A refined theory of torsional deformation of a circular shaft

Zhao, Bin; Gao, Yang; Wu, Xiue

doi:10.1007/s00707-008-0105-8

Cited by 8 publications

(6 citation statements)

References 11 publications

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“…Moreover, Zhao et al [10] supported the application proposed by Cheng by demonstrating a successful example using a circular cylinder. The significance of the method proposed by Cheng is that it opens a systematic way of developing the exact and approximate lower-dimensional theory from a 3D theory with the aid of the general solution of elasticity and symbolic computation.…”

Section: Introductionmentioning

confidence: 84%

Refined analysis of axi-symmetric circular cylinder in the axial magnetic field without ad hoc assumption

et al. 2011

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The refined theory for axi-symmetric magnetoelastic circular cylinder is deduced systematically and directly from linear magnetoelasticity theory. Based on the general solution of magnetoelastic equation and the Lur'e method, the refined theory yields the solutions for magnetoelastic circular cylinder without ad hoc assumptions. On the basis of the refined theory developed in the present study, solutions are obtained for magnetoelastic circular cylinder with homogeneous and non-homogenous boundary conditions, respectively. For the circular cylinder with homogeneous boundary conditions, the refined theory provides exact solutions that satisfy all of the governing equations. The exact solutions can be divided into three parts: the 2-orders equation, the transcendental equation, and the magnetic equation. In the case of non-homogenous boundary conditions, the approximate governing equations are accurate up to the high-order terms with respect to cylinder radius.

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Section: Introductionmentioning

confidence: 84%

Refined analysis of axi-symmetric circular cylinder in the axial magnetic field without ad hoc assumption

et al. 2011

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“…In Appendix of Ref. [10], it is proved that the solutions of Eq. 12 can be decomposed into two parts…”

Section: The Stresses Filed With Homogenous Boundary Conditionmentioning

confidence: 99%

“…In 2005, the connection between the refined theory and the decomposed theorem of an isotropic elasticity plate is analyzed by Zhao and Wang [9]. Zhao et al [10] extend the method to the cylindrical coordinate and deduced systematically and directly the refined theory and the decomposed theorem for torsional circular shaft of physical spaces from elasticity theory.…”

Section: Introductionmentioning

confidence: 99%

The Decomposed Theorem of Torsional Circular Shaft with Two-Dimensional Dodecagonal Quasicrystal

Zhao

Gao

2011

AMR

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Gregory’s decomposed theorem of isotropic plate is extended to investigate torsional circular shaft for two-dimensional dodecagonal quasicrystal (2D dodecagonal QCs)with homogeneous boundary conditions, and the theory of equivalence that Cheng’s refined theory and Gregory’s decomposed theorem is extended to the cylindrical coordinate. The decomposed theorem of torsional circular shaft of 2D dodecagonal QCs with homogeneous boundary conditions is proposed on the basis of the classical elasticity theory and stress-displacement relations of 2D dodecagonal QCs without ad hoc assumptions. At first expressions are obtained for all the displacements and stress components in term of some 1D functions. Using Lur’e method, the exact equations were given. And the exact equations for the torsional circular shaft on 2D dodecagonal QCs without surface loadings consist of four governing differential equations: two harmonic equations and two transcendental equations.

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“…In 2005, the connection between the refined theory and the decomposed theorem of an isotropic elasticity plate is analyzed by Zhao and Wang [6]. Zhao et al [7] extend the method to the cylindrical coordinate and deduced systematically and directly the refined theory and the decomposed theorem for torsional circular shaft of physical spaces from elasticity theory.…”

Section: Introductionmentioning

confidence: 99%

The General Solution for Torsional Circular Shaft of Cubic Quasicrystal

Zhao

Shi

Zhao

et al. 2011

AMR

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Gregory’s decomposed theorem of isotropic plate is extended to investigate torsional circular shaft of cubic quasicrystal with homogeneous boundary conditions, and the theory of equivalence that Cheng’s refined theory and Gregory’s decomposed theorem is extended to the cylindrical coordinate. The general solution of torsional circular shaft on cubic quasicrystal with homogeneous boundary conditions is proposed on the basis of the classical elasticity theory and stress-displacement relations of cubic quasicrystal without ad hoc assumptions. At first expressions are obtained for all the displacements and stress components in term of some 1D functions. Using Lur’e method, the exact equations were given. And the exact equations for the torsional circular shaft on cubic quasicrystal without surface loadings consist of four governing differential equations: two harmonic equations and two transcendental equations. Using basic mathematic method and the general solutions, an example is examined.

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A refined theory of torsional deformation of a circular shaft

Cited by 8 publications

References 11 publications

Refined analysis of axi-symmetric circular cylinder in the axial magnetic field without ad hoc assumption

Refined analysis of axi-symmetric circular cylinder in the axial magnetic field without ad hoc assumption

The Decomposed Theorem of Torsional Circular Shaft with Two-Dimensional Dodecagonal Quasicrystal

The General Solution for Torsional Circular Shaft of Cubic Quasicrystal

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