The influence of torsional-rigidity bounds for composite shafts with specific cross-sections

I. Tung Chan, Tungyang Chen, Min Sen Chiu

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We consider the Saint-Venant torsion problem of composite shafts. Two different kinds of imperfect interfaces are considered. One models a thin interphase of low shear modulus and the other models a thin interphase of high shear modulus. The imperfect interfaces are characterized by parameters given in terms of the thickness and shear modulus of the interphases. Using variational principles, we derive rigorous bounds for the torsional rigidity of composite shafts with cross-sections of arbitrary shapes. The analysis is based on the construction of admissible fields in the inclusions and in the matrix. We obtain the general expression for the bounds and demonstrate the results with some particular examples. Specifically, circular, elliptical and trianglar shafts are considered to exemplify the derived bounds. We incorporate the cross-section shape factor into the bounds and show how the position and size of the inclusion influence the bounds. Under specific conditions, the lower and upper bounds will coincide and agree with the exact torsional rigidity.

Original languageEnglish
Title of host publicationFracture and Strength of Solids VII
PublisherTrans Tech Publications Ltd
Number of pages6
ISBN (Print)9780878492107
Publication statusPublished - 2011

Publication series

NameKey Engineering Materials
ISSN (Print)1013-9826
ISSN (Electronic)1662-9795

All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering


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