Coupled Thermoelasticity Analysis Research Articles

The modified physics-informed neural network (PINN) method for the thermoelastic wave propagation analysis based on the Moore-Gibson-Thompson theory in porous materials

This paper presents novel contributions to both theory and solution methodology in AI-based analysis of solid mechanics. The physics-informed neural network (PINN) method is developed for thermoelastic wave propagation and Moore-Gibson-Thompson (MGT) coupled thermoelasticity analysis of porous media, a first in the field. The coupled thermoelasticity governing equations, based on the MGT heat conduction model, are derived for a porous half-space, with the thermal relaxation coefficient and strain relaxation factor being considered. Mechanical and thermal shock loading boundary conditions are imposed. The behavior of a magnesium-made porous body is analyzed using the PINN method, with highly accurate results being achieved for the system of coupled PDEs. An adaptive hyperparameter tuning approach, integrating a generalized subset design (GSD) and Bayesian optimization algorithm, is used to automatically select the optimal structure based on the L2 relative error. This hybrid methodology eliminates manual adjustment concerns. The proposed method is verified through a thorough comparison with the Lord-Shulman theory of coupled thermoelasticity. The strength of the methodology lies in its ability to operate without domain data, with only boundary and initial points being required. Four example sets are examined to demonstrate the capabilities of the modified PINN, and high-quality predictions of dimensionless fields’ variables over an extended time interval are obtained, confirming its extrapolation abilities.

A new modified deep learning technique based on physics-informed neural networks (PINNs) for the shock-induced coupled thermoelasticity analysis in a porous material

In this article, a new modified deep learning (DL) method based on physics-informed neural networks (PINNs) is proposed for analyzing generalized coupled thermoelasticity in a porous material under shock loadings using Lord–Shulman (LS) theory. The PINN-based method demonstrates remarkable capabilities in solving differential equations and identifying unknown parameters. It is employed to solve a system of coupled partial differential equations (PDEs) governing a porous half-space material, considering thermal and strain relaxation coefficients in the LS theory. The optimal structure of the PINN is investigated through sensitivity analyses. Two adaptive sampling techniques, residual-based adaptive refinement (RAR) and residual-based adaptive distribution (RAD), are employed to enhance solution quality within the optimized architecture. The proposed forward PINN utilizes known values of field variables at initial and boundary conditions. The efficiency and effectiveness of the proposed PINN approach are demonstrated through three distinct scenarios. Non-parametric statistical tests and L 2 relative error analysis validate the extraordinary potential of the proposed PINN-based method in accurately capturing the system behavior. The extrapolation results, represented as time history plots, showcase exceptional accuracy in this study, overcoming the limitations of conventional numerical methods in larger temporal domains.

Mechanically induced temperature oscillations in the coupled thermo-elasticity analysis of articulated dynamical systems

This article discusses a new approach for predicting and quantifying mechanically induced temperature oscillations in the coupled thermo-elasticity analysis of articulated mechanical systems (AMS). In this approach, the constrained equations of motion are solved simultaneously with discrete temperature equations obtained by converting heat partial-differential equation to a set of first-order ordinary differential equations. Dependence of the temperature gradients and their spatial derivatives on the position gradients, spinning motion, and curvatures is discussed. The approach captures dependence of the temperature-oscillation frequencies on the mechanical-displacement frequencies. The temperature field can be selected to ensure continuity of the temperature gradients at the nodal points. To generalize the AMS coupled thermo-elasticity formulation and capture the effect of the boundary and motion constraints (BMC) on the thermal expansion, the proposed method is based on integrating thermodynamics and Lagrange-D’Alembert principles. The absolute nodal coordinate formulation (ANCF) is used to describe continuum displacement and obtain accurate description of the reference-configuration geometry and change of this geometry due to deformations. A thermal-analysis large-displacement formulation is used to allow converting heat energy to kinetic energy, ensuring stress-free thermal expansion in case of unconstrained uniform thermal expansion. Cholesky heat coordinates are used to define an identity coefficient matrix for the efficient solution of the discretized heat equations. The approach presented is applicable to the two different forms of the heat equation used in the literature; one form is explicit function of the stresses while the other form does not depend explicitly on the stresses. Because of the need for using ANCF finite elements to achieve a higher degree of continuity in the coupled thermomechanical approach introduced in this article, the concept of the ANCF mesh topology is discussed.

Transient coupled thermo-elasticity analysis of a temperature-dependent thick-walled cylinder under cyclic thermo-mechanical loads

AbstractSeveral studies have reported the solution of the classical coupled thermo-elasticity for thick-walled cylinders under different boundary conditions; however very limited studies have been conducted on the analysis of temperature-dependent thick-walled cylinders under cyclic nonlinear boundary conditions. Therefore, this study investigates the transient response of temperature-dependent thick-walled cylinders under cyclic nonlinear thermo-mechanical loads based on classical coupled thermo-elasticity. Also, it studies the impact of considering temperature-dependent material properties (TDMP) and temperature-independent material properties (TIMP) hypotheses on the accuracy of the results. The governing equations of the classical nonlinear coupled thermo-elasticity are numerically solved based on the finite-difference method, namely the Crank-Nicolson method. Then, an experimental setup is designed to further investigate the impact of considering TDMP and TIMP through a temperature measurement of the outer surface of a machine gun barrel under burst shooting. It has been found that considering TIMP overestimates the residual temperature and residual stress values through the cylinder thickness compared with TDMP. Moreover, based on the temperature measurement, TDMP estimates results with higher accuracy of 7% than TIMP.

A novel edge center-based gradient-smoothing element method for 2D and 3D coupled thermoelasticity analyses

In this paper, an edge center-based gradient-smoothing element method is proposed for coupled thermoelasticity problems. The main achievement in our work is to construct the linear gradient field inside the element and ensure the consistency of gradient at the junction center of the element, including edge center of triangular element and face center of tetrahedral element. Hence, smoother stress and temperature gradient fields using low-order element are obtained in coupled thermoelasticity analysis without additional post-processing. With the proposed methods, superior accuracy and convergence characteristics are demonstrated compared with other methods through a series of 2D and 3D numerical tests.

Coupled thermoelastic fracture analysis of a cracked fiber reinforced composite hollow cylinder by fractional Cattaneo-Vernotte models

Coupled thermoelastic fracture problem of a fiber reinforced composite hollow cylinder containing an embedded circumferential crack is investigated in the present paper based on generalized fractional Cattaneo-Vernotte heat conduction models. The temperature and stress fields are obtained by solving the coupled partial differential equations, and then corresponding thermal axial stress with minus sign is applied to the crack surface to form a mode I crack problem. Integral transform techniques are employed to reduce the mixed boundary value problem to a series of singular integral equations. The effects of different fractional Cattaneo-Vernotte models, fractional order, convective heat transfer coefficient, volume fraction, and thermodynamic coupling coefficient on the transient temperature and thermal stress intensity factors are analyzed. The results show that each physical parameter has a significant effect on the responses, which is important to make predictions regarding the stability of crack growth, thermal fatigue life etc.

Geometrically Non-Linear Vibration and Coupled Thermo-Elasticity Analysis with Energy Dissipation in FG Multilayer Cylinder Reinforced by Graphene Platelets Using MLPG Method

Geometrically Non-Linear Vibration and Coupled Thermo-Elasticity Analysis with Energy Dissipation in FG Multilayer Cylinder Reinforced by Graphene Platelets Using MLPG Method

Thermal shock-induced Moore-Gibson-Thompson generalized coupled thermoelasticity analysis based on the strain gradient Love-Bishop theory in a nanorod resonator

Thermal shock-induced Moore-Gibson-Thompson generalized coupled thermoelasticity analysis based on the strain gradient Love-Bishop theory in a nanorod resonator

Large Deformation Hermitian Finite Element Coupled Thermoelasticity Analysis of Wave Propagation and Reflection in a Finite Domain

In the present paper, a finite element nonlinear coupled thermoelasticity formulation is presented for analysis of the wave propagation, reflection, and mixing phenomena in the finite length isotropic solids. The governing equations are derived based on the second Piola-Kirchhoff stress and the full form of Green’s strain-displacement tensors to account for the large deformations and finite strains. In contrast to the available researches, the assumption of very small temperature changes compared to the reference temperature is released in the present research. Galerkin’s method, a weak formulation, and cubic elements are employed to obtain the time-dependent non-linear finite element governing equations. The proposed solution procedure to the resulting highly nonlinear and time-dependent governing equations employs an updating algorithm and Newmark’s numerical time integration method. The wave propagation and reflection phenomena are investigated for both the mechanical and thermal shocks and time variations of distributions of the resulting displacements, temperature rises, and stresses are illustrated graphically and discussed comprehensively. Furthermore, the effects of the non-linear terms are discussed comprehensively. Results reveal that in the non-linear analysis, no fixed speed of wave propagation can be defined.

Scale Effects on Thermoelastic Coupling Wave Propagation of Micro-Beam Resonator Using Nonlocal Stain Gradient and Generalized Thermoelasticity

Coupled thermoelastic analysis in the study of microscale solid mechanics has attracted considerable attention along with the miniaturization and functionalization of devices. Higher-order continuum mechanics theories have considered scale effects; however, the theories to predict thermoelastic performances of structures in micro-scale are still incomplete. The purpose of this paper is to study scale and thermal-induced effects by considering stress nonlocality and strain gradient elasticity in micro-structure resonators. The thermoelastic constitutive relations are established based on the nonlocal strain gradient (NSG) theory. The wave propagation problem of a Timoshenko micro-beam in conjunction with Green and Naghdi’s generalized thermoelastic (G–N) theory is investigated. The governing equations are derived and analytically solved by the eigenvalue method. Finally, the dispersion relation of a frequency spectrum is determined and the influences of scale parameters and coupled thermoelastic effect are discussed; in addition, the analysis results are compared with those under different size-dependent theories accordingly.

A deep learning approach based on a data-driven tool for classification and prediction of thermoelastic wave’s band structures for phononic crystals

This article deals with the data-driven prediction of the band structures of thermoelastic waves in the nano-scale phononic crystal beams considering nano-size effects. The computational intelligence methods are developed using a data-driven tool to discover the design space of phononic crystals, which are subjected to thermal shock loading. For this purpose, a rich dataset is created utilizing an analytical solution, which was previously proposed for the nonlocal coupled thermoelasticity analysis in a nano-sized phononic crystal beam. The preprocessing methods, hyperparameters optimization, and shallow and deep neural networks are used to classify and predict the bandgaps. Also, according to the created dataset and the data-driven method, the phononic crystal feature importance and behavior based on the design parameters are assessed in detail. The detailed investigation reveals the importance of the design parameters according to the deep neural network’s results. It is demonstrated by numerical results that the proposed final data-driven model can predict the characteristics of the phononic crystals pretty well. Also, the results show that the deep neural network outperforms the shallow neural network for the classification and prediction of the band structures. The final results can be a helpful tool to have a fast numerical framework for the prediction of photonic crystals’ bandgaps before the application of time-consuming accurate frameworks.

Gaussian thermal shock-induced thermoelastic wave propagation in an FG multilayer hybrid nanocomposite cylinder reinforced by GPLs and CNTs

In this paper, a new modified micromechanical model is proposed to obtain the mechanical and thermal properties of a reinforced functionally graded (FG) multilayer hybrid nanocomposite cylinder for thermoelastic wave propagation analysis with energy dissipation using Green–Naghdi theory. The FG multilayer hybrid nanocomposite cylinder is assumed to be under Gaussian thermal shock loading and also it is reinforced by graphene platelets (GPLs) and carbon nanotubes (CNTs). The cylinder is assumed to be made of multi-layers (sub-cylinders), and each layer is reinforced by a uniform distribution of GPLs and CNTs. A modified micromechanical model is proposed to calculate the thermo-mechanical properties with nonlinear grading patterns of the GPLs and CNTs along the radial direction of the cylinder. The nonlinear grading patterns of the GPLs and CNTs distributions along the radial direction of the whole cylinder can be created using a suitable arrangement of the layers (sub-cylinders). An effective meshless collocation method based on the generalized finite difference (GFD) method and the Newmark method are employed to solve the coupled governing equations of the GN-based coupled thermoelasticity analysis. The effects of the key parameters such as the weight fraction of the GPLs and CNTs and volume fraction index on the thermoelastic wave propagations and dynamic behaviors of the field variables are studied in detail. Also, the effects of the reinforcement by GPLs and/or CNTs in a hybrid nanocomposite on the transient behaviors of cylinder in both temperature and displacement fields are compared. The accuracy and stability of the presented meshless method and also the proposed new modified micromechanical model is verified by the published reference data.

A GN-based modified model for size-dependent coupled thermoelasticity analysis in nano scale, considering nonlocality in heat conduction and elasticity: An analytical solution for a nano beam with energy dissipation

This investigation deals with a size-dependent coupled thermoelasticity analysis based on Green-Naghdi (GN) theory in nano scale using a new modified nonlocal model of heat conduction, which is based on the GN theory and nonlocal Eringen theory of elasticity. In the analysis based on the proposed model, the nonlocality is taken into account in both heat conduction and elasticity. The governing equations including the equations of motion and the energy balance equation are derived using the proposed model in a nano beam resonator. An analytical solution is proposed for the problem using the Laplace transform technique and Talbot technique for inversion to time domain. It is assumed that the nano beam is subjected to sinusoidal thermal shock loading, which is applied on the one of beam ends. The transient behaviors of fields\' quantities such as lateral deflection and temperature are studied in detail. Also, the effects of small scale parameter on the dynamic behaviors of lateral deflection and temperature are obtained and assessed for the problem. The proposed GN-based model, analytical solution and data are verified and also compared with reported data obtained from GN coupled thermoelasticity analysis without considering the nonlocality in heat conduction in a nano beam.

Coupled thermoelasticity analysis of FGM plate integrated with piezoelectric layers under thermal shock

Based on theory of piezoelectricity and using generalized coupled thermoelasticity, transient response of a simply supported functionally graded material rectangular plate embedded in sensor and actuator piezoelectric layers under applied electric field and thermal shock is studied. Thermoelastic properties of the plate vary continuously along the thickness direction according to exponential functions and Poisson ratio is assumed to be constant. Applying Fourier series state space technique to the basic coupled thermoelastic differential equations results in the ordinary differential equations which are solved analytically by using Laplace transform. Validation of the present approach is assessed by comparing the numerical results with the available results in literature. In parametric study, effect of the relaxation time, applied voltage and temperature and time history of the thermoelastic response of FGM plate attached to piezoelectric layers are investigated.

Coupled thermoelasticity analysis of carbon nano tube reinforced composite rectangular plate subjected to thermal shock

In the frame work of Lord-Shulman theory, transient response of a simply supported carbon nanotube reinforced composite (CNTRC) rectangular plate with different pattern of CNT distribution and under thermal shock is studied using generalized coupled thermoelasticity. Applying Fourier series expansion along the in-plane direction and state space technique along the thickness direction to the constitutive equations and governing differential equations of motion results in first state space differential equations which can be solved analytically in Laplace transform. Then response is obtained in time domain using inverse Laplace transform. Moreover, parametric study is conducted to assess the effect of pattern of CNT distribution, CNT volume fraction and pick of thermal shock on transient thermoelastic behavior of FG-CNTRC rectangular plate are examined.

Coupled thermoelastic analysis of an FG multilayer graphene platelets-reinforced nanocomposite cylinder using meshless GFD method: A modified micromechanical model

The coupled thermoelasticity analysis based on the Green–Naghdi theory with energy dissipation is carried out to assess the thermoelastic wave propagations in an FG multilayer graphene platelets-reinforced nanocomposite cylinder. The cylinder is assumed to be made of multi-layers (sub-cylinders), and each layer is reinforced by a uniform distribution of graphene platelets (GPLs). A modified micromechanical model is used to calculate the thermal and mechanical properties considering nonlinear grading patterns of the GPLs along the radial direction of the cylinder. Using a proper arrangement of the layers, the nonlinear grading patterns of the GPLs are created along the radial direction of the whole cylinder. To solve the obtained governing partial differential equations (PDEs), the meshless generalized finite-difference (GFD) method and the Newmark method are employed. The inner surface of the cylinder is excited by three types of the thermal shock loading including the suddenly temperature increase described by the Heaviside step function, as well as sinusoidal and ramp pulses. The effects of the key parameters such as the weight fraction of the GPLs and volume fraction index on the thermoelastic wave propagations and dynamic behaviors of the field variables are studied in details. Also, the effects of the key parameters on the thermoelastic damping in the temperature field are illustrated using the presented modified micromechanical model. The accuracy and stability of the presented meshless method and the numerical results are verified by the published reference data.

Analytical solution for nonlocal coupled thermoelasticity analysis in a heat-affected MEMS/NEMS beam resonator based on Green–Naghdi theory

• An analytical solution is proposed for transient coupled thermoelasticity of NEMS. • The micro/nano beam resonator is excited by thermal shock loading. • The size effects are taken into account employing nonlocal Rayleigh beam theory. • The energy is dissipated in the employed model based on the GN theory. • The fields’ variables are presented in the close forms for a NEMS. In this article, an analytical solution is presented for coupled thermoelasticity analysis (with energy dissipation) in a micro/nano beam resonator, considering small scale effects on the transient behaviors of fields’ variables. The Green–Naghdi (GN) theory of generalized coupled thermoelasticity and nonlocal Rayleigh beam theory (NRBT) are employed to derive the temperature and lateral deflection in the closed forms. The presented analytical solution is based on Laplace transform. To find the dynamic and transient behaviors of fields’ variables in time domain, an inversion Laplace technique is utilized, which is called Talbot method. The effects of some parameters such as small scale parameter and dimensions of the beam on the dynamic behaviors of temperature and lateral deflections are discussed in details. The propagation of wave fronts in both temperature and lateral deflection domains are obtained and graphically illustrated at various time instants.

Shock-induced nonlocal coupled thermoelasticity analysis (with energy dissipation) in a MEMS/NEMS beam resonator based on Green–Naghdi theory: A meshless implementation considering small-scale effects

ABSTRACTIn this article, a meshless method based on the generalized finite difference (GFD) method is developed for coupled thermoelsaticity analysis (with energy dissipation) considering small-scale effects in a micro-electromechanical-systems/nano-electromechanical-systems beam resonator. The Green–Naghdi theory of the generalized coupled thermoelasticity and nonlocal Rayleigh beam theory are utilized for dynamic analysis of a micro/nanobeam resonator subjected to thermal shock loading. The small-scale effects and energy dissipation are considered to derive the governing equations for both displacement and temperature fields. The governing equations are discretized in the Laplace domain using GFD method. To find the dynamic and transient behaviors of fields’ variables in time domain, an inversion Laplace technique is utilized, which is called the Talbot method. The effects of some parameters such as small-scale parameter and height of the micro/nanobeam on the dynamic behaviors of temperature and lateral deflection are discussed in detail.

Coupled thermoelastic analysis of a multi-layered hollow cylinder based on the C–T theory and its application on functionally graded materials

The coupled thermoelastic behavior of a multi-layered or functionally graded hollow cylinder under generally transient thermal and mechanical loadings is investigated in this paper. The generalized Chandrasekharaiah–Tzou (C–T) thermoelasticity theory, based on the dual-phase-lag hyperbolic heat conduction model, is used to describe the nature of finitely thermal and elastic wave speeds. The Kapitza thermal interface model indicates that the temperature can jump across the interface but the heat flux in the radial direction is continuous. With the Laplace transform method eliminating the time-dependence of the coupled partial differential equations, the problem is theoretically solved by introducing a displacement potential function. A numerical Laplace inversion technique is then employed to transform the results into the time domain. Finally, the effect of heat conduction models, inertial and coupling effects, loading types, interfacial imperfection, Biot number, and functionally graded profiles on the thermal and elastic results is analyzed. Also, the physically unrealistic discontinuity in displacement is observed when the cylinder is subjected to a Dirac delta-type thermal loading.

A novel meshless local Petrov–Galerkin method for dynamic coupled thermoelasticity analysis under thermal and mechanical shock loading

A meshless local Petrov–Galerkin method (MLPG) based on the moving Kriging interpolation is further developed for two-dimensional linear dynamic coupled thermoelasticity problems under thermal and mechanical shock loading. In this method the moving Kriging interpolation is employed to construct the shape functions, and the Heaviside step function is applied in the local weak-form as the test functions. The equations of motion and transient heat conduction equations of the coupled thermoelasticity interact on each other. So these equations must be solved simultaneously. In this paper the backward difference method is applied to approximate the time derivatives. The main idea of treating the time-dependent problem is based on the reduction procedure of the equations of motion, in which the displacements, velocities and temperature are taken as the field variables. Then a unified explicit expression of the system of differential algebraic equations is obtained. Numerical examples are presented to illustrate the accuracy of this method.