw a clear line to define when a shell treatment is inappropriate and a continuum model becomes essential. This is a particularly important question for the bending of tubular members, pipelines, chimneys, piles, towers and similar structures. This study is therefore concerned solely with the uniform bending of thin tubes or thick shells which fail by plastic buckling well into the strain-hardening range. The analyses employ finite element formulations available in the commercial software ABAQUS because this is the most widely used tool for parametric research studies in this domain with an extensive and diverse element library. The results are of general validity and are applicable to other finite element implementations. This paper thus seeks to determine the adequacy of a thin or thick shell approximation, taking into account geometric nonlinearity, complex equilibrium paths, limit points and bifurcation buckling, extensive material, ductility and linear strain hardening. It aims to establish when it is viable to employ shell elements and when this decision will lead to outcomes that lack sufficient precision for engineering design purposes.

The results show that both thin and thick (shear-flexible) shell elements may give a reasonably accurate prediction of the buckling moment under global uniform bending for cylindrical tubes as thick as R/t=10. A finite strain and thick shell formulation is additionally shown to model the ductility of such thick tubes well, even when ovalisation of the cross-section and strain hardening are included. The use of solid continuum elements to model tubes in bending is found to become increasingly uneconomical as the R/t ratio rises above 25 with reduced advantages over shell elements, both in terms of the accuracy of the solution and the computation time. (C) 2013 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)143-153
Number of pages11
JournalInternational journal of mechanical sciences
Publication statusPublished - Sep 2013


  • Shell finite elements
  • Continuum solid finite elements
  • Plasticity
  • Strain hardening
  • Thick cylindrical shells
  • Bending


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