A novel generalized thermoelasticity model based on memory-dependent derivative

Yu, Yajun; Hu, Wei; Tian, Xiaogeng

doi:10.1016/j.ijengsci.2014.04.014

Cited by 230 publications

(41 citation statements)

References 33 publications

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“…The quotient-difference algorithm based NILT method is more numerically stable giving the same results in a practical way and it has the minimum error. NILT has been widely evaluated in the context of generalized thermoelasticity with fractional calculus, memory-dependent derivative and the nonlocal effect considered [45][46][47].…”

Section: Numerical Implementationmentioning

confidence: 99%

Transient responses of bi-layered structure based on generalized thermoelasticity: Interfacial conditions

Xue

Tian

2015

International Journal of Mechanical Sciences

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Section: Numerical Implementationmentioning

confidence: 99%

Transient responses of bi-layered structure based on generalized thermoelasticity: Interfacial conditions

Xue

Tian

2015

International Journal of Mechanical Sciences

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“…Thus the strain tensor components are given by, e rr = ∂u ∂r , e ψψ = u r , e zz = e rz = e rψ = e ψz = 0 (26) Hence the cubical dilatation e will be of the form, e = ∂u ∂r + u r (27) From equation 18we obtain the stress tensor components as follows:…”

Section: Fig 1 Schematic Diagram Of the Problemmentioning

confidence: 99%

Thermal Memory Response in Magneto-thermoelastic Medium Having Long Cylindrical Cavity

Banerjee

Mukhopadhyay

Shaw

2020

Wseas Transactions on Circuits and Systems

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The present paper deals with the memory response on thermal disturbances emanating from a cylindrical cavity in an unbounded thermoelastic solid. Here we have theoretically demonstrated the memory response of thermal disturbances in the generalized magneto-thermo-elastic materials. Firstly, the characteristics of thermoelastic disturbances originated from the cavity in an unbounded elastic solid under the light of generalized magnetothermoelasticity theory with memory dependent derivatives (MDD). For numerical computation, cylindrical-polar coordinate system with radial symmetry subjected to two different types of heat sources into the cavity are considered. An integral transform method and, while in inverse transformation, an efficient and pragmatic NILT (Numerical Inverse Laplace Transform) is adopted. Finally, parameter studies are performed to evaluate the effect of the kernel function and time delay. For thermal wave the results show appreciable differences with those in the usual magneto-thermoelasticity theory.

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“…Yu et al. [11]) to investigate micro/nano scale sudden heating problem and estimate the nonlocal parameter's effect on the responses. For size effect on heat conduction, Sobolev [12] and Tzou [2] suggested that heat conduction at micro/nanoscale is essentially nonlocal, and classical heat conductive law should be further perfected by introducing material's characteristic length.…”

Section: Introductionmentioning

confidence: 99%

Thermoelastic responses of a nonlocal elastic rod due to nonlocal heat conduction

Sarkar

2020

Z Angew Math Mech

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This is an attempt to design a dynamic model of nonlocal heat conduction in a nonlocal elastic bounded rod. This model is drafted using the Lord-Shulman theory of generalized thermoelasticity due to the involvement of one relaxation time to the heat conduction equation and the equation of motion. This model is then employed to discuss the thermal behavior of the rod when subjected to a moving heat source. Both ends of the rod are assumed to be rigidly fixed and thermally insulated. Analytical solutions for the distribution of temperature, displacement and thermal stresses are obtained using integral transform in the Laplace transform technique is used to obtain the analytical solutions for the field variables such as temperature, displacement and stress. The inverse Laplace transform based on the Zakian method is used to invert the results in the space-time domain. Specific attention is paid to study the effect of thermal nonlocal parameter and the velocity of the moving heat source on the distribution of the field variables. K E Y W O R D SLaplace transform, LS model, nonlocal heat conduction, thermal nonlocal parameter, Zakian algorithm

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A novel generalized thermoelasticity model based on memory-dependent derivative

Cited by 230 publications

References 33 publications

Transient responses of bi-layered structure based on generalized thermoelasticity: Interfacial conditions

Transient responses of bi-layered structure based on generalized thermoelasticity: Interfacial conditions

Thermal Memory Response in Magneto-thermoelastic Medium Having Long Cylindrical Cavity

Thermoelastic responses of a nonlocal elastic rod due to nonlocal heat conduction

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