Axisymmetric deformation in transversely isotropic magneto-thermoelastic solid with Green–Naghdi III due to inclined load

When a two-dimensional elastic body that contains a notch or a crack is under a plane stress or plane strain deformation, the asymptotic solution of the stress near the apex of the notch or crack is simply a series of eigenfunctions of the form ρδf (ψ,δ) in which (ρ,ψ) is the polar coordinate with origin at the apex and δ is the eigenvalue. If the body is a three-dimensional elastic solid that contains axisymmetric notches or cracks and subjected to an axisymmetric deformation, the eigenfunctions associated with an eigenvalue contains not only the ρδ term, but also the ρδ+1, ρδ+2… terms. Therefore, the second and higher-order terms of the asymptotic solution are not simply the second and subsequent eigenfunctions. We present the eigenfunctions for transversely isotropic materials under an axisymmetric deformation. The degenerate case in which the eigenvalues p1 and p2 of the elasticity constants are identical is also considered. The latter includes the isotropic material as a special case.

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Singularity at the Interface Edge of Bonded Transversely Isotropic Piezoelectric Dissimilar Materials. 2nd Report. The Solution for an Interface Edge under Axisymmetric Deformation.

TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series A ◽

10.1299/kikaia.66.1590 ◽

2000 ◽

Vol 66 (648) ◽

pp. 1590-1596

Author(s):

Jinquan XU ◽

Yoshiharu MUTOH

Keyword(s):

Dissimilar Materials ◽

Transversely Isotropic ◽

Axisymmetric Deformation ◽

Interface Edge

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Reflection of Plane Waves in a Rotating Transversly Isotropic Magneto-Thermoelastic Solid Half-Space

Journal of Theoretical and Applied Mechanics ◽

10.2478/v10254-012-0013-0 ◽

2012 ◽

Vol 42 (3) ◽

pp. 33-60 ◽

Cited By ~ 12

Author(s):

Baljeet Singh ◽

Anand Yadav

Keyword(s):

Magnetic Fields ◽

Half Space ◽

Plane Waves ◽

Transversely Isotropic ◽

Reflection Coefficients ◽

Governing Equations ◽

Thermoelastic Medium ◽

Reflected Waves ◽

Velocity Equation ◽

Thermoelastic Solid

Reflection of Plane Waves in a Rotating Transversly Isotropic Magneto-Thermoelastic Solid Half-SpaceThe governing equations of a rotating transversely isotropic magneto-thermoelastic medium are solved to obtain the velocity equation, which indicates the existence of three quasi plane waves. Reflection of these plane waves from a stress-free thermally insulated surface is studied to obtain the reflection coefficients of various reflected waves. The effects of anisotropy, rotation, thermal and magnetic fields are shown graphically on these coefficients.

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A Circular Elastic Cylinder Under Extension

Journal of Mechanics ◽

10.1017/jmech.2011.42 ◽

2011 ◽

Vol 27 (3) ◽

pp. 399-407 ◽

Cited By ~ 1

Author(s):

W.-D. Tseng ◽

J.-Q. Tarn

Keyword(s):

Transversely Isotropic ◽

Elastic Cylinder ◽

Axisymmetric Deformation ◽

Axial Stiffness ◽

Stress Distributions ◽

End Effect ◽

Rigorous Solution ◽

Concentrated Load ◽

End Conditions ◽

Space Formalism

ABSTRACTAnalysis of deformation and stress field in a circular elastic cylinder under the extension is presented, with emphasis on the end effect. The problem is formulated on the basis of the state space formalism for axisymmetric deformation of transversely isotropic materials. A rigorous solution that satisfies the prescribed end conditions is determined by using symplectic eigenfunction expansion, thereby, the applicability of the Saint-Venant solution is examined. The results show that the end effect is significant but confined to a local region near the base of the cylinder where the end plane is perfectly bonded or subjected to a concentrated load. As the axial stiffness increases, the end effect on the stress state increases at the loaded end but decreases at the bonded end. The displacement and stress distributions across the section are uniform throughout the length of the cylinder except near the ends.

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