Galerkin-based quasi-smooth manifold element(QSME)method for anisotropic heat conduction problems in composites with complex geometry

The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method(FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element(QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional(2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity.The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom(DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations.

A Novel Localized Meshless Method for Solving Transient Heat Conduction Problems in Complicated Domains

This paper first attempts to solve the transient heat conduction problem by combining the recently proposed local knot method(LKM)with the dual reciprocity method(DRM).Firstly,the temporal derivative is discretized by a finite difference scheme,and thus the governing equation of transient heat transfer is transformed into a non-homogeneous modified Helmholtz equation.Secondly,the solution of the non-homogeneous modified Helmholtz equation is decomposed into a particular solution and a homogeneous solution.And then,the DRM and LKM are used to solve the particular solution of the non-homogeneous equation and the homogeneous solution of the modified Helmholtz equation,respectively.The LKM is a recently proposed local radial basis function collocationmethod with themerits of being simple,accurate,and free ofmesh and integration.Compared with the traditional domain-type and boundary-type schemes,the present coupling algorithm could be treated as a really good alternative for the analysis of transient heat conduction on high-dimensional and complicated domains.Numerical experiments,including two-and three-dimensional heat transfer models,demonstrated the effectiveness and accuracy of the new methodology.

Numerical manifold method for thermo-mechanical coupling simulation of fractured rock mass

As a calculation method based on the Galerkin variation,the numerical manifold method(NMM)adopts a double covering system,which can easily deal with discontinuous deformation problems and has a high calculation accuracy.Aiming at the thermo-mechanical(TM)coupling problem of fractured rock masses,this study uses the NMM to simulate the processes of crack initiation and propagation in a rock mass under the influence of temperature field,deduces related system equations,and proposes a penalty function method to deal with boundary conditions.Numerical examples are employed to confirm the effectiveness and high accuracy of this method.By the thermal stress analysis of a thick-walled cylinder(TWC),the simulation of cracking in the TWC under heating and cooling conditions,and the simulation of thermal cracking of the SwedishÄspöPillar Stability Experiment(APSE)rock column,the thermal stress,and TM coupling are obtained.The numerical simulation results are in good agreement with the test data and other numerical results,thus verifying the effectiveness of the NMM in dealing with thermal stress and crack propagation problems of fractured rock masses.

Resistivity measurement of conductive asphalt concrete based on two-electrode method

The objective of this work is to develop a novel methodology for determining real resistivity of conductive asphalt concrete based on two-electrode method.Due to an influence of contact resistance,the measured resistivity is always not equal to the real resistivity.To determine the real resistivity,a linear relationship of the measured resistivity,contact resistance and the real resistivity was established.Then experiments for six specimens with varying graphite contents were designed and performed to validate the formulation.Results of experiments demonstrate that the slope of the line represents contact resistance,and the intercept indicates the real resistivity.The effects of graphite content on contact resistance and real resistivity are also revealed.Finally,results show that the influence of contact resistance on accuracy of resisitvity measurement becomes more serious if graphite content is beyond 3%.Hence,it is the time to choose this novel methodology to determine the real resistivity of asphalt concrete by taking account of contact resistance.

Chaotic Motion Analysis for a Coupled Magnetic-Flow-Mechanical Model of the Rectangular Conductive Thin Plate

The chaotic motion behavior of the rectangular conductive thin plate that is simply supported on four sides by airflow andmechanical external excitation in a magnetic field is studied.According to Kirchhoff’s thin plate theory,considering geometric nonlinearity and using the principle of virtualwork,the nonlinearmotion partial differential equation of the rectangular conductive thin plate is deduced.Using the separate variable method and Galerkin’s method,the system motion partial differential equation is converted into the general equation of the Duffing equation;the Hamilton system is introduced,and the Melnikov function is used to analyze the Hamilton system,and obtain the critical surface for the existence of chaos.The bifurcation diagram,phase portrait,time history response and Poincarémap of the vibration system are obtained by numerical simulation,and the correctness is demonstrated.The results showthatwhen the ratio of external excitation amplitude to damping coefficient is higher than the critical surface,the system will enter chaotic state.The chaotic motion of the rectangular conductive thin plate is affected by different magnetic field distributions and airflow.

A Novel Method of Fabricating Flexible Transparent Conductive Large Area Graphene Film

We fabricate flexible conductive and transparent graphene films on position-emission-tomography substrates and prepare large area graphene films by graphite oxide sheets with the new technical process. The multi-layer graphene oxide sheets can be chemically reduced by HNO3 and HI to form a highly conductive graphene film on a substrate at lower temperature. The reduced graphene oxide sheets show a high conductivity sheet with resistance of 476Ω/sq and transmittance of 76% at 550nm （6 layers）. The technique used to produce the transparent conductive graphene thin film is facile, inexpensive, and can be tunable for a large area production applied for electronics or touch screens.

Finite Difference-Peridynamic Differential Operator for Solving Transient Heat Conduction Problems

Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using the PDDO method,resulting in increased complexity and programming difficulty.In this work,the forward difference formula,the backward difference formula,and the centered difference formula are used to discretize the time derivative,while the PDDO method is used to discretize the spatial derivative.Three new schemes for solving transient heat conduction equations have been developed,namely,the forward-in-time and PDDO in space(FT-PDDO)scheme,the backward-in-time and PDDO in space(BT-PDDO)scheme,and the central-in-time and PDDO in space(CT-PDDO)scheme.The stability and convergence of these schemes are analyzed using the Fourier method and Taylor’s theorem.Results show that the FT-PDDO scheme is conditionally stable,whereas the BT-PDDO and CT-PDDO schemes are unconditionally stable.The stability conditions for the FT-PDDO scheme are less stringent than those of the explicit finite element method and explicit finite difference method.The convergence rate in space for these three methods is two.These constructed schemes are applied to solve one-dimensional and two-dimensional transient heat conduction problems.The accuracy and validity of the schemes are verified by comparison with analytical solutions.

Phase composition,conductivity,and sensor properties of cerium-doped indium oxide

The hydrothermal synthesis of In_(2)O_(3)and CeO_(2)–In_(2)O_(3)is investigated as well as the properties of sensor layers based on these compounds.During the synthesis of In_(2)O_(3),intermediate products In(OH)_(3)and InOOH are formed,which are the precursors of stable cubic(c-In_(2)O_(3))and metastable rhombohedral(rh-In_(2)O_(3))phases,respectively.A transition from c-In_(2)O_(3)to rh-In_(2)O_(3)is observed with the addition of CeO_(2).The introduction of cerium into rh-In_(2)O_(3)results in a decrease in the sensor response to hydrogen,while it increases in composites based on c-In_(2)O_(3).The data on the sensor activity of the composites correlate with XPS results in which CeO_(2)causes a decrease in the concentrations of chemisorbed oxygen and oxygen vacancies in rh-In_(2)O_(3).The reverse situation is observed in composites based on c-In_(2)O_(3).Compared to In_(2)O_(3)and CeO_(2)–In_(2)O_(3)obtained by other methods,the synthesized composites demonstrate maximum response to H_(2)at low temperatures by 70–100℃,and have short response time(0.2–0.5 s),short recovery time(6–7 s),and long-term stability.A model is proposed for the dependence of sensitivity on the direction of electron transfer between In_(2)O_(3)and CeO_(2).

Newton-type methods and their modifications for inverse heat conduction problems

This paper studies to numerical solutions of an inverse heat conduction problem.The effect of algorithms based on the Newton-Tikhonov method and the Newton-implicit iterative method is investigated,and then several modifications are presented.Numerical examples show the modified algorithms always work and can greatly reduce the computational costs.

Gap States of ZnO Thin Films by New Methods:Optical Spectroscopy,Optical Conductivity and Optical Dispersion Energy

The optical reflectance and transmittance spectra in the wavelength range of 300-2500 nm are used to compute the absorption coefficient of zinc oxide films annealed at different post-annealing temperatures 400, 500 and 600°C.The values of the cross point between the curves of the real and imaginary parts of the optical conductivity ɑ_1 and ɑ_1 with energy axis of films exhibit values that correspond to optical gaps and are about 3.25-3.3 eV. The maxima of peaks in plots dR/dλ and dT/dλ versus wavelength of films exhibit optical gaps at about 3.12-3.25 eV.The values of the fundamental indirect band gap obtained from the Tauc model are at about 3.14-3.2 eV. It can be seen that films annealed at 600°C have the minimum indirect optical band gap at about 3.15 eV. The films annealed at 600°C have Urbach＇s energy minimum of 1.38 eV and hence have minimum disorder. The dispersion energy d of films annealed at 500°C has the minimum value of 43 eV.

Application of the Adaptive Shrinkage Genetic Algorithm in the Feasible Region to TEM Conductive Thin Layer Inversion

Combining the adaptive shrinkage genetic algorithm in the feasible region with the imaging of apparent vertical conductance differential, we have inverted the TEM conductive thin layer. The result of the inversion demonstrates that by adaptive shrinkage in the feasible region, the calculation speed accelerates and the calculation precision improves. To a certain extent, in this method we surmount the transient electromagnetic sounding equivalence and reduced equivalence scope. Comparison of the inverted result with the forward curve clearly shows that we can image the conductive thin layer.

A universal calibration method for eliminating topographydependent current in conductive AFM and its application in nanoscale imaging

The topography and electrical properties are two crucial characteristics that determine the roles and functionalities of materials.Conductive atomic force microscopy(CAFM)is widely recognized for its ability to independently measure the topography and conductivity.The increasing trend towards miniaturization in electrical devices and sensors has encouraged an urgent demand for enhancing the accuracy of CAFM characterization.However,when performing CAFM tests on Bi_(0.5)Na_(0.5)TiO_(3)bulk ceramic,it is interesting to observe significant currents related to the topography.Why do insulators exhibit“conductivity”in CAFM testing?Herein,we thoroughly investigated the topography-dependent current during CAFM testing for the first time.Based on the linear dependence between the current and the first derivative of topography,the calibration method has been proposed to eliminate the topographic crosstalk.This method is evaluated on Bi_(0.5)Na_(0.5)TiO_(3)bulk ceramic,one-dimensional(1D)ZnO nanowire,twodimensional(2D)NbOI_(2)flake,and biological lotus leaf.The corresponding results of negligible topography-interference current affirm the feasibility and universality of this calibration method.This work effectively addresses the challenge of topographic crosstalk in CAFM characterization,thereby preventing the erroneous estimation of the conductivity of any unknown sample.

Study of the Conductance Characteristic of Doped Polymer by Monte Carlo Method

The conduct mechanism of the doped polymer is considered. In an asymmetrysystem composed of high polymer and doping conductive matte, chain or congeries framework will beformed between the conductive particles to improve the conductance characteristic. In thisprocession, the conductive particles interact to each other. In this paper, we describe theconductance of the doped polymer by Monte Carlo method. The results accord with the experimentsquite well. It can be concluded that there is an evident change of doped polymer from nonconductorto metal.

Fast precise integration method for hyperbolic heat conduction problems

A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to the fact that the matrix exponential is sparse. The presented method employs the sparsity of the matrix exponential to improve the original precise integration method. The merits are that the proposed method is suitable for large hyperbolic heat equations and inherits the accuracy of the original version and the good computational efficiency, which are verified by two numerical examples.

A new complex variable meshless method for transient heat conduction problems

In this paper, based on the improved complex variable moving least-square （ICVMLS） approximation, a new complex variable meshless method （CVMM） for two-dimensional （2D） transient heat conduction problems is presented. The variational method is employed to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. As the transient heat conduction problems are related to time, the Crank-Nicolson difference scheme for two-point boundary value problems is selected for the time discretization. Then the corresponding formulae of the CVMM for 2D heat conduction problems are obtained. In order to demonstrate the applicability of the proposed method, numerical examples are given to show the high convergence rate, good accuracy, and high efficiency of the CVMM presented in this paper.

Differential transformation method for studying flow and heat transfer due to stretching sheet embedded in porous medium with variable thickness, variable thermal conductivity,and thermal radiation

This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet embedded in a porous medium with the power law surface velocity and variable thickness in the presence of thermal radiation. The flow is caused by non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The governing partial differential equations （PDEs） are transformed into a system of coupled non-linear ordinary differential equations （ODEs） with appropriate boundary conditions for various physical parameters. The remaining system of ODEs is solved numerically using a differential transformation method （DTM）. The effects of the porous parameter, the wall thickness parameter, the radiation parameter, the thermal conductivity parameter, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction and the Nusselt numbers are presented. Comparison of the obtained numerical results is made with previously published results in some special cases, with good agreement. The results obtained in this paper confirm the idea that DTM is a powerful mathematical tool and can be applied to a large class of linear and non-linear problems in different fields of science and engineering.

Fuzzy finite difference method for heat conduction analysis with uncertain parameters

A new numerical technique named as fuzzy finite difference method is proposed to solve the heat conduction problems with fuzzy uncertainties in both the phys- ical parameters and initial/boundary conditions. In virtue of the level-cut method, the difference discrete equations with fuzzy parameters are equivalently transformed into groups of interval equations. New stability analysis theory suited to fuzzy difference schemes is developed. Based on the parameter perturbation method, the interval ranges of the uncertain temperature field can be approximately predicted. Subsequently, fuzzy solutions to the original difference equations are obtained by the fuzzy resolution theorem. Two numerical examples are given to demonstrate the feasibility and efficiency of the presented method for solving both steady-state and transient heat conduction problems.

Calibration of Soil Electromagnetic Conductivity in Inverted Salinity Profiles with an Integration Method

Various calibration methods have been propounded to determine profiles of apparent bulk soil electrical conductivity (ECa) and soil electrical conductivity of a saturated soil paste extract (ECe) or a 1:5 soil water extract (EC1:5) using an electromagnetic induction instrument (EM38). The modeled coefficients, one of the successful and classical methods hitherto, were chosen to calibrate the EM38 measurements of the inverted salinity profiles of characteristic coastal saline soils at selected sites of Xincao Farm, Jiangsu Province, China. However, this method required three parameters for each depth layer. An integration approach, based on an exponential decay profile model, was proposed and the model was fitted to all the calibration sites. The obtained model can then be used to predict EC1:5 at a certain depth from electromagnetic measurements made using the EM38 device positioned in horizontal and vertical positions at the soil surface. This exponential decay model predicted the EC1:5 well according to the results of a one-way analysis of variance, and the further comparison indicated that the modeled coefficients appeared to be slightly superior to, but not statistically different from, this exponential decay model. Nevertheless, this exponential decay model was more significant and practical because it depended on less empirical parameters and could be used to perform point predictions of EC1:5 continuously with depth.

Thermal conductivity measurements on xonotlite-type calcium silicate by the transient hot-strip method

The experimental results of the thermal conductivities of xonotlite-type calcium silicate insulation materials were presented at different temperatures and pressures. Two appropriative surroundings, i.e. an elevated temperature surrounding from ambient temperature to 1450 K and a vacuum surrounding from atmosphere pressure to 10-3 Pa, were designed for the transient hot-strip （THS） method. The thermal conductivities of xonotlite-type calcium silicate with four densities from ambient temperature to 1000 K and 0.045 Pa to atmospheric pressure were measured. The results show that the thermal conductivity of xonotlite-type calcium silicate decreases apparently with the fall of density, and decreases apparently with the drop of pressure, and reaches the least value at about 100 Pa. The thermal conductivity of xonotlite-type calcium silicate increases almost linearly with T0, and increases more abundantly with low density than with high density. The thermal conductivity measurement uncertainty is estimated to be approximately 3% at ambient temperature, and 6% at 800 K.

Increment-Dimensional Scaled Boundary Finite Element Method for Solving Transient Heat Conduction Problem

An increment-dimensional scaled boundary finite element method (ID-SBFEM) is developed to solve the transient temperature field.To improve the accuracy of SBFEM,the effect of high frequency factor on dynamic stiffness is considered,and the first-order continued fraction technique is used.After the derivation,the SBFE equations are obtained,and the dimensions of thermal conduction,the thermal capacity matrix and the vector of the right side term in the equations are doubled.An example is presented to illustrate the feasibility and good accuracy of the proposed method.