Exact connections of warping fields and torsional rigidities of symmetric composite bars

Tungyang Chen, Y. S. Lin, J. C. Ju

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Saint-Venant's torsion of symmetric cylindrical bars consisting of two or four homogeneous phases is studied. A symmetric section is meant that the cross section of the cylindrical bar possesses reflectional symmetry with respect to one or more axes. Each constituent region may have different shear modulus. The idea of the analysis is to superimpose suitably reflected potentials to obtain the torsion solution of the same composite section but with different moduli. For two-phase sections, we show that, if the warping fields for a given symmetric section with phase shear moduli μ1 and μ2 are known a priori, then the warping fields for the same configuration but with a different set of constituent moduli μ1′ and μ2′ are readily found through simple linear superpositions. Further, suppose that the torsional rigidities T (μ1, μ2) and T(μ1′, μ2′) for any two sets of phase moduli can be measured by some experimental tests or evaluated through numerical procedures, then the torsional rigidity for any other combinations of constituent moduli T(μ1″, μ2″) can be exactly determined without any recourse to the field solutions of governing differential equations. Similar procedures can be applied to a 4-phase symmetric section. But the coefficients of superposition are only found for a few branches. Specifically, we find that depending on the conditions of μ and μ′, admissible solutions can be divided into three categories. When the correspondence between the warping field is known to exist, a link between the torsional rigidities can be established as well.

Original languageEnglish
Pages (from-to)247-266
Number of pages20
JournalJournal of Elasticity
Volume67
Issue number3
DOIs
Publication statusPublished - 2002 Dec 1

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Rigidity
Torsional stress
Composite materials
Elastic moduli
Differential equations

All Science Journal Classification (ASJC) codes

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

Cite this

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abstract = "Saint-Venant's torsion of symmetric cylindrical bars consisting of two or four homogeneous phases is studied. A symmetric section is meant that the cross section of the cylindrical bar possesses reflectional symmetry with respect to one or more axes. Each constituent region may have different shear modulus. The idea of the analysis is to superimpose suitably reflected potentials to obtain the torsion solution of the same composite section but with different moduli. For two-phase sections, we show that, if the warping fields for a given symmetric section with phase shear moduli μ1 and μ2 are known a priori, then the warping fields for the same configuration but with a different set of constituent moduli μ1′ and μ2′ are readily found through simple linear superpositions. Further, suppose that the torsional rigidities T (μ1, μ2) and T(μ1′, μ2′) for any two sets of phase moduli can be measured by some experimental tests or evaluated through numerical procedures, then the torsional rigidity for any other combinations of constituent moduli T(μ1″, μ2″) can be exactly determined without any recourse to the field solutions of governing differential equations. Similar procedures can be applied to a 4-phase symmetric section. But the coefficients of superposition are only found for a few branches. Specifically, we find that depending on the conditions of μ and μ′, admissible solutions can be divided into three categories. When the correspondence between the warping field is known to exist, a link between the torsional rigidities can be established as well.",
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Exact connections of warping fields and torsional rigidities of symmetric composite bars. / Chen, Tungyang; Lin, Y. S.; Ju, J. C.

In: Journal of Elasticity, Vol. 67, No. 3, 01.12.2002, p. 247-266.

Research output: Contribution to journalArticle

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