Thermoelastic Model Research Articles

Uniform decay rates of a coupled suspension bridges with temperature

In this paper, we investigate the decay properties of the thermoelastic suspension bridges model. We prove that the energy is decaying exponentially. To our knowledge, our result is new and our method of proof is based on the energy method to build the appropriate Lyapunov functional.

Robust topology optimization for thermoelastic hierarchical structures with hybrid uncertainty

This paper presents a robust topology optimization (RTO) framework for thermoelastic hierarchical structures with hybrid uncertainty. Firstly, the thermoelastic concurrent optimization model is established and the uncertainties with interval random parameters are integrated into the thermoelastic hierarchical structure. Then, a reliable and cost-effective hybrid uncertainty perturbation analysis method (HUPAM) is derived for a quick estimate of the robust objective function subject to the mechanical and thermal loads. Finally, by calculating the design variables sensitivities of macroscale and microscale, the robust topological design can be generated efficiently. To obtain clear and optimal topologies for both macro- and micro- structures, the bi-directional evolutionary structural optimization (BESO) method is adopted. Some 2D and 3D numerical examples are presented to demonstrate the influences of the hybrid uncertainties on the final designs. The results also show that the proposed method can effectively improve the thermoelastic structural performance when it comes to uncertainties.

Advanced thermoelastic heat conduction model with two fractional parameters and phase-lags

In this paper, a generalized thermoelastic model is established by incorporating two-fractional thermal conduction and multi-phase-lags. The Fourier heat conduction model is replaced by a more general formulation. Several models of generalized thermoelasticity including fractional derivatives are extracted from the considered model. The adopted model is examined to solve the problem of a semi-infinite medium subjected to a body force together with decaying heat source. Moreover, by utilizing the Laplace transform approach, the analytical solution of the problem is achieved. To illustrate the effects of decaying parameter, two fractional variables and also the external force, several numerical examples are conducted and the results are presented through some graphs and tables. Finally, our findings are justified compared to those reported in the literature.

Topology optimization of thermo-hyperelastic structures utilizing inverse motion based form finding

The inverse motion concept is used to optimize thermo-hyperelastic structures using an exact description of the deformed geometry. This method prescribes the shape of the structure in the deformed state, and the optimization yields the shape of the undeformed configuration, i.e. the manufactured state. The kinematics of the thermoelastic model is defined through the multiplicative decomposition of the deformation gradient in combination with neo-Hookean hyperelasticity. To regularize the optimization problem and obtain distinct boundaries, the mathematical design field is thresholded using a smoothed Heaviside function and smeared using a partial differential equation. The sensitivity analyses of the objective function and constraints are both based on the adjoint method. The capabilities of the proposed approach are shown by numerical examples wherein the weight is minimized and the performance of multi-material compliant mechanisms is optimized.

Variable thermal conductivity during photo-thermoelasticy theory of semiconductor medium induced by laser pulses with hyperbolic two-temperature theory

In this work, the effects of interaction between elastic and plasma-thermal waves are studied in the framework of the hyperbolic two-temperature theory. The basic equations are formed during the photo-excitation processes in the context of the photothermal theory. A laser pulse illuminates the outer surface of a semiconductor medium whose thermal conductivity is variable. Three different models of the generalized photo-thermoelasticity theory are applied to a 2D deformation problem. The integral transforms technique are used to solve the problem by applying the double transforms Fourier and Laplace. The inversion of Fourier and Laplace transforms is obtained according to Honig and Hirdes technique. The thermal, mechanical and recombination plasma loads are utilized at the medium-free surface to attain the complete solutions of the main physical fields. A comparison between the three different models of thermoelasticity is performed; in addition, the influence of some physical parameters are studied. Si material has been utilized as an example to ensure the validity of the attained solution.

Higher-order time-differential heat transfer model with three-phase lag including memory-dependent derivatives

Memory-dependent derivative (MDD) has become a new hot spot in many fields, including vibration mechanics, particle physics and thermoelasticity due to its simple formulation and high expressive force. In this study, a new generalized mathematical thermoelastic model that includes a high-order heat transfer law with different phase delays is developed based on the MD derivatives. The time delay in this new concept represents the duration of the memory influence, while the kernel function represents the dependent weight. A problem of an infinite thermoelastic half-space whose surface is stress-free and periodically heated by a laser-pulse is described in order to validate the proposed model. The system of equations is solved using Laplace transforms technique as well as its inversion is applied based on an appropriate numerical technique. Changes in thermophysical fields are obtained with several values of higher-order time derivatives. The effects of kernel function, time delay parameters and laser pulse duration are also investigated and explained by giving some graphs and tables. Moreover, certain comparisons are made taking into account the various unique features of the current model as well as when the memory effect is ignored. The results indicate that MDD is more suitable for modeling thermoelasticity.

Analysis of two temperature thermoelastic diffusion plate with variable thermal conductivity and diffusivity

ABSTRACT The current study explores the transient response of a thermoelastic plate in the light of the two-temperature generalized thermoelastic diffusion model involving variable thermal conductivity and diffusivity. The boundary of the plate is designed as mechanical, thermal, and concentration loadings on one side and rigidly fixed, insulated and impermeable on the other side. The thermal conductivity and diffusivity are assumed to be the linear function of thermodynamic temperature and concentration, respectively. Hence, governing equations are non-linear and transformed into linear form by applying Kirchhoff's transform. Transformed governing equations are solved by using the Laplace–Fourier transform technique. In the transform region, the closed form of expressions for conductive and thermodynamic temperature, displacement and stress components, mass concentration, and chemical potential are obtained. Numerical results are obtained by mathematical inversion technique for various quantities obtained analytically in closed form in the transform domain and depicted graphically to illustrate the impacts of variable thermal conductivity, variable diffusivity, and two temperature.

Analytical solution for thermoelastic oscillations of nonlocal strain gradient nanobeams with dual-phase-lag heat conduction

In order to examine the impact of structural and thermal scale parameters on thermoelastic vibrations of Euler-Bernoulli nanobeams, this article intends to provide a size-dependent generalized thermoelasticity model with the help of nonlocal strain gradient theory (NSGT) in conjunction with dual-phase-lag (DPL) heat conduction model. To highlight the role of each scale parameter in size-dependent motion and heat conduction equations, normalized forms of these nonclassical coupled thermoelastic equations are extracted by introducing and exploiting some dimensionless parameters. By exploiting power series expansion as a general solution for arbitrary boundary conditions, system of partial differential equations reduces to system of ordinary differential equations in time domain. The Laplace transform is then utilized to attain the analytical solution of this set of differential equations. By conducting a case study on a hinged-hinged nanobeam, with the aim of illustrating the impact of nonclassical structural and thermal parameters on thermoelastic vibrations, size-dependent numerical results are compared with those estimated by classical elasticity theory and heat conduction model. Meaningful disparity between classical and nonclassical results reveals the pivotal role of scale parameters in realistic assessment of thermoelastic behavior of nanobeams. Outcomes also indicate that corresponding to the relationship between the magnitudes of two scale parameters of NSGT, the nonclassical model of nanobeam can exhibit either softening or hardening behavior compared to the classical one. This affirms the ability of NSGT to justify both stiffness softening and stiffness hardening phenomenon in nanostructures.

Memory Response in Thermoelastic Plate with Three-Phase-Lag Model

In this article, using memory-dependent derivative (MDD) on three-phase-lag model of thermoelasticity, a new generalized model of thermoelasticity theory with time delay and kernel function is constructed. The governing coupled equations of the new generalized thermoelasticity with time delay and kernel function are applied to two dimensional problem of an isotropic plate. The two dimensional equations of generalized thermoelasticity with MDD are solved using state space approach. Numerical inversion method is employed for the inversion of Laplace and Fourier transforms. The displacements, temperature and stress components for different thermoelastic models are presented graphically and the effect of different kernel and time delay on the considered parameters are observed.

Thermo‐viscoelastic behavior in an infinitely thin orthotropic hollow cylinder with variable properties under the non‐Fourier MGT thermoelastic model

AbstractThe purpose of this work is to investigate the influences of viscosity and the variation of thermal conductivity on the thermoelastic vibrations in a very thin hollow cylinder. The generalized thermal model has been developed using the Moore Gibson‐Thompson (MGT) equation by adding relaxation time in the developed Fourier law according to Green‐Naghdi theories. In addition to the initial conditions, some boundary conditions have been taken into consideration on the inner and external surface of the hollow solid cylinder. Unlike many problems in which the coefficient of thermal conductivity is assumed to be constant, it has been taken into account that it is variable and depends on the change of temperature. By applying the Laplace transform method, the numerical solutions are assigned to the studied physical quantities. The studied quantities have been presented graphically and in tabular form to compare the outcomes for various models of thermoelasticity and to illustrate the influences of changing thermal properties and viscosity on the physical fields.

Analysis of thermal performance and thermal stress using two-dimensional thermoelastic model for a 50 MWe external cylindrical solar receiver

Analysis of thermal performance and thermal stress using two-dimensional thermoelastic model for a 50 MWe external cylindrical solar receiver

The crack propagation and surface formation mechanism of single crystalline diamond by a nanosecond pulsed laser

In this article, the surface formation mechanism of single crystalline diamond (SCD) by a nanosecond pulsed laser is performed, where surface cracking, phase transformation, and typical surface morphology are involved. The nanometric surface characteristics of the ablated micro-grooves on the diamond caused by the thermal effect are first studied, where the crack generation and propagation are discussed by the thermoelastic bending model for the laser irradiation process. In addition, the composed phases and the formation mechanism of the induced metamorphic layer (IML) and deposited metamorphic layer (DML) near the ablated groove are investigated, where the diamond/graphite transition layer is the coexistence of the distributed crystalline diamond and the oriented graphite, the direction of which is at an angle of 60°–80° to the laser scanning direction and toward the center of the ablated groove. Based on the subsurface exploration and the grain growth kinetics analysis, the formation process of the DML is proposed as follows: the nucleation → the formation of carbon islands → the combination of the carbon islands → the formation of the deposited metamorphic layer.

Thermoelastic responses in rotating nanobeams with variable physical properties due to periodic pulse heating

Recently, many researchers have been interested in the so-called theories of nonlocal elasticity (NET) and modified couple stress (MCS). The effect of size and dependence on the micron scale was predicted using this theory. A new set of equations was created that governs this theory including the equation for a couple of moments and the use of the concept of couple stress elasticity. Also, the generalized thermoelastic model with phase lag is used. The present work concentrated on introducing thermoelastic rotating nanobeams structural analysis under periodic pulse heating by applying the non-local MCS theory and generalized thermoelastic theory. The thermal conductivity of the material is considered to be variable and linearly dependent on changes in temperature. Laplace transform and state space methods are used to obtain the physical fields of the nanobeam. The effects of size and non-local factors, variability of thermal conductivity, centrifugal force due to rotation and couple stress on different field variables are visually presented and examined in depth.

Time-nonlocal six-phase-lag generalized theory of thermoelastic diffusion with two-temperature

A mathematical model for time-nonlocal six-phase-lag generalized thermoelastic diffusion with two-temperature is proposed for a linear, isotropic and homogeneous thermoelastic diffusive continuum by considering modified Fourier's law of heat conduction together with modified Fick's law of mass diffusion. The modified Fourier's law includes temperature gradient and thermal displacement gradient among the constitutive variables whereas the modified Fick's law includes chemical potential gradient and the chemical potential displacement gradient among the constitutive variables. The Fourier's law of heat conduction is replaced by a fractional-order approximation to a modification of the Fourier's law with three different phase lags for the heat flux vector, the temperature gradient and the thermal displacement gradient whereas the Fick's law of mass diffusion is replaced by a fractional-order approximation to a modification of the Fick's law with three different phase lags for the mass flux vector, the chemical potential gradient and the chemical potential displacement gradient. The proposed model includes some of the existing thermoelastic diffusion models as special cases. A variational principle is derived and a uniqueness theorem is proved. Finally, a dynamic reciprocity theorem is established for the proposed generalized thermoelastic diffusion model.

Thermo-viscoelastic orthotropic constraint cylindrical cavity with variable thermal properties heated by laser pulse via the MGT thermoelasticity model

Abstract In the past few decades, many models have been proposed to address the shortcomings found in the classical theories of thermoelasticity and to allow limited speeds of heat waves. In this context, in the current paper a new generalized model of thermoelasticity based on the Moore–Gibson–Thompson (MGT) equation has been introduced. This new model can be derived by introducing the relaxation time factor into the third type of Green–Naghdi model (GN-III). In contrast to the previous works, it was taken into account that the physical properties of the material are dependent on temperature and on the viscous type. The viscoelastic medium has been assumed to obey the Kelvin–Voigt model. On the basis of the present model, thermo-viscoelastic interactions have been investigated in an unbounded orthotropic body with a cylindrical cavity. The surface of the cavity is restricted and exposed to a pulse-formed heat flow that dissolves exponentially. The characteristic thermal modulus of the material is assumed to be a linear function of temperature. The Laplace transform can be used to eliminate time dependency from control equations. Using a suitable approximate method, the transformed equations have been finally inverted by numerical inversion of the Laplace transform. Certain comparisons have been introduced to estimate the effects of the viscosity, pulsed heat, and thermal temperature-independent properties on all studied fields. A comparison with previous models of thermoelasticity is also performed in tables to verify the accuracy of the proposed model. We found from the results that the physical fields strongly depend on the viscoelastic parameter, the change of the thermal conductivity, and pulsed heat, so it is not possible to neglect their effect on the manufacturing process of machines and devices.

Computational Study on Skin Tissue Freezing Using Three-Phase Lag Bioheat Model

Abstract This paper considers the three-phase lag (TPL) bioheat model to study the phase change phenomena in skin tissue during cryosurgery. The considered TPL model is based on the model of thermo-elasticity, i.e., the combination of the rate of thermal conductivity and new phase lag (τv) due to thermal displacement. An effective heat capacity-based numerical algorithm is established to solve the nonlinear governing equation for biological tissue freezing. Space and time derivatives appearing in the mathematical model are approximated using the radial basis function (RBF) and finite difference method (FDM), respectively. The impact of three nonclassical models, single-phase lag (SPL), dual-phase lag (DPL), and TPL, on the freezing process is studied. The effects of phase lags involved in the models on freezing are also part of this study.

Ultrafast optical stress on BaFe2As2

We investigate the ultrafast lattice dynamics in ${\mathrm{BaFe}}_{2}{\mathrm{As}}_{2}$ via time-resolved x-ray diffraction measurements using an x-ray free-electron laser at SPring-8 Angstrom Compact free-electron LAser (SACLA). The profile of the Bragg peaks substantially changes after strong photoexcitation, where the $c$ axis length of the lattice initially contracts, followed by expansion. These ultrafast lattice contractions and expansions significantly depend on the pump fluence, and it is suggested that a strong normal stress is applied along the $c$ axis. To obtain a phenomenological understanding of the observed lattice dynamics, we performed calculations based on a two-temperature model and an ultrafast thermoelasticity model. Our results showed that a steep gradient of the electron temperature induced by photoexcitation generates a blast force, which acts as a strong normal stress. We propose that a temporal stress can be applied by a strong optical pump, and this scheme can be another route for the application of uniaxial stress to superconductors.

Dual-phase-lag model for a nonlocal micropolar thermoelastic half-space subjected to gravitational field and inclined load

PurposeThe purpose of this study is to analyze the disturbances in a two-dimensional nonlocal, micropolar elastic medium under the dual-phase-lag model of thermoelasticity whose surface is subjected to an inclined mechanical load. The present study is carried out under the influence of gravity.Design/methodology/approachThe normal mode technique is used to obtain the exact expressions of the physical fields.FindingsFor inclined mechanical load, the impact of micropolarity, nonlocal parameter, gravity and inclination angle have been highlighted on the considered physical fields.Originality/valueThe numerical results are computed for various physical quantities such as displacement, stresses and temperature for a magnesium crystal-like material and are illustrated graphically. The study is valuable for the analysis of thermoelastic problems involving gravitational field, nonlocal parameter, micropolarity and elastic deformations.

Generalized thermoelastic responses in an infinite solid cylinder under the thermoelastic-diffusion model with four lags

Understanding thermal diffusion through elastic materials is an important process that links the fields of temperature, strain, and mass diffusion. Certain mathematical and experimental models have been developed to explain this phenomenon, and defects flaws in the traditional theories have been discovered. In this context, a new and improved model of thermal diffusion has been introduced in which Fourier and Fick's laws are replaced by more general formulas. The equations for heat conduction and mass diffusion in the proposed model are extended to incorporate higher-order time derivatives and four lag phases. In special cases, some classical and generalized thermoelastic diffusion models may be obtained. The suggested model has been applied to investigate the thermoelastic diffusion processes in a solid cylinder caused by a possible thermal and chemical shock to its surface. The numerical findings of the thermodiffusion fields are shown and described graphically. The influence of the four-phase delay parameters on the various investigated fields has been compared between different models of thermal diffusion.

New insights on piezoelectric thermoelastic coupling and transient thermo-electromechanical responses of multi-layered piezoelectric laminated composite structure

In recent years there have been many papers that considered the pyroelectric effect in the investigations of thermo-mechanical coupling of piezoelectric ceramics serving in non-uniform thermal environment, particularly with extensive applications of ultrafast heating technologies (e.g., laser burst, laser ablation, etc.) in micro-machining of piezoelectric structures (e.g., piezoelectric sensor/actuator/generator/energy harvester, etc.). However, in such conditions, the existing piezoelectric thermoelasticity theories will not be applicable due to the lack of consideration of the memory-dependence feature in the constitutive relations and heat transport equation. To further refine the piezoelectric thermoelasticity models, present study develops a new theoretical model of generalized piezoelectric thermoelasticity which fully account for fractional order strain and heat conduction. By establishing constitutive equations within the extended thermodynamic framework, the governing equations are derived. In the aspect of application, the transient thermo-electromechanical responses of multi-layered piezoelectric laminated composite structure with non-idealized interfacial conditions is investigated. The effects of material constants ratio and fractional order parameters of each layer on structural responses are evaluated and summarized to offer some new insights and guidelines on the strength design, thermal protection, and vibration control of multi-layered piezoelectric laminated composite structure under ultrafast heating condition.