Static inconsistencies in certain axiomatic higher-order shear deformation theories for beams, plates and shells

R. M J Groh*, P. M. Weaver

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

45 Citations (Scopus)
403 Downloads (Pure)

Abstract

Static inconsistencies that arise when modelling the flexural behaviour of beams, plates and shells with clamped boundary conditions using a certain class of axiomatic, higher-order shear deformation theory are discussed. The inconsistencies pertain to displacement-based theories that enforce conditions of vanishing shear strain at the top and bottom surfaces a priori. First it is shown that the essential boundary condition of vanishing Kirchhoff rotation perpendicular to an edge (. w,x=0 or w,y=0) is physically inaccurate, as the rotation at a clamped edge may in fact be non-zero due to the presence of transverse shear rotation. As a result, the shear force derived from constitutive equations erroneously vanishes at a clamped edge. In effect, this boundary condition overconstrains the structure leading to underpredictions in transverse bending deflection and overpredictions of axial stresses compared to high-fidelity 3D finite element solutions for thick and highly orthotropic plates. Generalised higher-order theories written in the form of a power series, as in Carrera's Unified Formulation, do not produce this inconsistency. It is shown that the condition of vanishing shear tractions at the top and bottom surfaces need not be applied a priori, as the transverse shear strains inherently vanish if the order of the theory is sufficient to capture all higher-order effects. Finally, the transverse deflection of the generalised higher-order theories is expanded in a power series of a non-dimensional parameter and used to derive a material and geometry dependent shear correction factor that provides more accurate solutions of bending deflection than the classical value of 5/6.

Original languageEnglish
Pages (from-to)231-245
Number of pages15
JournalComposite Structures
Volume120
Issue numberFebruary
Early online date14 Oct 2014
DOIs
Publication statusPublished - 1 Feb 2015

Keywords

  • Higher-order theories
  • Transverse shear deformation
  • Principle of virtual displacements

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