Fundamental solution for transversely isotropic thermoelastic materials

We use the compact harmonic general solutions of transversely isotropic thermoelastic materials to construct the three-dimensional fundamental solutions for a steady point heat source in an infinite transversely isotropic thermoelastic material and a steady point heat source on the surface of a semi-infinite transversely isotropic thermoelastic material by three newly introduced harmonic functions, respectively. All components of coupled field are expressed in terms of elementary functions and are convenient to use. Numerical results for hexagonal zinc are given graphically by contours.     

Green''s functions for transversely isotropic piezoelectric solids

Closed-form expressions are obtained for the infinite-body Green's functions for a transversely isotropic piezoelectric medium. The four Green's functions represent the coupled elastic and electric response to an applied point force or point charge. The Green's functions are obtained using a formulation where the three displacements and the electric potential are derivable from two potential functions. When piezoelectric coupling is absent, the results reduce to those for uncoupled elasticity and electrostatics.     

Fundamental solutions of the thermoelastic equations for transversely isotropic plates

The problem of thermoelasticity for transversely isotropic plates acted upon by concentrated heat sources is solved. The {1, 2}-order equations of thermoelasticity that incorporate the transverse shear and normal stresses are used. A bending heat source with symmetric heat transfer is considered. The dependence of thermal stress components on the thermal and thermomechanical parameters of transversely isotropic plates is studied     

Allowance for complex loading in transversely isotropic solids

A model of plasticity for a transversely isotropic material with allowance for complex loading is developed, based on results of experiments with homogeneous cylindrical specimens of isotropic materials. An empirical model of plasticity for isotropic metals is constructed with allowance for vector properties of the material. The model is extended to a particular case of anisotropy. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 128–133, January–February, 2009.     

INTERFACIAL CRACK ANALYSIS IN THREE-DIMENSIONAL TRANSVERSELY ISOTROPIC BI-MATERIALS BY BOUNDARY INTEGRAL EQUATION METHOD

The integral-differential equations for three-dimensional planar interfacial cracks of arbitrary shape in transversely isotropic bimaterials were derived by virtue of the Somigliana identity and the fundamental solutions, in which the displacement discontinuities across the crack faces are the unknowns to be determined. The interface is parallel to both the planes of isotropy. The singular behaviors of displacement and stress near the crack border were analyzed and the stress singularity indexes were obtained by integral equation method. The stress intensity factors were expressed in terms of the displacement discontinuities. In the non-oscillatory case, the hyper-singular boundary integral-differential equations were reduced to hyper-singular boundary integral equations similar to those of homogeneously isotropic materials.     

Transient thermoelastic contact problem of a transversely isotropic cylinder

Summary This paper concerns a transient thermoelastic contact problem in a transversely isotropic infinite cylinder inserted into a heated rigid ring. It is assumed that the heat transfer coefficient at the bonded surface is different from the coefficient at the traction-free boundary surface. A finite difference formulation with respect only to time is used to solve the three-dimensional transient heat conduction equation for the temperature field. The thermal stress field is analyzed by means of the transversely isotropic potential function method. The radial, hoop and axial stresses have singularities at the end of the contact surface. The concentration factors that may be used to evaluate the strength of the stress singularities are introduced.

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Ein transientes thermoelastisches Kontaktproblem eines transversal-isotropen Zylinders

Übersicht Behandelt wird ein transientes thermoelastisches Kontaktproblem eines transversal-isotropen unendlichen Zylinders, der in einen geheizten starren Ring eingesetzt wird. Der Wärmeübergang in der Kontaktfläche und der freien Oberfläche seien verschieden. Bei der Lösung der instationären dreidimensionalen Wärmeleitungsgleichung wird bezüglich der Zeit eine Finite-Differenzen-Formulierung benutzt. Die Wärmespannungen werden nach der Potentialfunktionen-Methode im transversalisotropen Fall ermittelt. Radial-, Umfangs- und Axialspannung weisen am Ende der Kontaktzone Singularitäten auf, die durch eingeführte Spannungskonzentrationsfaktoren beschrieben werden.

     

Completeness of general solutions for three-dimensional transversely isotropic piezoelectricity

In this paper, a general solution for three-dimensional transversely isotropic piezoelectricity in terms of four quasi-quadri-harmonic functions is established first. Owing to complexity of the higher-order equation, it is difficult to obtain rigorous analytic solutions and in most cases this general solution is not applicable. By virtue of the generalized Almansi’s Theorem, the simplified generalized LHN solution and E–L solution expressed by lower order functions are achieved, respectively, by taking a decomposition and superposition technique. In the absence of piezoelectric coupling, these two simplified general solutions can be degenerated into those for transversely isotropic elasticity, i.e. LHN and E–L solutions. More importantly, the completeness of these two generalized solutions is proved if the domain is z-convex, no matter whether the characteristic roots are distinct or possibly equal to each other.     

Propagation of Lamb waves in transversely isotropic thermoelastic diffusive plate

The constitutive relations and field equations for anisotropic generalized thermoelastic diffusion are derived and deduced for a particular type of anisotropy, i.e. transverse isotropy. Green and Lindsay (GL) theory, in which, thermodiffusion and thermodiffusion–mechanical relaxations are governed by four different time constants, is selected for study. The propagation of plane harmonic thermoelastic diffusive waves in a homogeneous, transversely isotropic, elastic plate of finite width is studied, in the context of generalized theory of thermoelastic diffusion. According to the characteristic equation, three quasi-longitudinal waves namely, quasi-elastodiffusive (QED-mode), quasi-massdiffusive (QMD-mode) and quasi-thermodiffusive (QTD-mode) can propagate in addition to quasi-transverse waves (QSV-mode) and the purely quasi-transverse motion (QSH-mode), which is not affected by thermal and diffusion vibrations, gets decoupled from the rest of the motion of wave propagation. The secular equations corresponding to the symmetric and skew symmetric modes of the plate are derived. The amplitudes of displacements, temperature change and concentration for symmetric and skew symmetric modes of vibration of plate are computed numerically. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient and amplitudes of wave propagation are presented graphically in order to illustrate and compare the analytically results. Some special cases of frequency equation are also deduced from the existing results.     

轴对称横观各向同性热弹性圆柱的分解

为了得到精确的应力场、位移场、温度场,将扭转圆轴的精化理论研究方法推广到轴对称横观各向同性热弹性圆柱。利用Bessel函数以及轴对称横观各向同性热弹性圆柱的通解,给出了轴对称横观各向同性热弹性圆柱的分解定理。根据柱面齐次边界条件获得了精确的精化方程,精化方程可以分解为一阶方程、超越方程、温度方程,从而将横观各向同性热弹性圆柱的轴对称问题分解为轴向拉压问题、超越问题、热-应力耦合问题。超越部分对应端部自平衡情况,可以清晰地了解到端部应力分布对内部应力场的影响,热-应力耦合部分对应无外加应力场时圆柱内部因温度变化引起的热应力。     

General solution for the coupled equations of transversely isotropic magnetoelectroelastic solids

IntroductionMechanicsandphysicsofmediapossessingsimultaneouslypiezoelectric ,piezomagneticandmagnetoelectriceffects ,namely ,magnetoelectroelasticsolids,haveattractedmoreandmoreattentionduetotheirgreatpotentialapplicationsinthetechnologiesofsmartandadaptivematerialsystem[1] .Sometheoreticalinvestigationsappearedintheliteratureinclude :1)Theexistenceproblemofsurfacewavesinsemi_infiniteanisotropicmagnetoelectroelasticmediawithvariousboundaryconditions[2 ,3 ] ;2 )Green’sfunctions[4～ 7] ;3)Inho…     

Thermal stress analysis of a three-dimensional anticrack in a transversely isotropic solid

A three-dimensional analysis is performed for an infinite transversely isotropic elastic body containing an insulated rigid sheet-like inclusion (an anticrack) in the isotropy plane under a remote perpendicularly uniform heat flow. A general solution scheme is presented for the resulting boundary-value problems. Accurate results are obtained by constructing suitable potential solutions and reducing the thermal problem to a mechanical analog for the corresponding isotropic problem. The governing boundary integral equation for a planar anticrack of arbitrary shape is obtained in terms of a normal stress discontinuity. As an illustration, a complete solution for a rigid circular inclusion is obtained in terms of elementary functions and analyzed. This solution is compared with that corresponding to a penny-shaped crack problem.     

Rapid sliding indentation with friction on a transversely isotropic thermoelastic half-space

A rigid insulated die slides at a constant sub-critical speed on a transversely isotropic half-space in the presence of friction. In a two-dimensional analysis of the dynamic steady-state, the coupled equations of thermoelasticity are invoked. All elements of the Coulomb friction model are strictly enforced, thus giving rise to auxiliary conditions, including two unilateral constraints.Robust asymptotic forms of an exact solution to a related problem with unmixed boundary conditions lead to analytical solutions for the sliding indentation problem. The solution expressions, abetted by calculations for zinc, show the role of frictional heating on the half-space surface. The effects of friction and sliding speed on contact zone size and location and average contact zone temperature are also studied.The analysis is aided by factoring procedures that simplify the complicated forms that arise in anisotropic elasticity. A scheme that renders expressions for roots of certain irrational functions analytic to within a single quadrature also plays a role.     

Two-dimensional fractal-like finite element method for thermoelastic crack analysis

The fractal-like finite element method has been proved to be very efficient and accurate in two-dimensional static and dynamic crack problems. In this paper, we extend our previous study to include the thermal effect for two-dimensional isotropic thermal crack problems. Both the temperature intensity factor and thermal stress intensity factor can be calculated directly. The temperature distribution is first found, which is imposed thereafter as a thermal load in the elastic problem. The transformation function used in the study has been found analytically. The effects of different thermal loading on the thermal stress intensity factor are presented. The numerical examples are compared with the results from other methods and find to be in good agreement.     

Complete solutions of three-dimensional problems in transversely isotropic media

Continuum Mechanics and Thermodynamics - We present a systematic approach to the derivation of complete solutions for three-dimensional transversely isotropic elastic problems. The class of...     

Propagation of Rayleigh waves on free surface of transversely isotropic generalized thermoelastic diffusion

The present paper is devoted to the study of Rayleigh wave propagation in a homogeneous, transversely isotropic, thermoelastic diffusive half-space, subject to stress free, thermally insulated/isothermal, and chemical potential boundary conditions in the context of the generalized thermoelastic diffusion theory. The Green-Lindsay（GL） theory is used in the study. In this theory, thermodiffusion and thermodiffusion mechanical relaxations are governed by four different time constants. Secular equations for surface wave propagation in the considered media are derived. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient are graphically presented in order to present the analytical results and make comparison. Some special cases of frequency equations are derived from the present investigation.