Study On Thermoelastic Multi-field Coupling Problem Of Hollow Cylinder And Semi-infinite Rod

The diffused heat conduction equation obtained by the classical couped thermoelastic theory describing the heat propagate in the medium at an infinite speed,it is inconsistent with the observations of physical experiment..With the development of science and technology,the generalized thermoelastic theory has been applied widely.At present,Lord-Shulman(L-S)theory and Green-Lindsay(G-L)theory are the most commonly used theories in the generalized thermoelastic theory,both of the two theories have took the effects of multi-fields coupling into consideration,and at the same time they described the heat propagate at the limited speed in the medium.In terms of many materials and physical processes,it is difficult to describe the thermoelastic behaviors in these situations whether for the classical thermoelastic theory or for the generalized thermoelastic theory.In order to improve the applicability of the generalized thermoelastic theory,scholars introduced the fractional calculus into the generalized thermoelastic theory.The above theories describing the generalized thermoelastic theory is at the situation of microscopic time and macroscopic space.With the advance of high and new technology,the devices show a tendency of miniaturization,the correlations of size arise from these materials,that is the non-local effect.Scholars introduced the Eringen's non-local elastic theory,so as to solve the generalized thermoelastic problem with microscale of time and space,and established the non-localized generalized thermoelastic theory.This paper researched for the following issues based on the fractional calculus generalized thermaoelastic theory and the non-local generalized thermoelastic theory:(1)This paper researched the dynamic responses of the infinite spherical cavity with material characteristic parameters related to the temperature subjected to thermal and stress shock,according to the fractional calculus generalized thermoelasticity theory.The governing equations based on the fractional thermoelastic theory can solved by the Laplace Transform and the Numerical Inverse Transformation,and then we can get regularities of the dimensionless distribution about temperature,displacement,hoop stress and radial stress,and indicate the impacts on the predicted result caused by the fractional calculus.(2)This paper researched the thermal diffusion of the infinite spherical cavity subjected to thermal and chemical shock,according to the fractional calculus generalized thermoelasticity theory.The govering equations based on the fractional thermoelastic theory can solved by the Laplace Transform and the Numerical InverseTransformation,and then we can get the regularities of the dimensionless distributions about temperature,displacement,concentration,chemical potential,hoop stress and radial stress,and indicate the impacts on the physical quantities caused by the fractional calculus parameters.(3)This paper researched the thermal shock dynamic responses of the structure of semi-infinite bar of non-local elastic and non-local heat conduction,according to the generalized thermoelastic theory.The govering equations based on the generalized thermoelastic theory can solved by the Laplace Transform and the Numerical Inverse Transformation,and then we can get the regularities of the dimensionless distributions about temperature,displacement and stresses,and indicate the impacts on the physical quantities caused by the non-local elastic parameters and non-local thermal conduction parameters.