层合材料的非傅里叶热传导及热应力

论文建立了一个双层材料层合板受瞬态加热情况下的非傅里叶热传导分析模型,用向后差分法得到了温度场的数值解,并对该差分格式的稳定性进行了讨论.给出了温度场随导热时间、热扩散率、空间与时间步长之比以及弛豫时间的变化趋势.同时,通过已经求得的温度场,求得了层合板内的应力场,给出了层合板内的热应力随时间的变化.     

Thermal stresses factors of orthotropic graded layers with a finite line bond

In the paper, the problem of a finite line bond between two orthotropic functionally graded strips under thermal loading is considered. Considering some new boundary conditions, it is assumed that the temperature drop across the finite line bond is the result of the thermal conductivity index controlling heat conduction through the bond region. Using Fourier transforms technique, the therm-elastic mixed boundary value problems are reduced to a system of singular integral equations which can be solved approximately by applying the Chebyshev polynomials. The numerical results for the temperature and displacement field as well as the thermal stress intensity factors (TSIFs) are presented. The influence of the thickness of the layers and the thermo-elastic nonhomogeneity parameters on the temperature distribution and the TSIFs is discussed in detail. These results can be expected to be used for the purpose of gaining better understanding of the thermo-mechanical behavior of layered structures.     

Thermal stress intensity factors for an interface crack in a functionally graded layered structures

The fracture behavior of a functionally graded layered structure (FGLS) with an interface crack under thermal loading is investigated. Considering new boundary conditions, it is assumed that interface crack is partly insulated, and the temperature drop across the crack surfaces is the result of the thermal resistance due to the heat conduction through the crack region. The problem is formulated in terms of a system of singular integral equations. Numerical results are presented to show the influence of the material nonhomogeneity parameters and the dimensionless thermal resistance on the thermal stress intensity factors (TSIFs).     

THERMAL CONSOLIDATION OF LAYERED POROUS HALF-SPACE TO VARIABLE THERMAL LOADING

An analytical method was derived for the thermal consolidation of layered, saturated porous half-space to variable thermal loading with time. In the coupled governing equations of linear thermoelastic media, the influences of thermo-osmosis effect and thermal filtration effect were introduced. Solutions in Laplace transform space were first obtained and then numerically inverted. The responses of a double-layered porous space subjected to exponential decaying thermal loading were studied. The influences of the differences between the properties of the two layers (e.g., the coefficient of thermal consolidation, elastic modulus) on thermal consolidation were discussed. The studies show that the coupling effects of displacement and stress fields on temperature field can be completely neglected, however, the thermo-osmosis effect has an obvious influence on thermal responses.     

Vibrations and self-heating of a layered elastic-viscoelastic rectangular prism under a vibrating punch

The vibrations and self-heating of a layered metal-polymer rectangular prism kinematically excited by a normally vibrating punch are analyzed numerically. The effect of reinforcement layers on the rate of variation in and the spatial distribution of the temperature field is examined. It is established that thin metallic layers in a polymer matrix change the dissipation mechanism from shear to bulk. The effect of contact stress concentration on the localization of temperature field is studied. It is established that the energy flux through the load application area decreases due to softening of the material. Several reinforcement effects are revealed. It is shown that they are determined by the value of the load parameter. The numerical results are in good agreement with experimental data on self-heating kinetics __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 71–79, August 2007.     

Dynamic thermal shock in a layered cylinder with initial interface pressure

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｄｙｎａｍｉｃｐｒｏｂｌｅｍｏｆｓｔｒｕｃｔｕｒｅｓｔｒｅｎｇｔｈｉｓａｎｏｕｔｓｔａｎｄｉｎｇｐｒｏｂｌｅｍ．Ａｆｔｅｒｃｏｎｓｕｌｔｉｎｇｓｏｍｅｐａｐｅｒｓ,ｗｅｃａｎｋｎｏｗｔｈａｔｔｈｉｓｓｕｂｊｅｃｔｈａｓｂｅｅｎｓｔｕｄｉｅｄｅｘｔｅｎｓｉｖｅｌｙｂｙｓｅｖｅｒａｌａｕｔｈｏｒｓ［１～７］．Ｔｈｅｉｒｉｎｖｅｓｔｉｇａｔｉｏｎｓｏｎｌｙｂａｓｅｄｏｎｃａｌｃｕｌａｔｉｎｇｖｉｂｒａｔｉｏｎｉｎａｌａｙｅｒｅｄｓｔｒｕｃｔｕｒｅａｎｄｐｒｅｓｅｎｔｉｎｇ…     

Double-diffusive convection for a heated cylinder submerged in a salt-stratified fluid layer

Double-diffusive convection due to a cylindrical source submerged in a salt-stratified solution is numerically investigated in this study. For proper simulation of the vortex generated around the cylinder, a computational domain with irregular shape is employed. Flow conditions depend strongly on the thermal Rayleigh number, Ra _T , and the buoyancy ratio, R _ρ. There are two types of onset of instability existing in the flow field. Both types are due to either the interaction of the upward temperature gradient and downward salinity gradient or the interaction of the lateral temperature gradient and downward salinity gradient. The onset of layer instability due to plume convection is due to the former, whereas, the onset of layer instability of layers around the cylinder is due to the latter. Both types can be found in the flow field. The transport mechanism of layers at the top of the basic plume belongs to former while that due to basic plume and layer around the cylinder are the latter. The increase in Ra _T reinforces the plume convection and reduces the layer numbers generated around the cylinder for the same buoyancy ratio. For the same Ra _T , the increase of R _ρ suppresses the plume convection but reinforces the layers generated around the cylinder. The profiles of local Nusselt number reflects the heat transfer characteristics of plume convection and layered structure. The profiles of averaged Nusselt number are between the pure conduction and natural convection modes and the variation is due to the evolution of layers. Received on 13 September 1996     

衰变热源作用下饱和多孔介质热固结问题的扩展精细积分法

热源作用下饱和多孔介质热固结效应是土木及能源工程领域的一个重要课题.由于问题的复杂性,已有的研究大多将介质假定为均匀各向同性,且将热源假定为恒定强度.实际工程中,天然饱和多孔介质常表现出明显的分层特性,热源强度也存在衰变性,为此本工作采用扩展精细积分法对衰变热源作用下层状饱和多孔介质的热固结问题进行研究.借助于积分变换,将饱和多孔介质热固结问题的偏微分方程转化为变换域内的常微分方程;然后对饱和多孔介质微层元进行合并消元,并结合边界条件,推导出衰变热源作用下层状饱和多孔介质热固结问题在积分变换域内的扩展精细积分解;对所得解答进行相应的数值积分逆变换,可获得所求温度、超静孔压及竖向位移在物理域内的解答.基于上述求解过程,编制相应的计算程序进行数值计算,通过与已有文献对比,验证本文扩展精细积分法在求解层状饱和多孔介质热固结问题中的适应性和正确性;最后通过几组算例,分析热源衰变周期、热源埋深及介质的成层性对热固结效应的影响.结果表明:热源衰变周期对温度和超静孔压的峰值、以及达到峰值的时间均有明显影响,衰变周期越长,二者峰值均越大,且达到峰值所需时间越长;热源埋深对超静孔压及竖向位移变化影响显著,深埋热源作用时热源两侧竖向位移呈对称分布,而浅埋热源两侧则无此现象;饱和多孔介质的分层特性对热固结效应影响明显.     

Classical and generalized coupled thermoelasticity analysis in one-dimensional layered media

The behavior of thermoelastic waves at the interface of layered medium and distributions of these waves through the domain are examined by applying the direct finite element method to obtain the field variables directly within the spatial and temporal domains. The analysis is performed in a one-dimensional domain with two different layers to provide a means to follow the behavior of the reflected thermoelastic waves at the interface. It appears that the distributions of thermoelastic waves in an isotropic slab with one layer are significantly different from those in multilayered slabs. For instance, the negative displacement waves, several stresses with positive or negative signs and temperature distributions produced in the multilayered domains, are quite different from those in a single layer. This method may be generalized to simulate the propagation of thermoelastic waves in various multilayered regions and analyze the behavior of the layered composite structures under the mechanical or thermal impact loads.     

Experimental and numerical investigations of fluid flow and heat transfer in a cryogenic tank at loss of vacuum

The transient process of thermal stratification in liquid nitrogen (LN₂) induced by lose of vacuum in a multi-layer insulated cryogenic tank is investigated both experimentally and numerically. In the experiments, distribution and evolution of the liquid temperature is obtained using thermocouples. Then, two-dimensional numerical computations are performed, using the two-fluid model together with nucleate boiling model as the closure correlations. Comparison of the numerical results against the experimental data illustrates that the process of thermal stratification forming and weakening, as well as the liquid temperature field are satisfactorily simulated. The computed results of liquid flow field contribute to the understanding of this transient process. It is also demonstrated that the two-phase flow in the tank plays an important role on thermal stratification.     

Force acting on a body in a nonuniformly heated magnetizable fluid

The force acting on a spherical particle in a nonuniformly heated magnetizable fluid is calculated in the case in which the permeability of the particle material depends arbitrarily on temperature and the strength of the magnetic field, and the permeability of the fluid on temperature. In calculating the force the difference between the thermal conductivities of the particle material and the fluid and, as distinct from [6], the distortion of the applied magnetic field due to the presence of a temperature gradient are taken into account. Accordingly, the expression for the force differs from that obtained in [6]. It is shown that the expression obtained for the force is correct up to terms of the order of a certain power of a small parameter — the ratio of the particle size to the characteristic interval of variation of the parameters (temperature, strength of magnetic field, etc.). A condition determining the value of this power is derived.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 76–83, March–April, 1989.     

Mixed convection flow investigation in a rectangular horizontal tube stenosis via liquid crystal thermography and planar PIV

The temperature and velocity field in a horizontal convergent-divergent rectangular channel heated from below is studied experimentally for a Reynolds range 8-120, Grashof numbers from 0.44 × 10⁵ to 2.56 × 10⁵ and Richardson numbers from 3 to 4000, using water as working fluid. The duct aspect ratio (width/height) varies from 1 at its inlet to 2.28 at the stenosis neck, and both the upper and bottom walls are tilted with an angle of ±15.7° with respect to the horizontal. The temperature of the bottom wall is kept constant above that of the issuing fluid. The temperature field is recorded by liquid crystals in the vertical mid plane whereas the velocity field is measured in this plane as well as in four cross sections of the divergent passage by planar PIV, revealing the characteristics of the secondary velocity field. For all the examined cases the flow in the convergent passage is free of thermal plumes, and the thermal boundary layer is thin. In contrast, the divergent passage is characterized by a thermal plume which is shifted upstream with increasing Gr or reducing Re. Both transversal and longitudinal rolls emerge in this diffuser the strength of which depend on Re and Gr influencing the streamwise distribution of Nusselt which for low Re presents a minimum.     

Radiative-convective heat transfer in a plane layer of a selectively absorbing mist

This paper deals with the thermal field in a plane layer of selectively absorbing gas which has been injected into a steady turbulent stream of high-temperature gas flowing around a porous plate. The boundary-value problem in terms of the energy equation reduces to a nonlinear integral equation in terms of a dimensionless temperature, and this equation is solved numerically by the Newton-Kantorovich method. The results are presented on graphs of temperature and thermal flux in the absorbing gas layer as functions of the space coordinate. Such a problem has been analyzed in [1] for the case of an injected gray gas.Translated from Zhurnal Prikladnoi Mekhaniki i Technicheskoi Fiziki, No. 3, pp. 179–182, May–June, 1972.     

A decoupled modal analysis for nonlinear dynamics of an orthotropic thin laminate in a simply supported boundary condition subject to thermal mechanical loading

In this paper, we analyze the nonlinear dynamic response of an orthotropic laminate in a simply supported boundary condition subject to thermal and mechanical loading. The equation of motion for the laminate’s deflection is obtained in a decoupled Duffing equation by means of a Galerkin-type method without Berger’s approximations. The Duffing equation incorporates an arbitrary thermal field, with both the in-plane and transverse temperature variations in a steady-state and a transient state. The formulation indicates that the transverse temperature variation produces an additional pressure load, while the in-plane temperature variation affects the system frequency. The equation allows for characterization of the laminate behaviors in nonlinear thermal buckling, thermal vibration and thermal mechanical response.     

采用包络-准则法优化考虑瞬态传热的薄板结构

刚度和强度是薄板结构的两个主要性能。在瞬态传热过程中,考虑热-力耦合,随时间和空间变化的非均匀温度场在结构中会引起热变形和热应力,温度场随时间变化的规律和空间分布依赖于板的厚度变化,进而影响板的刚度和强度。因此,考虑瞬态传热的薄板优化问题具有更强的非线性,更加难以求解。本文给出一种包络-准则方法处理这类结构优化问题。首先,针对外力荷载,进行一个结构柔顺性的优化设计;以这一设计为基础,通过瞬态热-力耦合分析及优化准则,计算多个时刻的优化设计变量并取其包络,对上述优化结果进行迭代修正,以消除瞬态温度场作用下较高的局部应力。优化算例表明,该方法对于考虑瞬态传热薄板优化问题有效。     

Non-linear dynamic response of a thin laminate subject to non-uniform thermal field

Non-linear dynamics behavior of a thin isotropic laminate in a simply supported boundary condition is studied for its response with both mechanical and thermal loads in effect. The thermal effects of both the in-plane and transverse non-uniform temperature variations in steady-state are considered. The equation of motion for the laminate deflection is reduced to the Duffing equation in a decoupled modal form by means of a generalized Galerkin's method. The stress field as a function of deflection and temperature variation is also obtained in a plane stress condition for its non-linear elastic behavior with von Karman strain field.For an exemplary laminated microstructure used as a printed wiring board, it is found that a high rise of the in-plane temperature increases the resonance frequency and could significantly increase the stresses of the lamina. The through thickness temperature variation has no significant effect on the deflection. Failure analysis is also made based on the composite failure criteria for a laminate to identify the critical mechanical and thermal loads.     

Influence of the Prandtl Number on the Unsteady Thermo-Fluid Dynamic Field Around a Thick Plate

The problem of a semi-infinite “thick” plate impulsively accelerated to a constant speed is discussed, considering a compressible laminar boundary layer when the thermo-fluid dynamic field in the flow is coupled with the thermal field in the solid (conjugated heat transfer). Different cases are defined by the boundary condition for the thermal field on the unwetted plate side, A first-order analytical approximation of a more general method of solution is here proposed, with emphasis to the analysis of the effects of the Prandtl number (Pr), when the temperature on the unwetted side of the plate is assumed constant. The comparison with some reference solution available for the limiting conditions of steady flow and plate of infinite length shows a very satisfactory accuracy of the present results in spite of the first order approximation.     

Static analysis for functionally graded piezoelectric actuators or sensors under a combined electro-thermal load

Based on the theory of piezoelasticity, a functionally graded piezoelectric sandwich cantilever under an applied electric field and/or a heat load is studied. All materials may be arbitrary functional gradients in the thickness direction. The static solution for the mentioned problems is presented by the Airy stress function method. As a special case, assuming that the material composition varies continuously in the direction of the thickness according to a power law distribution, a comprehensive parametric study is conducted to show the influence of electromechanical coupling (EMC), functionally graded index, temperature change and thickness ratio on the bending behavior of actuators or sensors. The distribution of electric field or normal stress in present FGPM actuators is continuous along the thickness, which overcomes the problem in traditional layered actuators. The solution facilitates the design optimization for different piezoelectric actuators and has another potential application for material parameter identification.     

A decoupled modal form Duffing equation for an orthotropic laminate in a clamped boundary condition with thermal diffusion

The non-linear thermo-elasticity response of an orthotropic laminate in a clamped boundary condition is analyzed by means of the method of weighted residuals for its behaviors subject to thermal and mechanical loading. The equation of motion for the laminate's deflection is obtained in the form of a decoupled modal form Duffing equation, without Berger's approximation. The thermal field, with both the in-plane and transverse temperature variations, is incorporated in both a steady-state and transient state. The formulation indicates that a transverse thermal field with a temperature rise produces a load onto the laminate, while the in-plane temperature variation affects the system frequency and stability. We demonstrate the numerical results of the modal response of an isotropic laminate for the thermal buckling and vibration.