Investigations On The Semi-infinite Body Problem Subjected To Steady-state And Transient Heat Source In Nanoscale

With the incessant development of nanoscience and nanotechnology,the production,testing and analysis of nano-structure/material are all related to the thermoelastic problem of nano-scale heat source heating solid material's surface.The interaction,relaxation,reconstruction and transport of atoms at(or near)the surface have significant effects on the thermal properties of such materials at nano-scale,such as scale correlation and thermoelasticity.However,in the existing theory of the thermoelasticity,since the constitutive equation does not have intrinsic length,its theoretical prediction is independent of scale.The theory of thermoelasticity which takes into account the surface effect can well reflect the thermoelastic behavior of the surface heating by the nanometer scale heat source.In this paper,based on the surface thermaloelastc theory,the problem of semi-infinite surface heated by nano-scale heat source is studied.The main work is as follow:?The basic theory of surface/interface elasticity and thermoelastic are explained in detail.The basic theory and numerical method of hyper-singular integral equation are discussed.The hyper-singular integral equation is transformed into a linear equation by using the definition of the Chebyshev orthogonal polynomial finite-part integral and its function series to fit the integral function,and then the numerical solution of the unknown function is obtained.The above work lays the theoretical foundation for the follow-up work.?The half-space problem heated by nano-scale steady-state heat source is studied.Employing the double Fourier transforms,the basic solutions of thermoelasticity considering the surface effect are deduced.As the application and verification of the model,the displacement fields and stress fields of the surface of the aluminum metal loaded by a steady-state heat source in nanoscale are studied and compared with the classical linear thermoelastic solutions.The results show that the surface effect has a significant effect on the thermoelastic field near the surface of the material.The smaller the heating radius is,the more obvious the surface effect is.Thus the scale effect existing in such problems are explained.Beside,compared with classical results(Sneddon and Lockett,1960),the new results render the significant effects of the surface stress and thermal expansion coefficient on the stress distributions in the half-space when the radius of heating area is reduced to the nano-scale.Indeed,under the nanoscale heated radius the stress component in the heating zone in relation to the vertical direction of the surface is not zero.?The thermoelastic problem due to a transient point heat source loading over the surface of a half-plane is investigated.Using the nonclassical boundary conditions,the problem of gaining the displacement solutions of the half-plane heated by transient point heat source is transformed into a mathematical model of the hyper-singular integral equations with respect to the normal displacement and tangential displacement of the surface.Then,the numerical solutions of the displacement field are obtained by using the algorithm of hyper-singular integral function.The validity of the algorithm is verified by the coincidence of the curves between the numerical solution and the theoretical solution.As a special case,only the displacement solution considering the effect of surface tension is solved.The results of numerical computing show that the solutions considering the surface effect are significantly different from those of classical thermoelasticityand the existence of residual surface tension makes the normal displacement of the surface heating region significantly reduced,but has little effect on the corresponding tangential displacement.