In this paper, we first establish the global existence and asymptotic behavior of solutions by multiplicative techniques, then further prove the existence of a uniform attractor for a thermoelastic system by using the...In this paper, we first establish the global existence and asymptotic behavior of solutions by multiplicative techniques, then further prove the existence of a uniform attractor for a thermoelastic system by using the method of uniform contractive functions. We finally investigate an alternative result of solutions for the semilinear thermoelastic systems by virtue of the semigroup method.展开更多
This study investigates the stabilization challenge at the boundaries of a type II thermoelastic network with n-star configuration and terminal masses,which experiences non-uniform bounded external disturbances at its...This study investigates the stabilization challenge at the boundaries of a type II thermoelastic network with n-star configuration and terminal masses,which experiences non-uniform bounded external disturbances at its control boundary.This research employs an advanced active disturbance rejection control framework,incorporating an innovative observer with adaptive gain characteristics for precise disturbance estimation,coupled with a robust feedback control mechanism for disturbance compensation.The theoretical analysis establishes rigorous convergence proofs for the proposed time-dependent extended state observer.Furthermore,this investigation utilizes semigroup theory to validate the closed-loop system’s well-posed.Through comprehensive Lyapunov-based analysis,this study confirms the system’s capability to achieve exponential convergence of tracking errors while effectively mitigating disturbance effects.Extensive numerical experiments corroborate the theoretical findings,demonstrating the control scheme’s practical efficacy.展开更多
This paper is concerned with the well-posedness,uniform asymptotic stability and dynamics for a semilinear thermoelastic system with time-varying delay boundary feedback and nonlinear weight,which can be used to descr...This paper is concerned with the well-posedness,uniform asymptotic stability and dynamics for a semilinear thermoelastic system with time-varying delay boundary feedback and nonlinear weight,which can be used to describe the physical procedure of meridian retraction and release therapy.The perturbation theory of inear operators by Kato is used to deal with the invalidity of Lumper-Phillips theorem on non-autonomous PDEs operator,the multiplier approach and quasi-stability method lead to the stability and dynamics for our semilinear problem,which are also true for linear thermoelastic system without weight.展开更多
In this paper, we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques, then further prove the existence of a uniform attractor for a no...In this paper, we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques, then further prove the existence of a uniform attractor for a non-autonomous thermoelastic system by using the method of uniform contractive functions. The main advantage of this method is that we need only to verify compactness condition with the same type of energy estimates as that for establishing absorbing sets. Moreover, we also investigate an alternative result of solutions to the semilinear thermoelastic systems by virtue of the semigroup method.展开更多
The problem of the coupled thermoelasticity has a W. A. Day has studied the nature of the solution ofthe system in which the constant b ￣ 0. In this paper,the existence,uniqueness and properly posed problem of the so...The problem of the coupled thermoelasticity has a W. A. Day has studied the nature of the solution ofthe system in which the constant b ￣ 0. In this paper,the existence,uniqueness and properly posed problem of the solution of the system in which the constant b 4 0 is studied.展开更多
In this paper, we consider a class of Sine-Gordon equations which arise from the model of the thermoelastic coupled rod. Firstly, by virtue of the classical semigroup theory, we prove the existence and uniqueness of t...In this paper, we consider a class of Sine-Gordon equations which arise from the model of the thermoelastic coupled rod. Firstly, by virtue of the classical semigroup theory, we prove the existence and uniqueness of the mild solution under certain initial-boundary value for above-mentioned equations. Secondly, we obtain the boundedness of solutions by the priori estimates. Lastly, we prove the existence of a global attractor.展开更多
This study introduces a novel mathematical model that combines the finite integral transform(FIT)and gradientenhanced physics-informed neural network(g-PINN)to address thermomechanical problems in functionally graded ...This study introduces a novel mathematical model that combines the finite integral transform(FIT)and gradientenhanced physics-informed neural network(g-PINN)to address thermomechanical problems in functionally graded materials with varying properties.The model employs a multilayer heterostructure homogeneous approach within the FIT to linearize and approximate various parameters,such as the thermal conductivity,specific heat,density,stiffness,thermal expansion coefficient,and Poisson’s ratio.The provided FIT and g-PINN techniques are highly proficient in solving the PDEs of energy equations and equations of motion in a spherical domain,particularly when dealing with space-time dependent boundary conditions.The FIT method simplifies the governing partial differential equations into ordinary differential equations for efficient solutions,whereas the g-PINN bypasses linearization,achieving high accuracy with fewer training data(error<3.8%).The approach is applied to a spherical pressure vessel,solving energy and motion equations under complex boundary conditions.Furthermore,extensive parametric studies are conducted herein to demonstrate the impact of different property profiles and radial locations on the transient evolution and dynamic propagation of thermomechanical stresses.However,the accuracy of the presented approach is evaluated by comparing the g-PINN results,which have an error of less than 3.8%.Moreover,this model offers significant potential for optimizing materials in hightemperature reactors and chemical plants,improving safety,extending lifespan,and reducing thermal fatigue under extreme processing conditions.展开更多
With the miniaturization of devices and the development of modern heating technologies,the generalization of heat conduction and thermoelastic coupling has become crucial,effectively emulating the thermodynamic behavi...With the miniaturization of devices and the development of modern heating technologies,the generalization of heat conduction and thermoelastic coupling has become crucial,effectively emulating the thermodynamic behavior of materials in ultrashort time scales.Theoretically,generalized heat conductive models are considered in this work.By analogy with mechanical viscoelastic models,this paper further enriches the heat conduction models and gives their one-dimensional physical expression.Numerically,the transient thermoelastic response of the slim strip material under thermal shock is investigated by applying the proposed models.First,the analytical solution in the Laplace domain is obtained by the Laplace transform.Then,the numerical results of the transient responses are obtained by the numerical inverse Laplace transform.Finally,the transient responses of different models are analyzed and compared,and the effects of material parameters are discussed.This work not only opens up new research perspectives on generalized heat conductive and thermoelastic coupling theories,but also is expected to be beneficial for the deeper understanding of the heat wave theory.展开更多
Laser debonding technology has been widely used in advanced chip packaging,such as fan-out integration,2.5D/3D ICs,and MEMS devices.Typically,laser debonding of bonded pairs(R/R separation)is typically achieved by com...Laser debonding technology has been widely used in advanced chip packaging,such as fan-out integration,2.5D/3D ICs,and MEMS devices.Typically,laser debonding of bonded pairs(R/R separation)is typically achieved by completely removing the material from the ablation region within the release material layer at high energy densities.However,this R/R separation method often results in a significant amount of release material and carbonized debris remaining on the surface of the device wafer,severely reducing product yields and cleaning efficiency for ultra-thin device wafers.Here,we proposed an interfacial separation strategy based on laser-induced hot stamping effect and thermoelastic stress wave,which enables stress-free separation of wafer bonding pairs at the interface of the release layer and the adhesive layer(R/A separation).By comprehensively analyzing the micro-morphology and material composition of the release material,we elucidated the laser debonding behavior of bonded pairs under different separation modes.Additionally,we calculated the ablation threshold of the release material in the case of wafer bonding and established the processing window for different separation methods.This work offers a fresh perspective on the development and application of laser debonding technology.The proposed R/A interface separation method is versatile,controllable,and highly reliable,and does not leave release materials and carbonized debris on device wafers,demonstrating strong industrial adaptability,which greatly facilitates the application and development of advanced packaging for ultra-thin chips.展开更多
The Euler-Bernoulli(E-B)beam theory is combined with Green-Lindsay's(G-L)generalized thermoelasticity theory to analyze the vibration of microbeams.The frequency control equation,based on the two-parameter Winkler...The Euler-Bernoulli(E-B)beam theory is combined with Green-Lindsay's(G-L)generalized thermoelasticity theory to analyze the vibration of microbeams.The frequency control equation,based on the two-parameter Winkler-Pasternak elastic foundation for simply-supported microbeams,is presented.This study investigates the effects of the side-to-thickness ratio and relaxation time parameters on the vibrational natural frequency of thermoelastic microbeam resonators.The frequencies derived from the present model are compared with those from Lord and Shulman's(L-S)theory.The fourthorder solutions for natural vibration frequencies are graphically displayed for comparison.Therefore,attention should be paid to the use of effective foundations to prevent microbeam damage caused by contraction and expansion problems caused by high temperatures.展开更多
In this paper,the multi-scale computational method for a structure of composite materials with a small periodic configuration under the coupled thermoelasticity condition is presented. The two-scale asymptotic(TSA)exp...In this paper,the multi-scale computational method for a structure of composite materials with a small periodic configuration under the coupled thermoelasticity condition is presented. The two-scale asymptotic(TSA)expression of the displacement and the increment of temperature for composite materials with a small periodic configuration under the condition of thermoelasticity are briefly shown at first,then the multi-scale finite element algorithms based on TSA are discussed.Finally the numerical results evaluated by the multi-scale computational method are shown.It demonstrates that the basic configuration and the increment of temperature strongly influence the local strains and local stresses inside a basic cell.展开更多
In extreme heat transfer environments, functionally graded materials(FGMs)have aroused great concern due to the excellent thermal shock resistance. With the development of micro-scale devices, the size-dependent effec...In extreme heat transfer environments, functionally graded materials(FGMs)have aroused great concern due to the excellent thermal shock resistance. With the development of micro-scale devices, the size-dependent effect has become an important issue. However, the classical continuum mechanical model fails on the micro-scale due to the influence of the size-dependent effect. Meanwhile, for thermoelastic behaviors limited to small-scale problems, Fourier's heat conduction law cannot explain the thermal wave effect. In order to capture the size-dependent effect and the thermal wave effect, the nonlocal generalized thermoelastic theory for the formulation of an FGM microbeam is adopted in the present work. For numerical validation, the transient responses for a simply supported FGM microbeam heated by the ramp-type heating are considered.The governing equations are formulated and solved by employing the Laplace transform techniques. In the numerical results, the effects of the ramp-heating time parameter, the nonlocal parameter, and the power-law index on the considered physical quantities are presented and discussed in detail.展开更多
In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractiona...In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractional order generalized thermoelastic diffusive medium are presented. Uniqueness and reciprocity theorems are proved. The plane wave propagation in the homogeneous transversely isotropic thermoelastic diffusive medium with fractional order derivative is studied. For the two-dimensional problem, there exist a quasi-longitudinal wave, a quasi-transverse wave, a quasi-mass diffusion wave, and a quasi-thermal wave. From the obtained results, the different characteristics of waves, like phase velocity, attenuation coefficient, specific loss, and penetration depth, are computed numerically and presented graphically. Some special cases are also discussed.展开更多
This article is concerned with the effect of rotation on the general model of the equations of the generalized thermoe- lasticity for a homogeneous isotropic elastic half-space solid, whose surface is subjected to a M...This article is concerned with the effect of rotation on the general model of the equations of the generalized thermoe- lasticity for a homogeneous isotropic elastic half-space solid, whose surface is subjected to a Mode-I crack problem. The fractional order theory of thermoelasticity is used to obtain the analytical solutions for displacement components, force stresses, and temperature. The boundary of the crack is subjected to a prescribed stress distribution and temperature. The normal mode analysis technique is used to solve the resulting non-dimensional coupled governing equations of the problem. The variations of the considered variables with the horizontal distance are illustrated graphically. Some particular cases are also discussed in the context of the problem. Effects of the fractional parameter, reinforcement, and rotation on the varia- tions of different field quantities inside the elastic medium are analyzed graphically. Comparisons are made between the results in the presence and those in the absence of fiber-reinforcing, rotating and fractional parameters.展开更多
Considering the thermal contact resistance and elastic wave impedance at the interface,in this paper we theoretically investigate the thermo-hydro-mechanical(THM)coupling dynamic response of bilayered saturated porous...Considering the thermal contact resistance and elastic wave impedance at the interface,in this paper we theoretically investigate the thermo-hydro-mechanical(THM)coupling dynamic response of bilayered saturated porous media.Fractional thermoelastic theory is applied to porous media with imperfect thermal and mechanical contact.The analytical solutions of the dynamic response of the bilayered saturated porous media are obtained in frequency domain.Furthermore,the effects of fractional derivative parameters and thermal contact resistance on the dynamic response of such media are systematically discussed.Results show that the effects of fractional derivative parameters on the dynamic response of bilayered saturated porous media are related to the thermal contact resistance at the interface.With increasing thermal contact resistance,the displacement,pore water pressure,and stress decrease gradually.展开更多
The equations of generalized thermoelasticity with one relaxation time with variable modulus of elasticity and the thermal conductivity were used to solve a problem of an infinite material with a spherical cavity.The ...The equations of generalized thermoelasticity with one relaxation time with variable modulus of elasticity and the thermal conductivity were used to solve a problem of an infinite material with a spherical cavity.The inner surface of the cavity was taken to be traction free and acted upon by a thermal shock to the surface. Laplace transforms techniques were used to obtain the solution by a direct approach.The inverse Laplace transforms was obtained numerically.The temperature,displacement and stress distributions are represented graphically.展开更多
The present work is concerned with the solution of a problem on thermoelastic interactions in a functional graded material due to thermal shock in the context of the fractional order three-phase lag model. The governi...The present work is concerned with the solution of a problem on thermoelastic interactions in a functional graded material due to thermal shock in the context of the fractional order three-phase lag model. The governing equations of fractional order generalized thermoelasticity with three-phase lag model for functionally graded materials(FGM)(i.e., material with spatially varying material properties) are established. The analytical solution in the transform domain is obtained by using the eigenvalue approach.The inversion of Laplace transform is done numerically. The graphical results indicate that the fractional parameter has significant effects on all the physical quantities. Thus, we can consider the theory of fractional order generalized thermoelasticity an improvement on studying elastic materials.展开更多
Thermoelastic damping(TED)is one of the main internal energy dissipation mechanisms in micro/nano-resonators.Accurate evaluation of TED is important in the design of micro-electromechanical systems and nano-electromec...Thermoelastic damping(TED)is one of the main internal energy dissipation mechanisms in micro/nano-resonators.Accurate evaluation of TED is important in the design of micro-electromechanical systems and nano-electromechanical systems.In this paper,a theoretical analysis on the TED in functionally graded material(FGM)micro-beam resonators is presented.Equations of motion and the heat conduction equation governing the thermodynamic coupling free vibration of non-homogenous micro-beams are established based on the Euler Bernoulli beam theory associated with the modified couple stress theory.Material properties of the FGM micro-beam are assumed to change in the depth direction as power-law functions.The layer-wise homogenization method is used for solving the heat conduction equation.By using the mathematical similarity of eigenvalue problem between the FGM beam and the reference homogeneous one,the complex natural frequency including TED is expressed in terms of the natural frequency of the isothermal homogenous beam.In the presented numerical results,influences of various characteristic parameters,such as beam thickness,material gradient index,structure size,vibration mode and boundary conditions,on TED are examined in detail.It shows that TED decreases with the increases in the values of length scale parameters because the latter lead to the increase in structural stiffness.展开更多
The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate a...The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate axis on the boundary of the medium. Eigen value approach is applied to study the disturbance in Laplace-Fourier transform domain for a two dimensional problem. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using a numerical technique for the inversion of Laplace transform based on Fourier expansion techniques. These expressions are calculated numerically for a copper like material and depicted graphically. As special cases, the results in generalized thermoelastic and elastic media are obtained. Effect of presence of diffusion is analyzed theoretically and numerically.展开更多
The present investigation is concerned with wave propagation in an electro-microstretch generalized thermoelastic solid half space. Two different cases have been discussed： （i） reflection of plane wave at the free ...The present investigation is concerned with wave propagation in an electro-microstretch generalized thermoelastic solid half space. Two different cases have been discussed： （i） reflection of plane wave at the free surface of an electro-microstretch generalized thermoelastic solid; and （ii） propagation of Rayleigh waves in an electro-microstretch generalized thermoelastic solid half space. In case （i）, the amplitude ratios of the various reflected waves have been computed numerically and depicted graphically against angle of incidence. In case （ii）, the frequency equation is derived and dispersion curves giving phase velocity and attenuation coefficient as a function of wave number, have been plot- ted graphically for a specific model. Some special cases of interest are also deduced, for both the cases.展开更多
文摘In this paper, we first establish the global existence and asymptotic behavior of solutions by multiplicative techniques, then further prove the existence of a uniform attractor for a thermoelastic system by using the method of uniform contractive functions. We finally investigate an alternative result of solutions for the semilinear thermoelastic systems by virtue of the semigroup method.
文摘This study investigates the stabilization challenge at the boundaries of a type II thermoelastic network with n-star configuration and terminal masses,which experiences non-uniform bounded external disturbances at its control boundary.This research employs an advanced active disturbance rejection control framework,incorporating an innovative observer with adaptive gain characteristics for precise disturbance estimation,coupled with a robust feedback control mechanism for disturbance compensation.The theoretical analysis establishes rigorous convergence proofs for the proposed time-dependent extended state observer.Furthermore,this investigation utilizes semigroup theory to validate the closed-loop system’s well-posed.Through comprehensive Lyapunov-based analysis,this study confirms the system’s capability to achieve exponential convergence of tracking errors while effectively mitigating disturbance effects.Extensive numerical experiments corroborate the theoretical findings,demonstrating the control scheme’s practical efficacy.
基金partially supported by Henan Overseas Expertise Introduction Center for Discipline Innovation(No.CXJD2020003)the innovation grant for Ph.D in Henan Normal University.
文摘This paper is concerned with the well-posedness,uniform asymptotic stability and dynamics for a semilinear thermoelastic system with time-varying delay boundary feedback and nonlinear weight,which can be used to describe the physical procedure of meridian retraction and release therapy.The perturbation theory of inear operators by Kato is used to deal with the invalidity of Lumper-Phillips theorem on non-autonomous PDEs operator,the multiplier approach and quasi-stability method lead to the stability and dynamics for our semilinear problem,which are also true for linear thermoelastic system without weight.
基金Supported by the National Natural Science Foundation of China(No.1127106611671075)a grant from Shanghai Municipal Eduction Commission(No.13ZZ048)
文摘In this paper, we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques, then further prove the existence of a uniform attractor for a non-autonomous thermoelastic system by using the method of uniform contractive functions. The main advantage of this method is that we need only to verify compactness condition with the same type of energy estimates as that for establishing absorbing sets. Moreover, we also investigate an alternative result of solutions to the semilinear thermoelastic systems by virtue of the semigroup method.
文摘The problem of the coupled thermoelasticity has a W. A. Day has studied the nature of the solution ofthe system in which the constant b ￣ 0. In this paper,the existence,uniqueness and properly posed problem of the solution of the system in which the constant b 4 0 is studied.
文摘In this paper, we consider a class of Sine-Gordon equations which arise from the model of the thermoelastic coupled rod. Firstly, by virtue of the classical semigroup theory, we prove the existence and uniqueness of the mild solution under certain initial-boundary value for above-mentioned equations. Secondly, we obtain the boundedness of solutions by the priori estimates. Lastly, we prove the existence of a global attractor.
文摘This study introduces a novel mathematical model that combines the finite integral transform(FIT)and gradientenhanced physics-informed neural network(g-PINN)to address thermomechanical problems in functionally graded materials with varying properties.The model employs a multilayer heterostructure homogeneous approach within the FIT to linearize and approximate various parameters,such as the thermal conductivity,specific heat,density,stiffness,thermal expansion coefficient,and Poisson’s ratio.The provided FIT and g-PINN techniques are highly proficient in solving the PDEs of energy equations and equations of motion in a spherical domain,particularly when dealing with space-time dependent boundary conditions.The FIT method simplifies the governing partial differential equations into ordinary differential equations for efficient solutions,whereas the g-PINN bypasses linearization,achieving high accuracy with fewer training data(error<3.8%).The approach is applied to a spherical pressure vessel,solving energy and motion equations under complex boundary conditions.Furthermore,extensive parametric studies are conducted herein to demonstrate the impact of different property profiles and radial locations on the transient evolution and dynamic propagation of thermomechanical stresses.However,the accuracy of the presented approach is evaluated by comparing the g-PINN results,which have an error of less than 3.8%.Moreover,this model offers significant potential for optimizing materials in hightemperature reactors and chemical plants,improving safety,extending lifespan,and reducing thermal fatigue under extreme processing conditions.
基金Project supported by the Guangdong Basic and Applied Basic Research Foundation of China(No.2023A1515012809)the Natural Science Foundation of Shaanxi Province of China(No.2023-JC-YB-073)the Fundamental Research Funds for the Central Universities of China(No.D5000230066)。
文摘With the miniaturization of devices and the development of modern heating technologies,the generalization of heat conduction and thermoelastic coupling has become crucial,effectively emulating the thermodynamic behavior of materials in ultrashort time scales.Theoretically,generalized heat conductive models are considered in this work.By analogy with mechanical viscoelastic models,this paper further enriches the heat conduction models and gives their one-dimensional physical expression.Numerically,the transient thermoelastic response of the slim strip material under thermal shock is investigated by applying the proposed models.First,the analytical solution in the Laplace domain is obtained by the Laplace transform.Then,the numerical results of the transient responses are obtained by the numerical inverse Laplace transform.Finally,the transient responses of different models are analyzed and compared,and the effects of material parameters are discussed.This work not only opens up new research perspectives on generalized heat conductive and thermoelastic coupling theories,but also is expected to be beneficial for the deeper understanding of the heat wave theory.
基金the National Natural Science Foundation of China(62174170)the Natural Science Foundation of Guangdong Province(2024A1515010123)+4 种基金the Shenzhen Science and Technology Program(20220807020526001)the Strategic Priority Research Program of the Chinese Academy of Sciences(XDB0670000)the Shenzhen Science and Technology Program(KJZD20230923114708018,KJZD20230923114710022)the Talent Support Project of Guangdong(2021TX06C101)the Shenzhen Basic Research(JCYJ20210324115406019).
文摘Laser debonding technology has been widely used in advanced chip packaging,such as fan-out integration,2.5D/3D ICs,and MEMS devices.Typically,laser debonding of bonded pairs(R/R separation)is typically achieved by completely removing the material from the ablation region within the release material layer at high energy densities.However,this R/R separation method often results in a significant amount of release material and carbonized debris remaining on the surface of the device wafer,severely reducing product yields and cleaning efficiency for ultra-thin device wafers.Here,we proposed an interfacial separation strategy based on laser-induced hot stamping effect and thermoelastic stress wave,which enables stress-free separation of wafer bonding pairs at the interface of the release layer and the adhesive layer(R/A separation).By comprehensively analyzing the micro-morphology and material composition of the release material,we elucidated the laser debonding behavior of bonded pairs under different separation modes.Additionally,we calculated the ablation threshold of the release material in the case of wafer bonding and established the processing window for different separation methods.This work offers a fresh perspective on the development and application of laser debonding technology.The proposed R/A interface separation method is versatile,controllable,and highly reliable,and does not leave release materials and carbonized debris on device wafers,demonstrating strong industrial adaptability,which greatly facilitates the application and development of advanced packaging for ultra-thin chips.
基金the Deanship of Research and Graduate Studies at King Khalid University for funding this work through a large research project(No.RGP2/80/45)。
文摘The Euler-Bernoulli(E-B)beam theory is combined with Green-Lindsay's(G-L)generalized thermoelasticity theory to analyze the vibration of microbeams.The frequency control equation,based on the two-parameter Winkler-Pasternak elastic foundation for simply-supported microbeams,is presented.This study investigates the effects of the side-to-thickness ratio and relaxation time parameters on the vibrational natural frequency of thermoelastic microbeam resonators.The frequencies derived from the present model are compared with those from Lord and Shulman's(L-S)theory.The fourthorder solutions for natural vibration frequencies are graphically displayed for comparison.Therefore,attention should be paid to the use of effective foundations to prevent microbeam damage caused by contraction and expansion problems caused by high temperatures.
基金The project supported by the National Natural Science Foundation of China(19932030)Special Funds for Major State Basic Research Projects
文摘In this paper,the multi-scale computational method for a structure of composite materials with a small periodic configuration under the coupled thermoelasticity condition is presented. The two-scale asymptotic(TSA)expression of the displacement and the increment of temperature for composite materials with a small periodic configuration under the condition of thermoelasticity are briefly shown at first,then the multi-scale finite element algorithms based on TSA are discussed.Finally the numerical results evaluated by the multi-scale computational method are shown.It demonstrates that the basic configuration and the increment of temperature strongly influence the local strains and local stresses inside a basic cell.
基金Project supported by the National Natural Science Foundation of China (Nos. 11972176 and12062011)the Incubation Programme of Excellent Doctoral Dissertation-Lanzhou University of Technology。
文摘In extreme heat transfer environments, functionally graded materials(FGMs)have aroused great concern due to the excellent thermal shock resistance. With the development of micro-scale devices, the size-dependent effect has become an important issue. However, the classical continuum mechanical model fails on the micro-scale due to the influence of the size-dependent effect. Meanwhile, for thermoelastic behaviors limited to small-scale problems, Fourier's heat conduction law cannot explain the thermal wave effect. In order to capture the size-dependent effect and the thermal wave effect, the nonlocal generalized thermoelastic theory for the formulation of an FGM microbeam is adopted in the present work. For numerical validation, the transient responses for a simply supported FGM microbeam heated by the ramp-type heating are considered.The governing equations are formulated and solved by employing the Laplace transform techniques. In the numerical results, the effects of the ramp-heating time parameter, the nonlocal parameter, and the power-law index on the considered physical quantities are presented and discussed in detail.
基金the Council of Scientific and Industrial Research(CSIR),India
文摘In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractional order generalized thermoelastic diffusive medium are presented. Uniqueness and reciprocity theorems are proved. The plane wave propagation in the homogeneous transversely isotropic thermoelastic diffusive medium with fractional order derivative is studied. For the two-dimensional problem, there exist a quasi-longitudinal wave, a quasi-transverse wave, a quasi-mass diffusion wave, and a quasi-thermal wave. From the obtained results, the different characteristics of waves, like phase velocity, attenuation coefficient, specific loss, and penetration depth, are computed numerically and presented graphically. Some special cases are also discussed.
文摘This article is concerned with the effect of rotation on the general model of the equations of the generalized thermoe- lasticity for a homogeneous isotropic elastic half-space solid, whose surface is subjected to a Mode-I crack problem. The fractional order theory of thermoelasticity is used to obtain the analytical solutions for displacement components, force stresses, and temperature. The boundary of the crack is subjected to a prescribed stress distribution and temperature. The normal mode analysis technique is used to solve the resulting non-dimensional coupled governing equations of the problem. The variations of the considered variables with the horizontal distance are illustrated graphically. Some particular cases are also discussed in the context of the problem. Effects of the fractional parameter, reinforcement, and rotation on the varia- tions of different field quantities inside the elastic medium are analyzed graphically. Comparisons are made between the results in the presence and those in the absence of fiber-reinforcing, rotating and fractional parameters.
基金Project supported by the National Natural Science Foundation of China(Nos.52108347 and 51779217)the Primary Research and Development Plan of Zhejiang Province(Nos.2019C03120 and 2020C01147),China。
文摘Considering the thermal contact resistance and elastic wave impedance at the interface,in this paper we theoretically investigate the thermo-hydro-mechanical(THM)coupling dynamic response of bilayered saturated porous media.Fractional thermoelastic theory is applied to porous media with imperfect thermal and mechanical contact.The analytical solutions of the dynamic response of the bilayered saturated porous media are obtained in frequency domain.Furthermore,the effects of fractional derivative parameters and thermal contact resistance on the dynamic response of such media are systematically discussed.Results show that the effects of fractional derivative parameters on the dynamic response of bilayered saturated porous media are related to the thermal contact resistance at the interface.With increasing thermal contact resistance,the displacement,pore water pressure,and stress decrease gradually.
文摘The equations of generalized thermoelasticity with one relaxation time with variable modulus of elasticity and the thermal conductivity were used to solve a problem of an infinite material with a spherical cavity.The inner surface of the cavity was taken to be traction free and acted upon by a thermal shock to the surface. Laplace transforms techniques were used to obtain the solution by a direct approach.The inverse Laplace transforms was obtained numerically.The temperature,displacement and stress distributions are represented graphically.
文摘The present work is concerned with the solution of a problem on thermoelastic interactions in a functional graded material due to thermal shock in the context of the fractional order three-phase lag model. The governing equations of fractional order generalized thermoelasticity with three-phase lag model for functionally graded materials(FGM)(i.e., material with spatially varying material properties) are established. The analytical solution in the transform domain is obtained by using the eigenvalue approach.The inversion of Laplace transform is done numerically. The graphical results indicate that the fractional parameter has significant effects on all the physical quantities. Thus, we can consider the theory of fractional order generalized thermoelasticity an improvement on studying elastic materials.
基金Project supported by the National Natural Science Foundation of China(No.11672260)the Natural Science Foundation of Jiangsu(No.BK20180894).
文摘Thermoelastic damping(TED)is one of the main internal energy dissipation mechanisms in micro/nano-resonators.Accurate evaluation of TED is important in the design of micro-electromechanical systems and nano-electromechanical systems.In this paper,a theoretical analysis on the TED in functionally graded material(FGM)micro-beam resonators is presented.Equations of motion and the heat conduction equation governing the thermodynamic coupling free vibration of non-homogenous micro-beams are established based on the Euler Bernoulli beam theory associated with the modified couple stress theory.Material properties of the FGM micro-beam are assumed to change in the depth direction as power-law functions.The layer-wise homogenization method is used for solving the heat conduction equation.By using the mathematical similarity of eigenvalue problem between the FGM beam and the reference homogeneous one,the complex natural frequency including TED is expressed in terms of the natural frequency of the isothermal homogenous beam.In the presented numerical results,influences of various characteristic parameters,such as beam thickness,material gradient index,structure size,vibration mode and boundary conditions,on TED are examined in detail.It shows that TED decreases with the increases in the values of length scale parameters because the latter lead to the increase in structural stiffness.
文摘The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate axis on the boundary of the medium. Eigen value approach is applied to study the disturbance in Laplace-Fourier transform domain for a two dimensional problem. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using a numerical technique for the inversion of Laplace transform based on Fourier expansion techniques. These expressions are calculated numerically for a copper like material and depicted graphically. As special cases, the results in generalized thermoelastic and elastic media are obtained. Effect of presence of diffusion is analyzed theoretically and numerically.
文摘The present investigation is concerned with wave propagation in an electro-microstretch generalized thermoelastic solid half space. Two different cases have been discussed： （i） reflection of plane wave at the free surface of an electro-microstretch generalized thermoelastic solid; and （ii） propagation of Rayleigh waves in an electro-microstretch generalized thermoelastic solid half space. In case （i）, the amplitude ratios of the various reflected waves have been computed numerically and depicted graphically against angle of incidence. In case （ii）, the frequency equation is derived and dispersion curves giving phase velocity and attenuation coefficient as a function of wave number, have been plot- ted graphically for a specific model. Some special cases of interest are also deduced, for both the cases.
