Zhang-Na Xue

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

ABSTRACT In this work, fractional order theory of thermoelasticity is applied to a bilayered structure being in imperfect thermal and mechanical contact. The model is subjected to a sudden heating at the traction-free end, assumed to be undisturbed at infinity. The heat conduction in each medium is described by the time-fractional heat conduction equations with two fractional order parameters, respectively. An analytical technique based on Laplace transform is adopted. Numerical results are computed and represented graphically, from which the effects of fractional derivative parameters of both media, thermal contact resistance, elastic wave impedance ratio on the responses are discussed.

Two-dimensional thermal shock problem of generalized thermoelastic multilayered structures considering interfacial conditions

ABSTRACT A two-dimensional model of the generalized thermoelasticity with one relaxation time is established. The resulting nondimensional coupled equations together with the Laplace and Fourier transform techniques are applied to a specific problem of multilayered structures considering thermal resistance subjected to thermal shock and traction-free surface. The solutions in the transformed domain are obtained by a direct approach. Numerical inversion techniques are used to obtain the inverse double transform. Numerical results are represented graphically to estimate the effects of the thermal resistance and thermal conductivities on the temperature, displacement, and stress distributions.

Nonlocal thermoelastic analysis with fractional order strain in multilayered structures

ABSTRACT Classical thermoelasticity may be challenged to give accurate responses with the miniaturization of devices and wide application of ultrafast lasers. In this work, to simulate the thermoelastic responses of multilayered structures, classical thermoelasticity is extended in two aspects: in mechanical sense, Eringen’s nonlocal elasticity is used to depict the size-dependence; meanwhile, fractional order strain is considered to describe the mechanical phenomena caused by viscoelasticity. Laplace transform is adopted, upon which the effects of elastic nonlocal parameter, mechanical relaxation time, and fractional order parameter on the thermoelastic responses under different theories are investigated. Finally, numerical results are given and illustrated graphically.

Study of a generalized thermoelastic diffusion bi-layered structures with variable thermal conductivity and mass diffusivity

Abstract Physical properties may change with temperature and concentration, especially in high temperature and concentration. In this work, the dynamical treatment of a bi-layered structure is implemented under the generalized thermoelastic diffusion theory. To distinguish from existed works, variable thermal conductivity and mass diffusivity of both media are considered. The model is subjected to a sudden thermal shock and a chemical shock, respectively. An analytical technique based on Laplace transform is adopted. Numerical results are evaluated and represented graphically, from which the effects of thermal conductivity and mass diffusivity of both media on the responses are discussed. And finally, some concluding remarks are summarized, based upon which the structure may be optimized by adopting suitable material parameter in both thermal and diffusive sense.

Effects of two-temperature parameter and thermal nonlocal parameter on transient responses of a half-space subjected to ramp-type heating

Abstract Based upon the coupled thermoelasticity and Green and Lindsay theory, the new governing equations of two-temperature thermoelastic theory with thermal nonlocal parameter is formulated. To more realistically model thermal loading of a half-space surface, a linear temperature ramping function is adopted. Laplace transform techniques are used to get the general analytical solutions in Laplace domain, and the inverse Laplace transforms based on Fourier expansion techniques are numerically implemented to obtain the numerical solutions in time domain. Specific attention is paid to study the effect of thermal nonlocal parameter, ramping time, and two-temperature parameter on the distributions of temperature, displacement and stress distribution.