Investigation On The Multi-field Coupling Problem Of Two-dimensional Elastomers Under Fractional Order Thermoelastic Theory

According to the classical Fourier's heat conduction law,the propagation velocity of heat is infinite,and the heat flux is directly proportional to the temperature gradient.For the steady-state heat transfer process with long heat action time and the unsteady conventional heat transfer process with fast heat propagation speed,the results obtained by classical Fourier's heat conduction law are accurate.But for some extreme conditions,such as ultra-high temperature heat transfer,ultra-low temperature heat transfer and micro scale heat transfer,the classical Fourier's heat conduction law is no longer applicable.In order to overcome the limitations of the classical Fourier's heat conduction law,the non-Fourier's heat conduction theory was put forward.With the development of non-Fourier heat conduction theory,some theories pointed out the existence of heat wave propagating at a finite velocity,and then these theories were collectively referred to as the generalized thermoelastic theory.The generalized thermoelastic theory mainly includes the L-S theory proposed by Lord-Shulman,which introduces a thermal relaxation time factor and heat flux term into the Fourier heat conduction equation;the G-L theory proposed by Green-Lindsay,which introduces a thermal relaxation time factor into the constitutive equation and the energy conservation equation respectively,and the rate of temperature change is considered in the heat conduction equation;the G-N theory without energy dissipation proposed by Green-Naghdi.With the development of science and technology,the thermoelastic behavior of some special materials and physical processes couldn't be described by the generalized thermoelastic theory.However,these "abnormal" phenomena could be accurately described by fractional calculus.Different from integer calculus,fractional calculus has the advantage of describing complex problems more accurately,and is widely used in scientific research,engineering technology and other fields.In order to establish a more widely applicable model,some scholars pointed out that fractional calculus could be used to modify the generalized thermoelastic theory,and fractional order generalized thermoelastic theory was gradually established.At present,Sherief type and Youssef type fractional order generalized thermoelastic theories are widely used.In this thesis,the Sherief type fractional order generalized thermoelastic theory is introduced to establish a two-dimensional isotropic homogeneous elastomer model,and the multi-field coupling problem of two-dimensional elastomer is studied.The main contents are as follows:(1)Based on Sherief type fractional order generalized thermoelasticity theory,the multi-field coupling problem of two-dimensional thermoelasticity considering gravity field is studied under the effect of thermal shock.By considering the influence of gravity on fiber reinforced medium,the governing equations are established.The governing equations are solved through numerical calculation by using the normal mode method.And the distributions of non-dimensional temperature,displacement and stress are obtained.The results show that the gravity field has a significant effect on the temperature,displacement and stress,while the influence of fractional order parameters on temperature,displacement and stress is finite.(2)Based on the Sherief type fractional order generalized thermoelastic theory,the multi-field coupling problem of two-dimensional electromagnetic thermoelasticity with the influence of gravity field is studied under the effect of the moving heat source.By considering the influence of magnetic field,gravity field and moving heat source on fiber reinforced medium,the governing equations are established.The distributions of non-dimensional temperature,displacement and stress are obtained through numerical calculation by using the normal mode method.The results show that the magnetic field,gravity field and moving heat source have significant effects on temperature,displacement and stress while the influence of fractional order parameters on temperature,displacement and stress is finite.(3)Based on Sherief type fractional order generalized thermoelastic theory,the multi-field coupling problem of two-dimensional electromagnetic thermoelasticity with the influence of rotation is studied under the effect of the moving heat source.By considering the influence of magnetic field,rotation and reinforcement on fiber reinforced medium,the governing equations are established.The distributions of non-dimensional temperature,displacement and stress are obtained through numerical calculation by using the normal mode method.The results show that the magnetic field,rotation and reinforcement have significant effects on the temperature,displacement and stress,while the influence of fractional order parameters on temperature,displacement and stress is finite.