粗糙表面之间接触热阻反问题研究

当两个固体表面相互接触时,由于接触面粗糙度的影响,界面间就形成了非一致接触,这种接触导致热流收缩,进而产生接触热阻. 目前的理论研究主要集中在正问题研究,对反问题的研究相对较少. 接触热阻反问题研究是通过研究部分边界温度、热流和部分测量点的温度来反演得到界面上的接触热阻. 反问题研究在很多工程领域都有应用,如航空航天、机械制造、微电子等,是工程中确定接触热阻一种快速有效的方法. 本文采用边界元法和共轭梯度法研究了二维空间随坐标变化的接触热阻反问题. 为了验证方法的准确性和可行性,假定在已知部分测量点温度和真实接触热阻的情况下,反演计算得到界面的温度和热流,进而得到接触热阻,并与真实接触热阻进行比较. 结果表明采用边界元法和共轭梯度法在无测量误差的情况下,可以准确反演获得界面的真实接触热阻. 若存在测量误差,反演计算结果对测量误差极其敏感,反演结果误差会由于测量误差的引入而被放大. 为处理这种不适定性, 采用最小二乘法对反演计算结果进行校正,结果表明采用最小二乘法能够避开反问题中一些偏离实际值较大的测量点,显著提高反演计算结果的准确性.      

Numerical nonlinear inverse problem of determining wall heat flux

The inverse problem of determining time-variable surface heat flux in a plane wall, with constant or temperature dependent thermal properties, is numerically studied. Different kinds of incident heat flux, including rectangular waveform, are assumed. The solution is numerically solved as a function estimation problem, so that no a priori information for the functional waveforms of the unknown heat flux is needed. In all cases, a solution in the form of a piece-wise function is used to approach the incident flux. Transient temperature measurements at the boundary, from the solution of the direct problem, served as the simulated experimental data needed as input for the inverse analysis. Both direct and inverse heat conduction problems are solved using the network simulation method. The solution is obtained step-by-step by minimising the classical functional that compares the above input data with those obtained from the solution of the inverse problem. A straight line of variable slope and length is used for each one of the stretches of the desired solution. The influence of random error, number of functional terms and the effect of sensor location are studied. In all cases, the results closely agree with the solution.     

Nonlinear bending and post-buckling of a functionally graded circular plate under mechanical and thermal loadings

Based on the classical nonlinear von Karman plate theory, axisymmetric large deflection bending of a functionally graded circular plate is investigated under mechanical, thermal and combined thermal–mechanical loadings, respectively, and axisymmetric thermal post-buckling behavior of a functionally graded circular plate is also investigated. The mechanical and thermal properties of functionally graded material (FGM) are assumed to vary continuously through the thickness of the plate, and obey a simple power law of the volume fraction of the constituents. Governing equations for the problem are derived, and then a shooting method is employed to numerically solve the equations. Effects of material constant n and boundary conditions on the temperature distribution, nonlinear bending, critical buckling temperature and thermal post-buckling behavior of the FGM plate are discussed in details.     

Inverse estimation for unknown fouling geometry on inner wall of forced-convection pipe

A conjugate gradient method (CGM) based on the inverse algorithm is used to estimate the unknown fouling-layer profile on the inner wall of a pipe system using simulated temperature measurements taken within the pipe wall. It is assumed that no prior information is available about the functional form of the unknown profile. Therefore, the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The accuracy of the inverse analysis is examined using the simulated exact and inexact temperature measurements. The results show that the excellent estimation of the fouling-layer profile can be obtained for the test case considered in this study. The technique presented in this study can be used in a warning system to call for pipe maintenance when the thickness of fouling exceeds a predefined criterion.     

Nodal predictive error model and Bayesian approach for thermal diffusivity and heat source mapping

This article aims at solving a two-dimensional inverse heat conduction problem in order to retrieve both the thermal diffusivity and heat source field in a thin plate. A spatial random heat pulse is applied to the plate and the thermal response is analysed. The inverse approach is based on the minimisation of a nodal predictive error model, which yields a linear estimation problem. As a result of this approach, the sensitivity matrix is directly filled with experimental data, and thus is partially noisy. Bayesian estimators, such as the Maximum A Posteriori and a Markov Chain Monte Carlo approach (Metropolis–Hastings), are implemented and compared with the Ordinary Least Squares solution. Simulated temperature measurements are used in the inverse analysis. The nodal strategy relies on the availability of temperature measurements with fine spatial resolution and high frequency, typical of nowadays infrared cameras. The effects of both the measurement errors and of the model errors on the inverse problem solution are also analysed.     

Thermal buckling of imperfect functionally graded plates

Thermal buckling analysis of rectangular functionally graded plates (FGPs) with geometrical imperfections is presented in this paper. The equilibrium, stability, and compatibility equations of an imperfect functionally graded plate are derived using the classical plate theory. It is assumed that the nonhomogeneous mechanical properties of the plate, graded through thickness, are described by a power function of the thickness variable. The plate is assumed to be under three types of thermal loading as uniform temperature rise, nonlinear temperature rise through the thickness, and axial temperature rise. Resulting equations are employed to obtain the closed-form solutions for the critical buckling temperature change of an imperfect FGP. The results are reduced and compared with the results of perfect functionally graded and imperfect isotropic plates.     

Contact melting materials with non-linear properties

The effects of nonlinear thermophysical properties on thermal and flow fields of the molten thin layer produced by contact melting are investigated. The molten layer is assumed to be a non-Newtonian fluid which has temperature-dependent viscosity and thermal conductivity. Heat transfer to solid and temperature field in solid with temperature-dependent conductivity are obtained. Choosing the heating surface of parabolic shape significantly reduce calculations, since closed-form solutions are obtained. Closed-form solutions for velocity, temperature, pressure, and thickness of the molten layer, and criterions to indicate the importance of taking into account the effects of nonlinear properties are provided. Received on 10 January 1997     

Flow and heat transfer of an electrically conducting third grade fluid past an infinite plate with partial slip

The effects of partial slip on the steady flow and heat transfer of an electrically conducting, incompressible, third grade fluid past a horizontal plate subject to uniform suction and blowing is investigated. Two distinct heat transfer problems are studied. In the first case, the plate is assumed to be at a higher temperature than the fluid; and in the second case, the plate is assumed to be insulated. The momentum equation is characterized by a highly nonlinear boundary value problem in which the order of the differential equation exceeds the number of available boundary conditions. Numerical solutions for the governing nonlinear equations are obtained over the entire range of physical parameters. The effects of slip, magnetic parameter, non-Newtonian fluid characteristics on the velocity and temperature fields are discussed in detail and shown graphically. It is interesting to find that the velocity and the thermal boundary layers decrease with an increase in the slip, and as the slip increases to infinity, the flow behaves as though it were inviscid.     

Inverse transient heat conduction problems and identification of thermal parameters

This work deals with the estimation of polymers properties. An inverse analysis based on finite element method is applied to identify simultaneously the constants thermal conductivity and heat capacity per unit volume. The inverse method algorithm constructed is validated from simulated transient temperature recording taken at several locations on the surface of the solid. Transient temperature measures taped with infrared camera on polymers were used for identifying the thermal properties. The results show an excellent agreement between manufacturer and identified values.     

Approximate Analytical Solution of a Physically Nonlinear Spatial Problem on the Elastic Equilibrium of a Multilayer Rectangular Plate

A three-dimensional boundary-value problem for a multilayer rectangular plate is solved under the physically nonlinear theory of elasticity. Various types of interlayer contact conditions are considered. The nonlinear relation between stresses and small strains is assumed to be of the Kauderer form. The solution is represented by a series in powers of a dimensionless small parameter. The problem posed is reduced to a recurrent sequence of linear boundary-value problems. The stress distribution and the effect of physical nonlinearity on the elastic equilibrium of the plate are studied     

Stochastic finite element nonlinear free vibration analysis of piezoelectric functionally graded materials beam subjected to thermo-piezoelectric loadings with material uncertainties

In this paper, second order statistics of large amplitude free flexural vibration of shear deformable functionally graded materials (FGMs) beams with surface-bonded piezoelectric layers subjected to thermopiezoelectric loadings with random material properties are studied. The material properties such as Young’s modulus, shear modulus, Poisson’s ratio and thermal expansion coefficients of FGMs and piezoelectric materials with volume fraction exponent are modeled as independent random variables. The temperature field considered is assumed to be uniform and non-uniform distribution over the plate thickness and electric field is assumed to be the transverse components E _z only. The mechanical properties are assumed to be temperature dependent (TD) and temperature independent (TID). The basic formulation is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strain kinematics. A C ⁰ nonlinear finite element method (FEM) based on direct iterative approach combined with mean centered first order perturbation technique (FOPT) is developed for the solution of random eigenvalue problem. Comparison studies have been carried out with those results available in the literature and Monte Carlo simulation (MCS) through normal Gaussian probability density function.     

Steady growth of a crack with a rate and temperature sensitive cohesive zone

The steady-state dynamic propagation of a crack in a heat conducting elastic body is numerically simulated. Specifically, a mode III semi-infinite crack with a nonlinear temperature dependent cohesive zone is assumed to be moving in an unbounded homogeneous linear thermoelastic continuum. The numerical results are obtained via a semi-analytical technique based on complex variables and integral transforms. The relation between the thermo-mechanical properties of the failure zone and the resulting crack growth regime are investigated. The results show that temperature dependent solutions are substantially different from purely mechanical ones in that their existence and stability strongly depends on the cohesive zone thermal properties.     

Axisymmetric static and dynamics snap-through phenomena in a thermally postbuckled temperature-dependent FGM circular plate

Thermal postbuckling analysis and the axisymmetric static and dynamic snap-through phenomena due to static/sudden uniform lateral pressure in a thermally postbuckled functionally graded material circular plate are performed in this research. Plate is formulated using the first order shear deformation plate theory. Thermo-mechanical properties of the plate are assumed to be temperature dependent where dependency is described according to the higher order Touloukian representation. Two types of temperature loading are considered. Uniform temperature rise and heat conduction across the thickness direction. The one dimensional heat conduction equation in the thickness direction is obtained and discreted via the central finite difference method. The obtained system of equations is nonlinear since the thermal conductivity itself is a function of the unknown nodal temperatures. Using the von-Kármán assumptions, the governing equations of the plate are obtained in a matrix representation with the aid of the conventional Ritz method whose shape functions are developed using the Gram-Schmidt process. At first thermal postbuckling analysis is performed which is a nonlinear problem with respect to both temperature and displacements. Afterwards, response of the bulged thermally postbuckled plate is obtained under the static and dynamic uniform pressure. Snap-through phenomenon may be observed in both static and dynamic loading cases, due to the immovability of the edge of the plate and the initial deflection caused by postbuckling deflection. To capture the snapping phenomenon and trace the path beyond the limit loads, cylindrical arch-length technique is used. In dynamic snap-through analysis, the effect of structural damping is also included. Numerical results of this study reveal that the structure is sensitive to the initial deflection caused by thermal postbuckling load. Increasing the temperature prior to mechanical loads enhances the snap-through intensity and also increases both the upper and lower limit loads. As shown, dynamic snap-through loads are lower than the static ones, however dynamic snap-through intensity is more than the static snap-though intensity. Furthermore, structural damping enhances the dynamic buckling loads of the plate and decreases the dynamic postbuckling deflection of the plate.     

The inverse identification problem and its technical application

This paper presents an overview of a loading force identification technique. Load identification methods are based on the solution of the inverse identification problem. Many different approaches for linear systems have been developed in this area. For both linear and nonlinear systems, methods based on the minimization of assumed objective functions are formulated. The least square error between the simulated and measured system responses is mainly used as the objective function. The dynamic programming optimization method formulated by Bellman is commonly used for the minimization of the objective function to estimate the excitation forces. The inverse identification problem in most practical cases is ill-posed because not all the state variables or initial conditions are known. Ill-posed inverse identification problems can be solved using several techniques, the most useful of which are: the generalized cross-validation method, the dynamic programming technique and Tikhonov’s method. This article presents the theoretical background and main limits to the application of inverse identification methods. Numerical and experimental tests on a laboratory rig were made to verify the formulated procedures. The method is applied to the identification of wheel–rail contact forces during rail vehicle operation. The method can be applied for indirect measurements of contact forces in railway equipment testing.     

An inverse problem for a functionally graded elliptical plate with large deflection and slightly disturbed boundary

This paper deals with the inverse problem of a functionally graded material (FGM) elliptical plate with large deflection and disturbed boundary under uniform load. The properties of functionally graded material are assumed to vary continuously through the thickness of the plate, and obey a simple power law expression based on the volume fraction of the constituents. Based on the classical nonlinear von Karman plate theory, the governing equations of a thin plate with large deflection were derived. In order to solve this non-classical problem, a perturbation technique was employed on displacement terms in conjunction with Taylor series expansion of the disturbed boundary conditions. The displacements of in-plane and transverse are obtained in a non-dimensional series expansion form with respect to center deflection of the plate. The approximate solutions of displacements are solved for the first three terms, and the corresponding internal stresses can also be obtained.     

Stochastic thermoelastic problem of a functionally graded plate under random temperature load

This study attempts to derive the statistics of temperature and thermal stress in functionally graded material (FGM) plates exposed to random external temperatures. The thermomechanical properties of the FGM plates are assumed to vary arbitrarily only in the plate thickness direction. The external temperatures are expressed as random functions with respect to time. The transient temperature field in the FGM plate is determined by solving a nonhomogeneous heat conduction problem for a multilayered plate with linear nonhomogeneous thermal conductivity and different homogeneous heat capacity in each layer. The autocorrelations and power spectrum densities (PSDs) of temperature and thermal stress are derived analytically. These statistics for FGM plates composed of partially stabilised zirconia (PSZ) and austenitic stainless steel (SUS304) are computed under the condition that the fluctuation in the external temperature can be considered as white noise or a stationary Markov process.     

Thermoelastic buckling behavior of thick functionally graded rectangular plates

Thermoelastic buckling behavior of thick rectangular plate made of functionally graded materials is investigated in this article. The material properties of the plate are assumed to vary continuously through the thickness of the plate according to a power-law distribution. Three types of thermal loading as uniform temperature raise, nonlinear and linear temperature distribution through the thickness of plate are considered. The coupled governing stability equations are derived based on the Reddy’s higher-order shear deformation plate theory using the energy method. The resulted stability equations are decoupled and solved analytically for the functionally graded rectangular plates with two opposite edges simply supported subjected to different types of thermal loading. A comparison of the present results with those available in the literature is carried out to establish the accuracy of the presented analytical method. The influences of power of functionally graded material, plate thickness, aspect ratio, thermal loading conditions and boundary conditions on the critical buckling temperature of aluminum/alumina functionally graded rectangular plates are investigated and discussed in detail. The critical buckling temperatures of thick functionally graded rectangular plates with various boundary conditions are reported for the first time and can be served as benchmark results for researchers to validate their numerical and analytical methods in the future.     

Stochastic nonlinear bending response of laminated composite plates with system randomness under lateral pressure and thermal loading

In this paper, the effect of sensitivity of randomness in system parameters on the nonlinear transverse central deflection response of laminated composite plates subjected to transverse uniform lateral pressure and thermal loading is examined. System parameters such as the lamina material properties, expansion of thermal coefficients, lamina plate thickness and lateral load are modelled as basic random variables. A higher order shear deformation theory in the von-Karman sense is used to model the system behavior of the laminated plate. A direct iterative-based C ⁰ nonlinear finite element method in conjunction with the first-order perturbation technique developed by the authors is extended for thermal problem to obtain the second-order response statistics, i.e., mean and variance of the nonlinear transverse deflection of the plate. Typical numerical results of composite plates with temperature independent and dependent material properties subjected to uniform temperature and combination of uniform and transverse temperature are obtained for various combinations of geometric parameters, uniform lateral pressures, staking sequences and boundary conditions. The results have been compared with those available in the literature and an independent Monte Carlo simulation.     

Correction of an effect of using a faulty model for the retrieval of a bulk wave slowness of a layered half space

This study concerns the retrieval of a single, real constitutive parameter (the bulk shear wave inverse velocity) of a simple, although representative, geophysical configuration involving two homogeneous, non-dissipative media, from its simulated response to pulsed plane wave probe radiation. This nonlinear inverse problem is solved exactly, at all frequencies, by equating the simulated frequency domain response incorporating the true real inverse velocity to the assumed response incorporating a trial complex inverse velocity. Due to discordance, caused by prior (a parameter of a model that is not retrieved, but rather assumed to be known, although its value may be wrong) uncertainty, between the models associated with the assumed and trial responses (the model giving rise to the latter is therefore qualified as being ‘faulty’), the imaginary part of the retrieved inverse velocity turns out to be non-nil, and, in fact, to be all the greater, the larger is the prior uncertainty. Moreover, the retrieved inverse velocity is found to be dispersive and its real part nearly equal to the true inverse velocity at all frequencies. The reconstructed signals (obtained by inserting the retrieved complex parameter into the faulty response model) are found to coincide exactly with the true signals for three types of probe pulses, even when the prior uncertainty is large.     

Impact of thermal radiation on MHD slip flow over a flat plate with variable fluid properties

The influence of partial slip, thermal radiation and temperature dependent fluid properties on the hydro-magnetic fluid flow and heat transfer over a flat plate with convective surface heat flux at the boundary and non-uniform heat source/sink is studied. The transverse magnetic field is assumed as a function of the distance from the origin. Also it is assumed that the fluid viscosity and the thermal conductivity vary as an inverse function and linear function of temperature respectively. Using the similarity transformation, the governing system of non-linear partial differential equations are transformed into similarity non-linear ordinary differential equations and are solved numerically using symbolic software MATHEMATICA 7.0. The numerical values obtained within the boundary layer for the dimensionless velocity, temperature, skin friction coefficient and the Nusselt number are presented through graphs and tables for several sets of values of the parameters. The effects of various physical parameters on the flow and heat transfer characteristics are discussed from the physical point of view.