Thermoelastic field of a transversely isotropic elastic medium containing a penny-shaped crack: exact fundamental solution

Chen, W.Q.; Ding, Hu; Ling, Daosheng

doi:10.1016/j.ijsolstr.2003.08.020

Cited by 75 publications

(50 citation statements)

References 28 publications

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“…from (5.4) and equation (47) in Chen et al [33]. The dimensionless crack surface displacements is illustrated in figure 6.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…where the constant g * 12 is defined in Chen et al [33] and the superscript e denotes the physical quantities derived from theory of thermo-elasticity. From (5.6) and (8.1), it is evident that σ e zz | z=0 , both of which characterize the influence of the phason field.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…Similar to the normal stress in figure 4, the present crack surface displacement and its thermo-elastic counterpart varies in the same fashion. In fact, the expression of the elastic crack surface displacement can be obtained from (32) in Chen et al [33] with the aid of the property of the Dirac-delta function. In our notation, it reads…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…where k 11 (k 33 ) is the coefficient of thermal conductivity, and the operator = ∂ 2 /∂x 2 + ∂ 2 /∂y 2 is the planar Laplacian. It is seen that the influence of body forces in the phonon field, the conservative component of the inner self-action shown in the study of Mariano [29] to exist, associated with the phason field, and the sink and source in the temperature field are not taken into account, in the equilibrium equations (2.1).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Fundamental solutions of penny-shaped and half-infinite plane cracks embedded in an infinite space of one-dimensional hexagonal quasi-crystal under thermal loading

2013

Proc. R. Soc. A.

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“…from (5.4) and equation (47) in Chen et al [33]. The dimensionless crack surface displacements is illustrated in figure 6.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fundamental solutions of penny-shaped and half-infinite plane cracks embedded in an infinite space of one-dimensional hexagonal quasi-crystal under thermal loading

2013

Proc. R. Soc. A.

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“…Yu [11] investigated Green's function for two-phase isotropic thermoelastic materials. By virtue of the general solution of Chen et al [12], Hou et al [13] constructed Green's function for a point heat source acting in the infinite, semi-infinite, and two-phase transversely isotropic thermoelastic materials. Besides, Berger and Tewary [14], Kattis et al [15] obtained two-dimensional Green's functions for the anisotropic thermoelastic materials.…”

Section: Introductionmentioning

confidence: 99%

Study on the Interface Effects Based on Two-Dimensional Green's Functions for the Fluid and Pyroelectric Two-Phase Plane under a Line Heat Source

Hou

Tian

Yuan

2014

Advances in Mechanical Engineering

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Two-dimensional Green's functions for a line heat source applied in the fluid and pyroelectric two-phase plane are presented in this paper. By virtue of the two-dimensional general solutions which are expressed in harmonic functions, six newly introduced harmonic functions with undetermined constants are constructed. Then, all the pyroelectric components in the fluid and pyroelectric two-phase plane can be derived by substituting these harmonic functions into the corresponding general solutions. And the undetermined constants can be obtained by the interface compatibility conditions and the mechanical, electric, and thermal equilibrium conditions. Numerical results are given graphically by contours.

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Green's functions for semi‐infinite transversely isotropic thermoelastic materials

Hou¹,

Leung

Chen

2007

Z Angew Math Mech

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We use the compact mono‐harmonic general solutions of transversely isotropic thermoelastic materials to construct the three‐dimensional Green's function of a steady point heat source in a semi‐infinite transversely isotropic thermoelastic material by three newly introduced mono‐harmonic functions. All components of coupled field are expressed in terms of elementary functions and are convenient to use. Numerical results for hexagonal zinc are given graphically by contours.

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Thermoelastic field of a transversely isotropic elastic medium containing a penny-shaped crack: exact fundamental solution

Cited by 75 publications

References 28 publications

Fundamental solutions of penny-shaped and half-infinite plane cracks embedded in an infinite space of one-dimensional hexagonal quasi-crystal under thermal loading

Fundamental solutions of penny-shaped and half-infinite plane cracks embedded in an infinite space of one-dimensional hexagonal quasi-crystal under thermal loading

Study on the Interface Effects Based on Two-Dimensional Green's Functions for the Fluid and Pyroelectric Two-Phase Plane under a Line Heat Source

Green's functions for semi‐infinite transversely isotropic thermoelastic materials

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