Bounds for the torsional rigidity of shafts with arbitrary cross-sections containing cylindrically orthotropic fibres or coated fibres

Tungyang Chen, Robert Lipton

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

In this paper we derive bounds for the torsional rigidity of a cylindrical shaft with arbitrary transverse cross-section containing a number of cylindrically orthotropic fibres or coated fibres. The exact upper and lower bounds depend on the constituent shear rigidities, the area fractions, the locations of the reinforcements as well as the geometric shape of the cross-sections. Specific bounds are derived for circular shafts, elliptical shafts and cross-sections of equilateral triangle. Simplified expressions are also deduced for reinforcements with isotropic constituents. We verify that when additional constraints between the constituent properties of the phases are fulfilled, the upper and lower bounds will coincide. In the latter case, the fibres or coated fibres become neutral under torsion and the bounds recover the previously known exact torsional rigidity.

Original languageEnglish
Pages (from-to)3291-3309
Number of pages19
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume463
Issue number2088
DOIs
Publication statusPublished - 2007 Dec 8

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy

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