Elasticity solution of laminated beams subjected to thermo-loads

According to the two-dimensional(2-D) thermo-elasticity theory, the exact elasticity solution of the simply supported laminated beams subjected to thermo-loads was studied. An analytical method was presented to obtain the temperature, displacement and stress fields in the beam. Firstly, the general solutions of temperature, displacements and stresses for a single-layered simply supported beam were obtained by solving the 2-D heat conduction equation and the 2-D elasticity equations, respectively. Then, based on the continuity of temperature, heat flux, displacements and stresses on the interface of two adjacent layers, the formulae of temperature, displacements and stresses between the lowest layer and the top layer of the beam were derived out in a recurrent manner. Finally, the unknown coefficients in the solutions were determined by the use of the upper surface and lower surface conditions of the beam. The distributions of temperature, displacement and stress in the beam were obtained by substituting these coefficients back to the recurrence formulae and the solutions. The excellent convergence of the present method has been demonstrated and the results obtained by the present method agree well with those from the finite element method. The effects of surface temperatures, thickness, layer number and material properties of the plate on the temperature distribution were discussed in detail. Numerical results reveal that the displacements and stresses monotonically increase with the increase of surface temperatures. In particular, the horizontal stresses are discontinuous at the interface.

ANALYSES ON NONLINEAR COUPLING OF MAGNETO-THERMO-ELASTICITY OF FERROMAGNETIC THIN SHELL—II:FINITE ELEMENT MODELING AND APPLICATION

Based on the generalized vaxiational principle of magneto-thermo-elasticity of a ferromagnetic thin shell established （see, Analyses on nonlinear coupling of magneto-thermo- elasticity of ferromagnetic thin shell--I）, the present paper developed a finite element modeling for the mechanical-magneto-thermal multi-field coupling of a ferromagnetic thin shell. The numerical modeling composes of finite element equations for three sub-systems of magnetic, thermal and deformation fields, as well as iterative methods for nonlinearities of the geometrical large-deflection and the multi-field coupling of the ferromagnetic shell. As examples, the numerical simulations on magneto-elastic behaviors of a ferromagnetic cylindrical shell in an applied magnetic field, and magneto-thermo-elastic behaviors of the shell in applied magnetic and thermal fields are carried out. The results are in good agreement with the experimental ones.

Generalized Thermo Elasticity in an Infinite Nonhomogeneous Solid Having a Spherical Cavity Using DPL Model

The induced temperature, displacement, and stress fields in an infinite nonhomogeneous elastic medium having a spherical cavity are obtained in the context dual-phase-lag model. The surface of the cavity is stress free and is subjected to a thermal shock. The material is elastic and has an in?homogeneity in the radial direction. The type of non homogeneity is such that the elastic constants, thermal conductivity and density are propor?tional to the nth power of the radial distance. The solutions are obtained analytically employing the Laplace transform technique. The numerical inversion of the transforms is carried out using Fourier series expansions. The stresses, temperature and displacement are computed and presented graphically. A comparison of the results for different theories is presented.

Uniqueness for the Linear Theory of Generalized Thermo-Elasticity

In this paper, the uniqueness for the linear theory of a new generalized thermo-elastic model of the continuum with the centre symmetry is shown under less assumptions, whose constitutive equations contain deformation, temperature and its rate as well as its gradient, electric field and its gradient. So the phase variation is pemitted when the deformation proceeds as long as the constitutive equations preserve their Original forms.

ANALYSES ON NONLINEAR COUPLING OF MAGNETO-THERMO-ELASTICITY OF FERROMAGNETIC THIN SHELL—I:GENERALIZED VARIATIONAL THEORETICAL MODELING

Based on the generalized variational principle of magneto-thermo-elasticity of the ferromagnetic elastic medium, a nonlinear coupling theoretical modeling for a ferromagnetic thin shell is developed. All governing equations and boundary conditions for the ferromagnetic shell are obtained from the variational manipulations on the magnetic scalar potential, temperature and the elastic displacement related to the total energy functional. The multi-field couplings and geometrical nonlinearity of the ferromagnetic thin shell are taken into account in the modeling. The general modeling can be further deduced to existing models of the magneto-elasticity and the thermo-elasticity of a ferromagnetic shell and magneto-thermo-elasticity of a ferromagnetic plate, which are coincident with the ones in literature.

Finite elastic torsional instability of incompressible thermo-hyperelastic cylinder

Torsional instability of an incompressible thermo-hyperelastic cylindrical rod, subjected to axial stretching and large torsions, is examined within the framework of finite elasticity. When the cylinder is stretched and twisted by a sufficiently large degree, a knot may form suddenly at one point. This inherent elastic instability is analyzed with the minimum potential energy principle and the critical values of torsion are obtained. The distribution of stresses as well as the tensile force and the torque are studied. Effect of tem- perature change is specifically discussed.

Magneto-thermo-elastic waves in an infinite perfectly conducting elastic solid with energy dissipation

The generalized thermo-elasticity theory, i.e., Green and Naghdi （G-N） Ⅲ theory, with energy dissipation （TEWED） is employed in the study of time-harmonic plane wave propagation in an unbounded, perfectly electrically conducting elastic medium subject to primary uniform magnetic field. A more general dispersion equation with com- plex coefficients is obtained for coupled magneto-thermo-elastic wave solved in complex domain by using the Leguerre＇s method. It reveals that the coupled magneto-thermoelastic wave corresponds to modified dilatational and thermal wave propagation with finite speeds modified by finite thermal wave speeds, thermo-elastic coupling, thermal diffusivity, and the external magnetic field. Numerical results for a copper-like material are presented.

THERMAL AND THERMO-ELASTIC-PLASTIC RESPONSE OF CERAMIC-METAL FUNCTIONALLY GRADED MATERIALS—THERMAL SHOCK PROBLEM

The thermal and thermo-elastic-plastic response of newly developed ceramic-metal functionally graded materials under a thermal shock load is studied. The materials are heated at the ceramic surface with a sudden high-intensity heat flux input, and cooled at the metal surface with a flowing liquid nitrogen. Emphasis is placed on two aspects: (1) the influence of the graded composition of the materials on the temperature and stress response; and (2) the optimum design of the graded composition from a unified viewpoint of the heat insulation property and stress relaxation property. Moreover, a comparison between the thermoelastic stress and the thermo-elastic-plastic stress is also made to indicate the plasticity effect.

Effect of 6H-SiC crystal growth shapes on thermo-elastic stress in the growing crystal

The effect of 6H-SiC crystal growth shapes on the thermo-elastic stress distribution in the growing crystal was systematically in- vestigated by using a finite element method. The thermo-elastic stress distribution in the crystal with a flat growth shape was more homoge- neous than that in the crystals with concave and convex growth shapes, and the value of thermo-elasticity in the crystal with a fiat growth shape was also smaller than that in the two other types of crystals. The maximum values of thermo-elastic stress appeared at interfaces be- tween the crystal and the graphite lid. If the lid was of the same properties as 6H-SiC, the thermo-elastic stress would decrease in two orders of magnitude. Thus, to grow 6H-SiC single crystals of high quality, a transition layer of SiC formed by deposition or reaction is suggested; meanwhile the thermal field in the growth chamber should be adjusted to maintain the crystals with fiat growth shapes.

Three-dimensional magneto-thermo-elastic analysis of functionally graded cylindrical shell

The present paper presents the three-dimensional magneto-thermo-elastic analysis of the functionally graded cylindrical shell immersed in applied thermal and magnetic fields under non-uniform internal pressure. The inhomogeneity of the shell is assumed to vary along the radial direction according to a power law function, whereas Poisson＇s ratio is supposed to be constant through the thickness. The existing equations in terms of the displacement components, temperature, and magnetic parameters are derived, and then the effective differential quadrature method （DQM） is used to acquire the analytical solution. Based on the DQM, the governing heat differential equations and edge boundary conditions are transformed into algebraic equations, and discretized in the series form. The effects of the gradient index and rapid temperature on the displacement, stress components, temperature, and induced magnetic field are graphically illustrated. The fast convergence of the method is demonstrated and compared with the results obtained by the finite element method （FEM）.

First-principles calculations on the elastic and thermodynamic properties of NbN

The elastic and thermodynamic properties of NbN at high pressures and high temperatures are investigated by the plane-wave pseudopotential density functional theory （DFT）. The generalized gradient approximation （GGA） with the Perdew-Burke Ernzerhof （PBE） method is used to describe the exchange-correlation energy in the present work. The calculated equilibrium lattice constant a0, bulk modulus B0, and the pressure derivative of bulk modulus B~ of NbN with rocksalt structure are in good agreement with numerous experimental and theoretical data. The elastic properties over a range of pressures from 0 to 80.4 GPa are obtained. Isotropic wave velocities and anisotropic elasticity of NbN are studied in detail. It is indicated that NbN is highly anisotropic in both longitudinal and shear-wave velocities. According to the quasi-harmonic Debye model, in which the phononic effect is considered, the relations of （V - Vo）/Vo to the temperature and the pressure, and the relations of the heat capacity Cv and the thermal expansion coefficient α to temperature are discussed in a pressure range from 0 to 80.4 GPa and a temperature range from 0 to 2500 K. At low temperature, Cv is proportional to T3 and tends to the Dulong Petit limit at higher temperature. We predict that the thermal expansion coefficient α of NbN is about 4.20 × 10-6/K at 300 K and 0 GPa.

A NEW UNIQUENESS THEOREM OF THE LINEAR THERMO-ELASTIC DYNAMICS ON UNBOUNDED DOMAINS

In the present paper, the uniqueness of the solution to the initial boundary value problem of the linear thermo-elastic dynamics on unbounded domains is obtained under less restrictive conditions, including abandoning the positive semi-definiteness of the elasticity tensor and boundness of the material tensor and restrictions on the acoustic tensor and the coupled tensor, and the results in [1] are refined. The conclusion here is valid for the case on bounded domains and the linear elastic dynamics on unbounded domains, hence the results in [2 similar to 4] are refined too. Abandoning the positive semi-definiteness of elasticity tensor permits that the uniqueness of the kinetic process is still valid for deformation of the wider materials, especially for the case that there are phase-transition during deformation process provided that the constitutive equations are unchanged in forms.

Analytical Solution for Thermo-Electro-Elastic Problems of an Orthotropic Piezoelectric Hollow Cylinder Subjected to Various Loading

An interpolation method was used to solve the Volterra integral equation of the second kind caused by interaction among thermal, electric and mechanical fields. The exact expressions for the transient responses of stresses, electric displacement and electric potential in an orthotropic piezoelectric hollow cylinder were obtained by means of the finite integral transforms. From the sample numerical calculations, it is seen that the present method is suitable for an orthotropic piezoelectric hollow cylinder subjected to arbitrary thermal shock, mechanical load and transient electric excitation. The result can be used as a reference to solve other transient coupled problems of thermo-electro-elasticity.

THE POINTWISE ESTIMATES TO SOLUTIONS FOR 1-DIMENSIONAL LINEAR THERMO-VISCO-ELASTIC SYSTEM

In this paper, we study the linear thermo-visco-elastic system in one-dimensional space variable. The mathematical model is a hyperbolic-parabolic partial differential system. The solutions of the system show some decay property due to the parabolicity. Based on detailed analysis on the Green function of the system, the pointwise estimates of the solutions are obtained, from which the generalized Huygens’ principle is shown.

Effects of Thermo-Mechanical Loads on Aeroelastic Instabilities of Metallic and Composite Panels

Panel flutter phenomena can be strongly affected by thermal loads,and so a refined aeroelastic model is presented.Higher-order shell theories are used as structural models.The aerodynamic forces are described using the Piston theory.The temperature is considered uniform over the thickness of the panel.The aero-thermo-elastic model is derived in the framework of the Carrera unified formulation(CUF),therefore the matrices are expressed in a compact form using the″fundamental nuclei″.Composite and sandwich structures are considered and different boundary conditions are taken into account.The effects of the thermal load on the aeroelastic behavior are investigated.

Identification of Time-Varying Modal Parameters for Thermo-Elastic Structure Subject to Unsteady Heating

A time-varying modal parameter identification method combined with Bayesian information criterion(BIC)and grey correlation analysis(GCA)is presented for a kind of thermo-elastic structures with sparse natural frequencies and subject to an unsteady temperature field.To demonstrate the method,the thermo-elastic structure to be identified is taken as a simply-supported beam with an axially movable boundary and subject to both random excitation and an unsteady temperature field,and the dynamic outputs of the beam are first simulated as the measured data for the identification.Then,an improved time-varying autoregressive(TVAR)model is generated from the simulated input and output of the system.The time-varying coefficients of the TVAR model are expanded as a finite set of time basis functions that facilitate the time-varying coefficients to be time-invariant.According to the BIC for preliminarily determining the scope of the order number,the grey system theory is introduced to determine the order of TVAR and the dimension of the basis functions simultaneously via the absolute grey correlation degree(AGCD).Finally,the time-varying instantaneous frequencies of the system are estimated by using the recursive least squares method.The identified results are capable of tracking the slow time-varying natural frequencies with high accuracy no matter for noise-free or noisy estimation.

The Quasi-Static Approximation of Heat Waves in Anisotropic Thermo-Elastic Media

The equilibrium equations of anisotropic media, coupled to the heat conduction equations, are studied here based on the standard spaces of the physical presentation, in which an new thermo-elastic model based on the second law of thermodynamics is induced. The uncoupled heat wave equation for anisotropic media is deduced. The results show that the equation of heat wave is of the properties of dissipative waves. In final part of this paper, we discuss the propagation behaviour of heat waves for transversely isotropic media.

Thermoelastic Stability of Closed Cylindrical Shell in Supersonic Gas Flow

In a linear framework,the problem of stability of closed cylindrical shell is briefly discussed.The cylindrical shell is immersed in a supersonic gas flow and under the influence of temperature field varying along the thickness.An unperturbed uniform velocity flow field,directed along the short edges of the shell,is applied.Due to the inhomogeneity of the temperature field distribution across the thickness shell buckling instability occurs.This instability accounts for the deformed shape of the shell,to be referred as the unperturbed state.Stability conditions and boundary for the unperturbed state of the system under consideration are presented following the basic theory of aero-thermo-elasticity.The stability boundary depends on the variables characterizing the flow speed,the temperature at the middle plane of the shell and the temperature gradient in the direction normal to that plane.It is shown that the combined effect of the temperature field and flowing stream regulates the process of stability,and the temperature field can significantly change the flutter critical speed.

Numerical Analysis of Thermo-Elastic Contact Problem of Disc Brakes for Vehicle on Gradient Surfaces

In this study, the thermo-elastic effects of frictional heat generation in a disc brake system due to braking actions were simulated. The mathematical model that defined the problem was developed from the kinetic and potential energies of moving vehicles on the gradient surfaces. This problem was solved for the selected geometry of disc brake and pad with their material properties selected from existing literatures using the finite element method and the computational results were obtained. The thermal deformation obtained was in good agreement with similar literature results. Also, for the same braking period and conditions, the results showed that a vehicle ascending a hill gave a higher temperature rise, Von Mises stress and thermal deformation on brake contact surfaces than when descending hill. Therefore, the braking period required to bring a moving vehicle in ascendent motion to a lower speed is expected to be shorter because of the gravity effect than horizontal motion, while descendent motion requires longer braking period.

Analysis of Thermo-Magneto-Elastic Nonlinear Dynamic Response of Shallow Conical Shells

The dynamic response study on thermo-magneto-elastic behavior of shallow conical shell in a time-dependent magnetic field is investigated, and the dynamic responses of displacement of shallow conical shell under mechanical loads, electromagnetic fields and temperature field coupling are analyzed. Based on Maxwell’s equations, heat conduction equation and nonlinear equations of classical plates and shells, the nonlinear dynamic response governing equations are derived. The electromagnetic field and temperature field equations are solved using variable separating technique, the nonlinear elastic field equations are solved by Galerkin method. The variation of temperature, magnetic field intensity and displacement with time under the coupling effect of the applied magnetic field and the surface uniform load were obtained. The influence of frequency of the applied magnetic field on the displacement wave forms is discussed.