Equations Of Thermoelasticity Research Articles

Generalized thermoelastic interaction in an isotropic solid cylinder without energy dissipation

In this paper, we constructed the generalized thermoelastic equations of an isotropic solid cylinder. The formulation is applied in the context of Green and Naghdi theory of types II (without energy dissipation). The material of the cylinder is supposed to be homogeneous isotropic both mechanically and thermally. The governing equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by an eigenvalue approach. Numerical results for the temperature distribution, displacement and radial stress are represented graphically.

A New Theory of Non-Linear Thermo-Elastic Constitutive Equation of Isotropic Hyperelastic Materials

Considering the influence of temperature and strain variables on materials. According to the relationship of conjugate stress-strain, a complete and irreducible non-linear constitutive equation of isotropic hyperelastic materials is derived and the constitutive equations of 16 types of isotropic hyperelastic materials are given we study the transformation methods and routes of 16 kinds of constitutive equations and the study proves that transformation of two forms of constitutive equation. As an example of application, the non-linear thermo-elastic constitutive equation of isotropic hyperelastic materials is combined with the natural vulcanized rubber experimental data in the existing literature base on MATLAB, The results show that the fitting accuracy is satisfactory.

Implementation of XFEM for dynamic thermoelastic crack analysis under non-classic thermal shock

In this paper, the extended finite element method is implemented to model a cracked finite domain in which the surface is subjected to a non-Fourier thermal shock. The dynamic fully coupled thermoelasticity equations based on Lord-Shulman theory are considered. The interaction integral is used to extract the stress intensity factors as well as the implicit version of the Newmark scheme as the time integration method to solve semidiscrete governing equations. The effect of relaxation time on the temperature distribution and stress intensity factors under thermal shock is investigated. Furthermore, secondary heat conduction near the tip of an inclined crack due to the reflection of the thermal wave from its surface and consequently local deviation in temperature and displacement fields is discussed in detail. The propagation of a curved crack under thermal shock is reported, as well.

A generalized thermoelastic dual-phase-lagging response of thick beams subjected to harmonically varying heat and pressure

The generalized thermoelastic problem of a thermo-mechanically loaded beam is studied. The upper surface of the beam is thermally isolated and subjected to a mechanical load while the bottom surface is traction free and subjected to a heating source. Based on the heat conduction equation containing the thermoelastic coupling term and the two-dimensional elasticity theory, thermoelastic coupling differential equations of motion are established. The generalized thermoelasticity theory with the dual-phase-laggings (DPLs) model is used to solve this problem. A closed-form analytical technique is used to calculate vibration of displacements and temperature. The effects of the phase-laggings (PLs), the intensity of the applied load and heat parameters on the field quantities of the beam are discussed. The variation along the axial direction and through-the-thickness distributions of all fields are investigated. Some comparisons have been also shown graphically to estimate the effects of the time on all the studied fields.

An analytical investigation of 2D-PPMs hollow infinite cylinder under thermo-electro-mechanical (TEM) loadings

The analytical solution of steady-state asymmetric thermo-electro-mechanical loads of a hollow thick infinite cylinder made of porous piezoelectric materials (2D-PPMs) based on two-dimensional equations of thermoelasticity is considered. The general form of thermal and mechanical boundary conditions is considered on the inside and outside surfaces. A direct method is used to solve the heat conduction equation and the non-homogenous system of partial differential Navier equations using the complex Fourier series and the powerexponential law functions method. The material properties are assumed to depend on the radial and circumferential variable and are expressed as power-exponential law functions along the radial and circumferential direction.

Prediction of thermo-poro-elastic properties of porous composites using an expanded unmixing-mixing model

This study proposes an expanded unmixing–mixing model to predict the material properties of porous composites. The poroelastic strain component that results from gas pressure within the pores was added in a thermo-elastic constitutive equation. The proposed model incorporates micro-state correction factors that represent micro-array effects from kinematic compatibilities in the boundaries of fibers and matrix. Finite element models were used to calculate the material properties of the porous matrix and composites. The results indicate that the material properties predicted by the proposed model are well correlated with those obtained from the finite element models. The results suggest that the proposed model adequately captures the change in the micro-state of porous composites due to pore generation. The model also illustrates the validity of the proposed model for composite thermo-poro-elasticity.

A general form of the heat conduction equation of thermoelasticity with voids and gravity field

PurposeThe purpose of this paper is to discuss the problem of thermoelasticity with voids under the gravity field in the context of a general form of heat conduction equation with some particular cases. The normal mode method used is to obtain the physical quantities.Design/methodology/approachThe analytical method used was the normal mode.FindingsNumerical results for the physical quantities are presented graphically and the results are analyzed thereafter. The comparisons are established between the theories for the physical quantities during the constant time and gravity and were shown graphically.Originality/valueIn the present work, the authors shall establish the general form for the heat conduction equation which contains the seven theories as well as the special cases in thermoelasticity with voids. The problem is very important in many dynamical systems.

Postbuckling and nonlinear vibration of composite Laminated trapezoidal plates

The thermal effects on the buckling, postbuckling and nonlinear vibration behaviors of composite laminated trapezoidal plates are studied. Aiming at the complex plate structure and to simulate the temperature distribution of the plate, a finite element method (FEM) is applied in this paper. In the temperature model, based on the thermal diffusion equation, the Galerkin\'s method is employed to establish the temperature equation of the composite laminated trapezoidal plate. The geometrical nonlinearity of the plate is considered by using the von Karman large deformation theory, and combining the thermal model and aeroelastic model, Hamilton\'s principle is employed to establish the thermoelastic equation of motion of the composite laminated trapezoidal plate. The thermal buckling and postbuckling of the composite laminated rectangular plate are analyzed to verify the validity and correctness of the present methodology by comparing with the results reported in the literature. Moreover, the effects of the temperature with the ply-angle on the thermal buckling and postbuckling of the composite laminated trapezoidal plates are studied, the thermal effects on the nonlinear vibration behaviors of the composite laminated trapezoidal plates are discussed, and the frequency-response curves are also presented for the different temperatures and ply angles.

The Analysis of the Heat Transfer Effect on the Thermoelastic Response of Metals under Pulsed Laser Impact

This paper presents an analysis of the effect of heat transfer in metals on the parameters of their thermal stresses caused by pulsed laser impact. The dynamic problem of thermoelasticity is regarded as a two-stage process. The first stage of the process is determined by the time of action of the radiation pulse; the second stage depends on the dynamics of the heat transfer process after the end of action of the laser pulse. It is shown that the analysis of stresses at the heat transfer stage based on the traditional system of thermoelasticity equations allows an adequate description of experimental results. The tensile stresses formed at the heat transfer stage lead to the possibility for metallic objects to move toward the heat source.

Calculation of Stress Intensity Factor for an Internal Circumferential Crack in a Rotating Functionally Graded Thick-Walled Hollow Circular Cylinder under Thermal Shock

Abstract In this article, the fracture behavior of functionally graded thick-walled cylinder under thermo-mechanical shock is investigated. For this purpose, classical coupled thermoelastic equations are used in calculations. First, these equations are discretized with extended finite element method (XFEM) in the space domain and then they are solved by the Newmark method in the time domain. The most general form of interaction integral is extracted for axially symmetric circumferential crack in a cylinder under thermal and mechanical loads in functionally graded materials and is used to calculate dynamic stress intensity factors (SIFs). The problem solution has been implemented in MATLAB software.

The existence of ‐bounded solution operators of the thermoelastic plate equation with Dirichlet boundary conditions

We consider the linearized thermoelastic plate equation with the Dirichlet boundary condition in a general domain Ω, given by urn:x-wiley:mma:media:mma4687:mma4687-math-0004 with the initial condition u|(t=0)=u0, ut|(t=0)=u1, and θ|(t=0)=θ0 in Ω and the boundary condition u=∂νu=θ=0 on Γ, where u=u(x,t) denotes a vertical displacement at time t at the point x=(x1,⋯,xn)∈Ω, while θ=θ(x,t) describes the temperature. This work extends the result obtained by Naito and Shibata that studied the problem in the half‐space case. We prove the existence of ‐bounded solution operators of the corresponding resolvent problem. Then, the generation of C0 analytic semigroup and the maximal Lp‐Lq‐regularity of time‐dependent problem are derived.

Considering Nonlinearities to Design Micro System's Vibrational Sensitivity

AbstractThis contribution analyses the impact of nonlinearities on the sensitivity of micro‐electro‐mechanical sensors measuring quantities based on a change in resonance frequency. The considered sensor is an array of cantilevers which have an integrated actuator and sensor. The mathematical model presented to describe the motion of this array is based on a coupled thermoelastic equation of motion which has a forced and a parametric excitation. Finally, a concept is presented to utilize a two‐to‐one internal resonance to increase a micro system's vibrational sensitivity. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

General decay of solutions to a one-dimensional thermoelastic beam with variable coefficients

The vibrations of flexible structures in practice are described by nonlinear models of strings, beams, plates, and so on. This paper is concerned with longitudinal vibrations of a thermoelastic beam equation. Our main result is the general decay of the system. Using the multiplier method and some properties of the convex functions, we establish the general decay of energy.

Topology optimization of thermal actuator and its support using the level set based multiple–type boundary method and sensitivity analysis based on constrained variational principle

Thermal actuator uses thermal expansion of an elastic body to produce motion at its output port. It needs to accumulate and amplify small local thermal expansion to ensure its output displacement is large enough. Also, its support should constrain the thermal expansion in irrelevant directions and steer the output displacement to a required direction. In the present paper, the task of designing a thermal actuator is formulated as a topology optimization problem. The design variables include two types of boundaries: the free boundary and the Dirichlet boundary. The optimization problem is solved by using a level set based multiple---type boundary method. Two level set functions are used to represent a thermal actuator and its two types of boundaries. Evolution of the two boundaries is modeled by two independent Hamilton---Jacobi equations. In order to analyze the shape derivatives of the two boundaries, the constrained variational principle is employed to explicitly include the Dirichlet boundary condition into the weak form equation of linear thermoelasticity. Numerical examples in two dimensions are investigated.

Nonlinear thermoelastic plate equations – Global existence and decay rates for the Cauchy problem

We consider the Cauchy problem in Rn for quasilinear thermoelastic Kirchhoff-type plate equations where the heat conduction is modeled by either the Cattaneo law or by the Fourier law. Additionally, we take into account possible inertial effects. Considering nonlinearities which are of fourth-order in the space variable, we deal with a quasilinear system which triggers difficulties typical for nonlinear Schrödinger equations. The different models considered are systems of mixed type comparable to Schrödinger–parabolic or Schrödinger–hyperbolic systems. The main task consists in proving sophisticated a priori estimates leading to obtaining the global existence of solutions for small data, neither known nor expected for the Cauchy problem in pure plate theory nor available before for the coupled system under investigation, where only special cases (bounded domains within with analytic semigroup setting, or the Cauchy problem with semilinear nonlinearities) had been treated before.

Research on thermally induced vibration of large hoop truss antenna moving through earth’s shadow

The coupled thermal-structural analysis of a spacecraft including a large hoop truss antenna in the on-orbital environment is studied. The structural strain is considered as the superposition of the thermal strain and the elastic strain. The thermo-elastic coupling equation of the cable-truss composited structure for the hoop truss antenna is established by introducing the thermo-elastic linear time-varying stiffness. The time-varying thermal field is modeled by considering the change of the attitude of the spacecraft and the influence of the spacecraft occlusion on the temperature changing of components. The obtained thermal field is used as the external load, and the influence of temperature changing when the spacecraft structure moves through earth’s shadow on the thermally induced vibration of the structure is analyzed. The results show that the temperature environment on-orbit has little influence on the structure. The data of on-orbit of a spacecraft is analyzed, and the efficiency of the numerical analysis is verified.

Three dimensional transient Green's functions in a thermoelastic transversely isotropic half‐space

AbstractA transversely isotropic thermoelastic half‐space in both mechanical and thermal points of view is considered as the domain of the initial boundary value problem involved in this paper. The governing partial differential equations of thermoelasticity in a cylindrical coordinate system are uncoupled with the aid of a complete set of displacement‐potential and temperature‐potential functions, which with the help of Fourier series decomposition and Hankel‐Laplace integral transforms, are reduced to ordinary differential equations in terms of depth. Then, the general solutions due to an arbitrary patch‐load and surface heat flux are investigated for the case of a point load varying with time as Heaviside step function and a point heat flux varying with time as Dirac delta function in order to compute the related Green's functions. The governing equations for the potential functions are in such a way that different longitudinal and transverse waves are recognized and the transport properties can be discovered from the governing equations. Some numerical illustrations are also presented to depict the dependency of response on the thermal properties as well as the anisotropy of the medium.

Three dimensional coupled thermoelasticity solution of sandwich plate with FGM core under thermal shock

Based on the Lord–Shulman formulation, time dependent response of sandwich plate with functionally graded material (FGM) core is performed by using generalized coupled thermoelasticity. Governing partial differential thermoelasticity equations are reduced to ordinary differential equations by applying Fourier series state space technique and then are solved analytically via Laplace transform. Solutions are then converted to time domain by using inverse Laplace transform. Validation of the present approach is assessed by comparing the numerical results with the available results in literature. Finally influence of time constant, applied temperature, mid radius to thickness ratio and time history on transient thermoelastic behavior of sandwich plate are studied.

Numerical solutions of a general coupled nonlinear system of parabolic and hyperbolic equations of thermoelasticity

In this paper, the weighted-average non-standard finite-difference (WANSFD) method is used to study numerically the general time-fractional nonlinear, one-dimensional problem of thermoelasticity. This model contains the standard system arising in thermoelasticity as a special case. The stability of the proposed method is analyzed by a procedure akin to the standard John von Neumann technique. Moreover, the accuracy of the proposed scheme is proved. Numerical results are presented graphically, which reveal that the WANSFD method is easy to implement, effective and convenient for solving the proposed system. The proposed method could also be easily extended to solve other systems of fractional partial differential equations.

THE IMPACT OF COUPLING THERMOELASTICITY EQUATIONS ON SETTLEMENT OF STRUCTURES ON FROZEN SOIL

This paper seeks to propose a numeric model for the determination of structure’s settlement on frozen soil. The settlement is driven by the dead weight of the soil, weight of the erected building and thawing of the soil underneath the building due to its heating. A benchmark task was solved both in coupled and uncoupled problem settings. A special analysis is dedicated to the impact of thermoelasticity equations being coupled or independent.