Thermoelastic Problem Research Articles

Analytical solutions for the plane thermoelastic problem of a nano-open crack in one-dimensional hexagonal quasicrystal non-periodic plane

As a stable material at high temperatures, the presence of cracks and other defects greatly reduces the performance of quasicrystals (QCs). The plane thermoelastic problem of one-dimensional hexagonal quasicrystals (1DHQ) non-periodic plane containing a nano-open crack is analyzed using surface elasticity theory. The closed form solutions are obtained to describe the thermoelastic field corresponding to the nano-crack by the Fourier integral transformation technique. The analytical solutions of the thermal stress intensity factors (TSIFs) and the strain energy density factor (SEDF) at the crack tip are derived explicitly. The influence of the applied loads, the surface effects and the multi-field coupling effects on the TSIFs and SEDF are discussed. The numerical results reveal that the surface effects have an obvious impact on TSIFs with small applied loads, and the surface effects will inhibit the propagation of nano-open cracks. The research results of this study provide some reliable theoretical references for the development of nano-QCs.

Complex-geometry simulations of transient thermoelasticity with the Shifted Boundary Method

We propose a formulation of the Shifted Boundary Method, an immersed/embedded/unfitted boundary method, for transient thermo-elasticity problems characterized by very complex geometries. With an extensive set of numerical experiments, we demonstrate that the SBM performs accurately and robustly, even when the geometry is represented in stereolithography format (STL, or Standard Tessellation Language) with gaps and overlaps. We conclude with a thermoelastic analysis of an advanced fluid tank design, obtained with topology optimization methodologies and a candidate for additive manufacturing processes. This final example represents what is foreseen as the typical application of the SBM in the context of the simulation of additively manufactured components.

Stationary Boundary Problems of Coupled Thermoelasticity for a Half-Plane and Their Solution

Stationary Boundary Problems of Coupled Thermoelasticity for a Half-Plane and Their Solution

A new combined asymptotic-tolerance model of thermoelasticity problems for thin uniperiodic cylindrical shells

AbstractThe objects of consideration are thin linearly thermoelastic Kirchhoff–Love-type circular cylindrical shells having a periodically microheterogeneous structure in circumferential direction (uniperiodic shells). The aim of this contribution is to formulate and discuss a new averaged mathematical model for the analysis of selecteddynamic thermoelasticity problemsfor the shells under consideration. This so-called combined asymptotic-tolerance model is derived by applying the combined modelling including the consistent asymptotic and the tolerance non-asymptotic modelling techniques, which are conjugated with themselves into a newprocedure. The starting equations are the well-known governing equations of linear Kirchhoff–Love theory of thin elastic cylindrical shells combined with Duhamel–Neumann thermoelastic constitutive relations and coupled with the known linearized Fourier heat conduction equation. For the periodic shells, the starting equations have highly oscillating, non-continuous and periodic coefficients, whereas equations of the proposed model have constant coefficients dependent also on a cell size.

Thermoelastic analysis of a bi-layered system with the single domain inclusion-based boundary element method

When a bi-layered composite system is subjected to prescribed thermal and elastic boundary conditions, material mismatch of layers and inhomogeneities causes intensive stress concentration, particularly with an initial crack, which causes delamination of the system. This paper combines the boundary element method and our recent work on the dual equivalent inclusion method (DEIM), namely the inclusion-based boundary element method (iBEM), to simulate the thermoelastic behavior without the whole domain integral. Using Galerkin’s stress vector technique, the bimaterial thermoelastic Green’s function mathematically transforms the entire domain integral to boundary integral equations. Because the inhomogeneities and matrix generally exhibit thermal and mechanical material mismatch, the DEIM simulates the inhomogeneity problem by inclusion with continuously distributed polynomial-form eigentemperature and eigenstrain. Therefore, iBEM avoids conventional multi-region solution scheme and convert the entire domain into boundary integral equations plus domain integrals within the inhomogeneity domain. The energy release rate (J-integral) can be utilized to reveal and judge the stability of the crack. For elastic problems, when one of the layers becomes stiffer or is embedded with the stiffer inhomogeneity, the J-integral decreases, and the system is more stable. However, this conclusion is not established for thermoelastic problems. Moreover, locations, distribution, and material mismatches are essential in (modified) J-integrals. Numerical case studies validate the single-domain algorithm, and parametric studies illustrate the effects of inhomogeneities on the (modified) J-integral for a bi-layered system.

Analysis of a thermoelastic problem with the Moore–Gibson–Thompson microtemperatures

In this paper, we study, from both an analytical and a numerical point of view, a poro-thermoelastic problem with microtemperatures. The so-called Moore–Gibson–Thompson equation is used to model the contribution for the temperature and microtemperatures. An existence and uniqueness result is proved by using the theory of linear semigroups of contractions and, for the one-dimensional case, the exponential energy decay is found under some conditions on the constitutive coefficients. Then, a fully discrete approximation is introduced by using the finite element method and the implicit Euler scheme. We show that the discrete energy decays and we obtain some a priori error estimates from which, under some adequate additional regularity conditions on the continuous solution, we derive the linear convergence of the approximations. Finally, we perform some numerical simulations to demonstrate the accuracy of the approximations and the behavior of the discrete energy and the solution.

A MGT thermoelastic problem with two relaxation parameters

In this paper, we consider, from both analytical and numerical viewpoints, a thermoelastic problem. The so-called MGT model, with two different relaxation parameters, is used for both the displacements and the thermal displacement, leading to a linear coupled system made by two third-order in time partial differential equations. Then, using the theory of linear semi-groups the existence and uniqueness to this problem is proved. If we restrict ourselves to the one-dimensional case, the exponential decay of the energy is obtained assuming some conditions on the constitutive parameters. Then, using the classical finite element method and the implicit Euler scheme, we introduce a fully discrete approximation of a variational formulation of the thermomechanical problem. A main a priori error estimates result is shown, from which we conclude the linear convergence under suitable additional regularity conditions. Finally, we present some one-dimensional numerical simulations to demonstrate the convergence of the fully discrete approximation, the behavior of the discrete energy decay and the dependence on a coupling parameter.

A Fast Reduced-Order Model for Radial Integration Boundary Element Method Based on Proper Orthogonal Decomposition in the Non-Uniform Coupled Thermoelastic Problems

To efficiently address the challenge of thermoelastic coupling in functionally graded materials, we propose an approach that combines the radial integral boundary element method (RIBEM) with proper orthogonal decomposition (POD). This integration establishes a swift reduced-order model to transform the high-dimensional system of equations into a more manageable, low-dimensional counterpart. The implementation of this reduced-order model offers the potential for rapid numerical simulations of functionally graded materials (FGMs) under thermal shock loading. Initially, the RIBEM is utilized to resolve the thermal coupling issue within the FGMs. From these solutions, a snapshot matrix is constructed, capturing the solved temperature and displacement fields. Subsequently, the POD modes are established and a POD reduced-order model is constructed for the boundary element format of the thermally coupled problem. Finally, a system of low-order discrete differential equations is solved. Numerical experiments demonstrate that the results obtained from the reduced-order model closely align with those of the full-order model, even when considering variations in structural parameters or impact loads. Thus, the introduction of the reduced-order model not only guarantees solution accuracy but also significantly enhances computational efficiency.

Accelerating the computational process for analyzing dynamic thermal behavior of an innovatively designed longitudinally-graded sandwich plate: Deep-learning approach

Employing the solutions through artificial intelligence (AI) to solve mechanical engineering problems can pave the way toward accelerating the computation process, especially for those engaged with the dynamic nature of the time-variable systems. In this regard, this article attempts to employ deep neural networks (DNN) for the coupled thermoelasticity assessment of the longitudinally sandwiched plates exposed to intensive thermal shock. The left and right face sheets of the sandwich plate are enriched with graphene platelets (GPLs) along the longitudinal direction. The thermal shock is considered as the instantaneous heat flux applied in the axial direction. Elasticity theory is employed for deriving the governing equations in an exact template and differential quadrature approach (DQA) in conjunction with the Laplace transform plays the role of solution approaches to attain the thermoelastic reaction of the sandwich system at training points. Then, the DNN utilizes these points to adjust a predictor mechanism for analyzing the behavior of the sandwich system in every load-exertion circumstances. Additionally, the DNN would be optimized by a brand-new metaheuristic algorithm according to some error estimation criteria to minimize the error of regression. The mentioned solution is validated by comparing its performance with the outcomes of the published literature. This study provides a novel platform to use the great potential of AI-based methods in solving dynamic thermoelastic problems in the world of solid structures.

Role of interface tension in the thermoelastic analysis of inclusions: Unified formulation and closed-form results

We study the thermoelastic problem of an inclusion of general shape surrounded by a foreign elastic matrix under plane deformation and the influence of an in-plane far-field heat flux. The small-scale interface effects, related to not only interface conductivity, interface stretching rigidity and interface thermal expansion but also (residual) interface tension, are incorporated in the corresponding analysis. We establish general boundary value formulations in both heat conduction and thermoelasticity for an arbitrary inclusion shape, allowing for analytic or at least semi-analytic treatment of the problem. Specially, we derive closed-form solutions for the case of circular inclusion and obtain concise expressions for describing the remote heat flux-induced thermal stress near the interface (at both the inclusion side and matrix side). Surprisingly, it is shown that for the case of circular inclusion, interface tension plays the same role as interface stretching rigidity in determining the full thermal stress field, or in other words, the full thermal stress field depends on only the sum of interface tension and interface stretching rigidity but not on the specific value of either of them. Numerical examples are also given to illustrate the influence of interface tension on the von Mises stress distribution in the vicinity of the interface.

Analytical solution of the temperature-dependent thermoelastic problem induced by Joule heating and the presence of an elliptic cavity

Joule heat induced by electric current may well lead to thermal stress and contribute to structural failure and crack evolution in a range of modern materials. In this paper, we use complex variable methods to obtain the thermoelastic fields around an elliptic cavity in a plate subjected to remote electric and thermal loads. Of particular interest is the fact that we consider the temperature dependency of the corresponding thermoelastic coefficients. We introduce an analytical method which is verified by the fact that it leads to results which reduce to the classical analytical results in the literature when the thermoelastic coefficients are taken to be temperature-independent. We find that when the elliptic cavity is reduced to the representation of a linear crack, the corresponding stress intensity factor increases to a greater extent under the temperature-dependent assumption versus the corresponding classical results. Our findings are significant in forming the basis for the analysis of the evolution of crack growth under severe temperature gradients such as those occurring as a result of Joule heat loading.

Stationary Boundary Problems of Coupled Thermoelasticity for a Half-Plane and Their Solution

Using the model of coupled thermoelasticity, the boundary value problems of the dynamics of a thermoelastic half-space are solved for plane deformation with periodic surface force and thermal effects associated with the desired boundary functions by linear algebraic relations. Green’s tensors are constructed for the stated boundary value problems, using their properties, analytical solutions of these problems are obtained. To solve them, we have used the method of incomplete separation of variables, the Fourier transform, and the properties of fundamental solutions. The presented algorithm solves the classical four boundary value problems of thermoelasticity, as well as non-classical ones with coupled thermal and force characteristics at the boundary of the half-plane.

Uniqueness and Stability of Solving the Inverse Problem of Thermoelasticity. Part 2. Regularization

Uniqueness and Stability of Solving the Inverse Problem of Thermoelasticity. Part 2. Regularization

The Role of the Coupling Coefficient in the Dynamic Problem of Thermoelasticity with Localized Inclusions

The Role of the Coupling Coefficient in the Dynamic Problem of Thermoelasticity with Localized Inclusions

ON THE ROLE OF COUPLING COEFFICIENT IN DYNAMIC PROBLEM OF THERMOELASTICITY WITH LOCALIZED INCLUSION

In the present paper paper the dynamic problem of thermoelasticity with a localized inclusion in the medium is considered. It is shown that in the resonant regime an important role is played by the coupling coefficient of the temperature and strain fields. The coupling of the problem and the presence of a discrete spectrum lead to the appearance of an additional term in the expression for temperature, which is localized and does not describe the diffusion process.

Solution of a Half-Space in Generalized Thermoelastic Problem in the Context of Two Models Using the Homotopy Perturbation Method

This paper estimated the problem of one-dimensional generalized thermoelastic half-space in medium considering two models: the Lord and Shulman (LS) model and the Dual-Phase-Lag (DPL) model. We assumed that the surface of the half-space was free from traction force and under an exponentially varying external heat source at the boundary with time. The technique of homotopy perturbation has been applied to find the approximate solution for the interactions of thermoelasticity with the applied boundary condition. The effect of a heat source that varies with the time and the free traction force are investigated for the temperature, displacement, and stress. The numerical results obtained are presented graphically to show the influence of the new external parameters. The results obtained illustrate the strong impacts on the displacement, temperature, and stress with the variations in the two models as well as the relaxation time parameter. The results show the agreement between the present results and the previous obtained results of the phenomenon and applicable, especially in biology, acoustics, engineering, and geophysics.

Transient Thermoelastic Analysis of Rectangular Plates with Time-Dependent Convection and Radiation Boundaries

Approximate analytical solutions are presented for the transient thermoelastic problem of rectangular plates with time-dependent convection and radiation boundaries. To include the nonlinear radiation boundary, the whole heating process is divided into several time steps, and a linearized approximation is used to simplify the radiation term for each step. The one-dimensional transient temperature along the thickness direction is solved using the technique of the separation of variables. The displacement and stress solutions are obtained by applying the state-space method to the three-dimensional thermoelasticity equations. The accuracy of the present solutions is demonstrated by comparison with the reported results in the open literature and the finite element solutions. In the numerical examples, two kinds of thermal boundaries, namely, time-independent convection boundaries and time-dependent convection and radiation boundaries, are considered to show the availability of the present solutions.

A reduced-order modeling for thermo-mechanical coupling analyses by using radial integration boundary element method

In order to efficiently solve thermo-mechanical coupling problems, this work combines the radial integration boundary element method (RIBEM) and the proper orthogonal decomposition (POD) to construct a fast reduced-order model. This model transforms high-dimensional systems into low-dimensional ones, enabling faster computation of thermo-mechanical coupling problems under thermal loads. Firstly, RIBEM is employed to solve coupled thermoelastic dynamic problems under thermal shock loads. Domain integrals are converted to boundary integrals using the radial integration method, establishing a purely boundary element algorithm without internal cells. Subsequently, finite difference techniques are applied to calculate the discretized algebraic equations, and the obtained field variables are used as a snapshot matrix to establish POD modes and construct the POD reduced-order model. Numerical examples demonstrate that the results of the reduced-order model are essentially consistent with the full-order model across various physical parameters and boundary conditions. Therefore, this reduced-order model significantly improves computational efficiency while maintaining high accuracy, especially when solving large-scale problems.

Thermodynamical interactions in a micropolar magneto-thermoelastic medium with photothermal effect

PurposeThe purpose of this paper is to establish a two-dimensional model of Green–Lindsay theory for micropolar magneto-thermoelastic medium to study the photothermal effect. The model is used to study the coupling between elastic waves and plasma waves generated due to thermal changes in a micropolar elastic medium.Design/methodology/approachNormal mode analysis is used to obtain the analytical solutions of the governing equations.FindingsEffects of magnetic field, micropolarity, photothermal and time are highlighted on various physical fields such as stresses, temperature, displacement and carrier density. The above physical fields also conform to the boundary conditions. It is further observed that all the physical quantities become zero outside some bounded region of space, thus confirming the notion of generalized theory of thermoelasticity.Originality/valueThe values of physical fields are computed numerically using MATLAB software considering material constants for silicon. Furthermore, the effects are depicted graphically and analyzed accordingly. The study is valuable for the analysis of thermoelastic problems involving magnetic field, micropolarity and elastic deformations.

A peridynamic model for coupled thermo-mechanical-oxygenic analysis of C/C composites with SiC coating

The oxidation induced by coating cracking is a general failure mode of high-temperature composites such as C/C and C/SiC. However, this failure mode has not been fully investigated due to the lack of a method suitable for both crack simulation and oxidation interface capture. In this paper, a coupled thermo-mechanical-oxygenic peridynamic model is proposed for SiC-coated C/C composites in an oxidizing environment. The ordinary state-based peridynamics is extended to plane strain thermoelastic problems for orthotropic media to calculate the crack distribution. Cracks in the coating are modeled as oxygen diffusion channels and the peridynamic oxidation equation is developed to simulate the oxidation of the C/C substrate. Furthermore, the peridynamic non-Fourier heat transfer equation is employed to consider the finite thermal propagation speed and the model is validated by experimental results. Numerical examples are presented to investigate the oxidation failure after thermal shock, non-Fourier thermal shock fracture, and stress oxidation failure of SiC-coated C/C composites.