Application of fractional order theory of thermoelasticity to a bilayered structure with interfacial conditions

Xue, Zhangna; Yu, Yajun; Li, Chen-Lin; Tian, Xiaogeng

doi:10.1080/01495739.2016.1192451

Cited by 16 publications

(5 citation statements)

References 24 publications

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“…When

{\eta _{\rm{T}}} = 1

, Equation (37a) is degraded into the jump thermal contact model 19,28 :

$$\begin{equation}q_T^{(J)}(z,t)\left| {_{z = \sum\nolimits_{n = 1}^J {{H_n}} }} \right. = {R_{\rm{T}}}\left[ {{{\left.

…”

Section: Interfacial Conditionsmentioning

confidence: 99%

“…Abd EI-Latief and Khader 18 compared the predictions of fractional order theory with those generalized theory of thermoelasticity in the temperature, displacement and stress distributions of layered structure. Xue et al 19 studied the thermal conductivity characteristics of a bi-layered structure based on the fractional order theory of thermoelasticity and discussed the effects of fractional derivative parameters. The above thermal elastic theory has deepened our understanding of the THM coupling process of multilayered media.…”

Section: Introductionmentioning

confidence: 99%

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Fractional derivative modelling for rheological characteristics of multilayered saturated porous rock with interfacial thermal contact resistance

Wen

et al. 2023

Num Anal Meth Geomechanics

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In this paper, the one‐dimensional rheological characteristics of multilayered saturated porous rock subjected to a ramp‐type heating is investigated. By introducing the fractional order parameter and material parameters, a viscoelastic constitutive model is proposed to describe the rheological characteristics of multilayered saturated porous rock. The general incomplete thermal contact model is established to predict the interfacial thermal contact resistance of multilayered saturated porous rock. Based on the coupled thermo‐hydro‐mechanical theory, the semi‐analytical solutions of the excess pore water pressure, temperature increment and displacement are obtained by using the Laplace transform method. The accuracy of the present solutions is verified by comparing with the classic elastic and viscoelastic models, and existing solutions. In addition, the influence of fractional order parameter, material parameter ratio, thermal contact transfer coefficient and thermal partition coefficient on the excess pore water pressure, temperature increment and displacement of multilayered saturated porous rock are investigated.

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“…When

{\eta _{\rm{T}}} = 1

, Equation (37a) is degraded into the jump thermal contact model 19,28 :

$$\begin{equation}q_T^{(J)}(z,t)\left| {_{z = \sum\nolimits_{n = 1}^J {{H_n}} }} \right. = {R_{\rm{T}}}\left[ {{{\left.

…”

Section: Interfacial Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fractional derivative modelling for rheological characteristics of multilayered saturated porous rock with interfacial thermal contact resistance

Wen

et al. 2023

Num Anal Meth Geomechanics

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show abstract

“…The analytical approach is expected to provide some supplement value for numerical methods that cannot capture the imperfect contact characteristics. Xue et al 38 . introduced the fractional‐order theory of thermoelasticity into the analysis of the thermoelastic responses of a bilayered structure.…”

Section: Introductionmentioning

confidence: 99%

“…The analytical approach is expected to provide some supplement value for numerical methods that cannot capture the imperfect contact characteristics. Xue et al 38 introduced the fractional-order theory of thermoelasticity into the analysis of the thermoelastic responses of a bilayered structure. Analytical results based on Laplace transform indicated that the increase of thermal contact resistance would increase the temperature difference at the interface and further led to increasing deformation of the contact layer.…”

Section: Introductionmentioning

confidence: 99%

A general interfacial thermal contact model for consolidation of bilayered saturated soils considering thermo‐osmosis effect

Wen

Tian

et al. 2022

Num Anal Meth Geomechanics

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In this paper, a general interfacial thermal contact model is proposed to investigate the heat conduction characteristics at the interface of bilayered saturated soils. The semianalytical solutions of thermal consolidation of the bilayered saturated soils considering thermo-osmosis effect under ramp-type heating are derived by using the Laplace transform. Then, the expressions of the temperature increment, excess pore water pressure, and displacement are obtained in time domain by using the Crump's method. Comparisons are performed to verify the rationality of the obtained solutions, and the influences of contact transfer coefficient, partition coefficient, and the thermo-osmosis coefficient on the thermal consolidation of the bilayered saturated soil are illustrated and discussed. Neglecting the thermal contact resistance would overestimate the thermal consolidation behavior of the bilayered saturated soils. The calculated excess pore water pressure and displacement considering thermo-osmosis effect are much larger than those without thermo-osmosis effect.

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“…Xue et al. [44, 45] dealt with a generalized thermoelastic problem for a bi-layered structure based on the fractional order theory and a two-dimensional thermal shock problem of generalized thermoelastic multi-layered structure, while the interface continuous conditions were applied.…”

Section: Introductionmentioning

confidence: 99%

Transient responses of sandwich structure based on the generalized thermoelastic diffusion theory with memory-dependent derivative

2018

Jnl of Sandwich Structures & Materials

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The present work is devoted to investigating the transient responses of a sandwich structure based on the generalized thermoelastic diffusion theory with memory-dependent derivative. Both the left and the right bounding surfaces are subjected to a thermal shock and a chemical potential shock simultaneously. It is assumed that the values of thermal contact resistance and diffusional contact impedance at the interface are zero with ideal adhesion. The coupled governing equations containing time delay factors and kernel functions, which can be chosen freely according to specific problems, are solved by the Laplace transform together with its numerical inversion. The influences of the material characteristic parameters at the interface on the structural responses are emphatically discussed, and the non-dimensional temperature, chemical potential, displacement, stress as well as concentration at different values of time delay factors and kernel functions are obtained and illustrated graphically. The results show that: the changes of the time delay factors, kernel functions, and material characteristic parameters have the varying degrees of influences on the considered variables. Based on the above conclusions, the sandwich structure working under the thermoelastic diffusion coupling condition can be designed reasonably.

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Application of fractional order theory of thermoelasticity to a bilayered structure with interfacial conditions

Cited by 16 publications

References 24 publications

Fractional derivative modelling for rheological characteristics of multilayered saturated porous rock with interfacial thermal contact resistance

Fractional derivative modelling for rheological characteristics of multilayered saturated porous rock with interfacial thermal contact resistance

A general interfacial thermal contact model for consolidation of bilayered saturated soils considering thermo‐osmosis effect

Transient responses of sandwich structure based on the generalized thermoelastic diffusion theory with memory-dependent derivative

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