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.     

Effect of rotation and relaxation times on plane waves in generalised thermo-elasticity

The propagation of harmonically time-dependent thermo-elastic plane waves of assigned frequency in infinite rotating media is studied using the theory of thermo-elasticity recently proposed by Green and Lindsay. A more general dispersion equation is deduced to determine the effect of rotation and relaxation times on the phase velocity of the coupled waves. The solutions for the phase velocity and the attenuation coefficient are obtained for small thermo-elastic coupling by a perturbation technique. Cases of low and high frequencies are also studied to determine the effect of rotation, the relaxation parameters and thermo-elastic coupling on the phase velocity and the attenuation coefficient of the waves.     

A solution to the thermo-elastic interface crack branching in dissimilar anisotropic bi-material media

An interface crack or delamination may often branch out of the interface in a laminated composite due to thermal stresses developing around the delamination/crack tip when the media is exposed to heat flow induced by environmental events such as a sudden short-duration fire. In this paper, the thermo-elastic problem of interface crack branching in dissimilar anisotropic bi-media is studied by using the theory of Stroh’s dislocation formalism, extended to thermo-elasticity in matrix notation. Based on the complex variable method and the analytical continuation principle, the thermo-elastic interface crack/delamination problem is examined and a general solution in compact form is derived for dissimilar anisotropic bi-media. A set of Green’s functions is proposed for the dislocations (conventional dislocation and thermal dislocation/heat vortex) in anisotropic bi-media. These functions may be more suitable than those which have appeared in the literature on addressing thermo-elastic interface crack branching in dissimilar anisotropic bi-materials. Using the contour integral method, a closed form solution to the interaction between the dislocations and the interface crack is obtained. Within the scope of linear fracture mechanics, the thermo-elastic problem of interface crack branching is then solved by modelling the branched portion as a continuous distribution of dislocations. The influence of thermal loading and thermal properties on the branching behavior is examined, and criteria for predicting interface crack branching are suggested, based on the extensive numerical results from the study of various cases.     

非傅里叶热弹性的时域间断迦辽金有限元方法

基于Lord-Shulman非傅里叶热弹性模型,提出了采用修正的时域间断迦辽金有限元方法(time discontinuousGalerkin finite element method, DGFEM)求解方法. DGFEM对温度场、位移场基本未知向量及其时间导数向量在时域中分别插值;在最终的求解公式中,引入了人工阻尼. 数值结果显示所发展的DGFEM 较好地捕捉了波的间断并消除了热冲击作用下虚假的数值振荡,能够良好地模拟热弹性问题并具有较高的精度.     

Thermo-elastic interaction with energy dissipation in an unbounded body with a spherical hole

The distribution of stresses due to step input of temperature at the boundary of a spherical hole in a homogeneous isotropic unbounded body is investigated by applying Laplace transform technique in the context of generalized theories of thermo-elasticity. The inverse of the transformed solution is carried out by applying a method of Bellman et al. The stresses are computed numerically and presented graphically in a number of figures for aluminum–epoxy composite material. The comparison among the theories i.e. classical thermo-elasticity (CTE), classical coupled thermo-elasticity (CCTE), temperature-rate-dependent thermo-elasticity (TRDTE(GL)) and thermo-elasticity with energy dissipation (TEWED(GN)) theory is presented graphically.     

“普适发展判据"对热弹性材料的适用条件

本文研究了普适发展判据对热弹性材料的本构限制,证明了该判据对热弹性材料适用的充要条件是机械变形与热传导互不耦合,因此一般情形下该判据对热弹性材料不能适用。     

Thermo-elastic crack branching in general anisotropic media

Thermal fields may exist in addition to mechanical loading, for example, due to short term exposure to fire. In this paper, the branching of cracks in the presence of combined thermal and mechanical loads is investigated for general anisotropic media by employing the theory of Stroh’s dislocation formalism, extended to thermo-elasticity in matrix notation. A general solution to the thermo-elastic crack problem for an anisotropic material under arbitrary loading is obtained in a compact form. Green’s functions are also presented for a thermal dislocation (heat vortex) and a conventional dislocation (or, referred as mechanical dislocation), which are formulated considering the cuts located at an arbitrary angle with respect to the x₁ axis of the coordinate system (x₁, x₂, x₃). Using the derived compact expressions, the interaction between the crack and the dislocation is studied and a closed form solution for this interaction is obtained. The branching portion of the thermo-elastic crack is modelled as a continuous distribution of dislocations. This problem is then converted into a set of singular integral equations. Numerical results are presented to illustrate the possible effects of thermal loading on the propagation of the branched crack.     

Generalized thermoelastic functionally graded orthotropic hollow sphere under thermal shock with three-phase-lag effect

This problem deals with the determination of thermo-elastic interaction due to step input of temperature on the boundaries of a functionally graded orthotropic hollow sphere in the context of linear theories of generalized thermo-elasticity. Using the Laplace transformation the fundamental equations have been expressed in the form of vector–matrix differential equation which is then solved by eigenvalue approach. The inverse of the transformed solution is carried out by applying a method of Bellman et al. Stresses, displacement and temperature distributions have been computed numerically and presented graphically in a number of figures. A comparison of the results for different theories (TEWOED(GN-II), TEWED(GN-III) and three-phase-lag model) is presented. When the material is homogeneous, isotropic and outer radius of the hollow sphere tends to infinity, the corresponding results agree with that of existing literature for GN-III model.     

MIXED TRANSFORM FINITE ELEMENT METHOD FOR SOLVING THE NON-LINEAR EQUATION FOR FLOW IN VARIABLY SATURATED POROUS MEDIA

A new computational method is developed for numerical solution of the Richards equation for flow in variably saturated porous media. The new method, referred to as the mixed transform finite element method, employs the mixed formulation of the Richards equation but expressed in terms of a partitioned transform. An iterative finite element algorithm is derived using a Newton–Galerkin weak statement. Specific advantages of the new method are demonstrated with applications to a set of one— dimensional test problems. Comparisons with the modified Picard method show that the new method produces more robust solutions for a broad range of soil– moisture regimes, including flow in desiccated soils, in heterogeneous media and in layered soils with formation of perched water zones. In addition, the mixed transform finite element method is shown to converge faster than the modified Picard method in a number of cases and to accurately represent pressure head and moisture content profiles with very steep fronts. © 1997 by John Wiley & Sons, Ltd.     

半空间饱和土内置点载荷作用下的热弹性波动

基于Biot波动理论及热弹性动力理论,利用已建立的饱和多孔弹性介质热流固耦合控制方程,研究半无限地基在内置点热力源作用下的动力响应问题. 求解过程引用Hankel变换技术,得到了热力源作用下土体中温度增量、应力、位移和孔隙水压力的积分形式解答.利用Hankel数值逆变换得到计算结果,分析了热流固耦合条件下激振频率对竖向位移和孔隙水压力响应的影响. 对热流固耦合、热弹性和多孔弹性模型计算结果进行了比较.      

核主泵用双锥度端面流体静压机械密封热弹流效应研究

针对核主泵用双锥度端面流体静压型机械密封热弹流效应研究在高压和高速条件下,其密封性能易受端面热弹变形影响的特点,提出了收敛型双锥面流体静压型机械密封,并建立了热-流-固耦合数学模型;通过采用有限差分法求解端面温度和端面流体膜压的控制方程组,采用有限元法求解密封环的热、弹变形,对密封进行了流、固、热耦合分析,研究了热弹变形对密封性能的影响,并对单锥面和双锥面2种流体静压型机械密封的密封性能、温度分布进行了对比研究.结果表明:双锥面密封与单锥面密封相比,不仅稳定性更好,而且端面温度分布更均匀,可靠性更高,但是泄漏率略有上升;在泄漏入口处即高压侧,外锥面锥度的大小对开启力影响较大,而在泄漏出口处即低压侧,内锥面锥度的大小对泄漏率影响较大;内锥面宽度比取0.05左右时能获得较大的刚漏比.     

热弹性薄板大挠度弯曲的BEM法

本文首先基于理性力学非线性几何场理论，建立了等效速率形式的热弹性薄板的Ｋａｒｍａｎ方程，通过将热弹性薄板大挠度弯曲问题的看成平板弯曲问题与平面大变形问题的耦合，在固定坐标系及拖带坐标系上推导出两组边界积分方程，从而建立起新的分析热性薄板大挠度弯曲问题的边界元。本文的方法较双往分析此问题的边界法在理论上更准确，合理，算例表明本文的方法理论可靠，精度良好。     

On quadruple integral equations related to a certain crack problem

An exact solution of a four part mixed boundary value problem representing a three colinear crack system connected with specified crack opening displacements between the cracks is obtained. The three cracks thus become one with pressure and/or opening displacement prescribed on the crack face. From considerations of dual symmetry and a formulation based on Papkovich-Neuber harmonic functions, the boundary value problem is reduced to solving a quadruple set of integral equations. An exact solution of these equations is derived using a modified finite Hilbert transform technique. The closed form results for the stress distributions and the crack-tip stress intensity factors are presented. Limiting cases of the solution yield results which agree with well known solutions.     

Free vibration of thermo-elastic microplate based on spatiotemporal fractional-order derivatives with nonlocal characteristic length and time

A fractional-order thermo-elastic model taking into account the small-scale effects of the thermo-elastic coupled behavior is developed to study the free vibration of a higher-order shear microplate. The nonlocal strain gradient theory is modified with the introduction of the fractional-order derivatives and the nonlocal characteristic length. The Fourier heat conduction is replaced by the non-Fourier heat conduction with the introduction of the fractional order and the memory characteristic tim...     

An axisymmetric stress analysis in a single fibre composite of finite length under a thermal expansion mismatch

In this paper, an exact solution is derived for the characterization of thermal stresses in a single-fibre composite of finite length. All the required boundary and interfacial conditions of the thermo-elastic problem are thus satisfied exactly. The proposed method involves a particular solution that is added to a three-dimensional (3D) complementary displacement field which satisfies automatically the Navier's equations. Based on experimental data provided by fibre Bragg grating sensors, an axisymmetric analysis is used then to determine the residual stress field inside the composite due to matrix shrinkage. The numerical results clearly indicate that all stress components vary significantly near the ends. An abrupt change of the shear stresses is thus predicted close to the edges. The results of the model are also found to be in good agreement with those obtained from finite element simulations. A comparison of the proposed approach with three other published theoretical models is also presented.     

TRANSIENT THERMAL RESPONSE IN THICK ORTHOTROPIC HOLLOW CYLINDERS WITH FINITE LENGTH： HIGH ORDER SHELL THEORY

The transient thermal response of a thick orthotropic hollow cylinder with finite length is studied by a high order shell theory. The radial and axial displacements are assumed to have quadratic and cubic variations through the thickness, respectively. It is important that the radial stress is approximated by a cubic expansion satisfying the boundary conditions at the inner and outer surfaces, and the corresponding strain should be least-squares compatible with the strain derived from the strain-displacement relation. The equations of motion are derived from the integration of the equilibrium equations of stresses, which are solved by precise integration method （PIM）. Numerical results are.obtained, and compared with FE simulations and dynamic thermo-elasticity solutions, which indicates that the high order shell theory is capable of predicting the transient thermal response of an orthotropic （or isotropic） thick hollow cylinder efficiently, and for the detonation tube of actual pulse detonation engines （PDE） heated continuously, the thermal stresses will become too large to be neglected, which are not like those in the one time experiments with very short time.     

Axisymmetric Thermoelastic Interactions without Energy Dissipation in an Unbounded Body with Cylindrical Cavity

The linear theory of thermoelasticity without energy dissipation is employed to study thermoelastic interactions in a homogeneous and isotropic unbounded body containing a cylindrical cavity. The interactions are supposed to be due to a constant step in radial stress or temperature applied to the boundary of the acvity, which is maintained at a constant temperature or zero radial stress (as the case may be). By using the Laplace transform technique, it is found that the interactions consist of two coupled waves both of which propagate with a finite speed but with no attenuation. The discontinuities that occurs at the wavefronts are computed. Numerical results applicable to a copper-like material are presented.     

Three-dimensional solutions for the stress fields in functionally graded cylindrical panel with finite length and subjected to thermal/mechanical loads

Three-dimensional thermo-elastic analysis of a functionally graded cylindrical panel with finite length and subjected to nonuniform mechanical and steady-state thermal loads are carried out in this paper. Thermal and mechanical properties of the functionally graded material are assumed to be temperature independent and continuously vary in the radial direction of the panel. Analytical solutions for the temperature and stress fields expressed in terms of trigonometric and power series for the simply supported boundary conditions are derived and graphically presented.     

Thermoelastic interaction with energy dissipation in a transversely isotropic thin circular disc

The distribution of stresses due to step input of temperature on the boundaries of a homogeneous transversely isotropic circular disc is investigated by applying Laplace transform technique in the context of generalized theories of thermo-elasticity. The inverse of the transformed solution is carried out by applying a method of Bellman et al. The stresses are computed numerically and presented graphically in a number of figures. A comparison of the results for different theories (CTE, CCTE, TRDTE(GL), TEWED(GN)) and the effect of anisotropy on the stresses are also presented. When the material is isotropic and outer radius of the disc tends to infinity, the corresponding result agrees with that of existing literature.     

The Background Concept in Structural Analyses: with Remarks on Deformation Control

A review of the modern multiple field theory is given. The theory is derived from the classical two-field theory of linearized thermo-elasticity. Extensions of Maysel's formula are described. They allow formulating an optimal solution strategy using the Green function. Various applied problems are solved and commented on. The advantages of the multiple field theory are discussed