Thermoelastic responses in a nonlocal infinite solid with a circular cylindrical cavity due to a moving heat supply under the MGT model of thermal conductivity

Abstract

Since the non-local continuum theory includes additional information regarding the long-range forces of molecules and atoms, the external length scale parameter may be included in the formulation of physical and engineering modeling. In this study, a new non-local thermoelastic model is presented in which the size-dependent effect has been included in the equations of motion and constitutive relations. To establish the proposed generalized model of heat conduction, the Moore-Gibson-Thompson concept was used. As an application to the presented model, a problem of thermally induced behavior in an infinite nonlocal solid with a cylindrical hole whose surrounding surface is free of traction and affected by a time-dependent moving heat supply is studied. In the transformed field of the Laplace transform, analytical formulas for thermophysical fields have been derived. To obtain the numerical results of the physical field, an approximate approach was applied to find the numerical inversion. The effect of non-localization and heat source velocity on the responses of the investigated fields is graphically illustrated and discussed in detail. The results show that Eringen’s non-local elasticity model is a promising criterion for analyzing nanostructures, taking into account the effect of small size.