Heat transfer analysis of composite slabs using meshless element Free Galerkin method

This paper deals with three dimensional heat transfer analysis of composite slabs using meshless element free Galerkin method. The element free Galerkin method (EFG) method utilizes moving least square (MLS) approximants to approximate the unknown function of temperature Tx). These approximants are constructed by using a weight function, a basis function and a set of coefficients that depends on position. Penalty and Lagrange multiplier techniques have been used to enforce the essential boundary conditions. MATLAB codes have been developed to obtain the EFG results. Two new basis functions namely trigonometric and polynomial have been proposed. A comparison has been made among the results obtained using existing (linear) and proposed (trigonometric and polynomial) basis functions for three dimensional heat transfer in composite slabs. The effect of penalty parameter on EFG results has also been discussed. The results obtained by EFG method are compared with those obtained by finite element method     

对流扩散方程的特征线EFG算法

为了消除对流扩散方程因对流占优引起的数值震荡,本文首先将其转化为特征形式,并利用移动最小二乘基函数,构建了特征线无单元Galerkin方法．再对新建方法进行收敛性分析,分别给出关于支持域半径和时间步长的两种误差估计．最后,分别针对一维和二维算例进行了数值计算,并与有限元法进行了比较．数值结果表明,本文算法收敛性好,可以消除数值震荡,且通过选取合适的罚因子和支持域的无量纲尺寸,计算精度比有限元法更高,是求解对流占优扩散方程的一种有效程数值计算方法．     

无单元Galerkin方法中周期边界条件的处理

本文研究了无单元Galerkin方法中周期边界条件的处理技术,将Lagrange乘子法用于周期边界条件的处理.数值计算结果表明,该方法具有较高的计算精度.另外,它与无单元Galerkin方法中本质边界条件处理的Lagrange乘子法具有统一性,对于周期、本质混合型边界条件的处理尤为方便.     

Free Vibration Analysis of Folded Plate Structures by the FSDT Mesh-free Method

Based on the first-order shear deformation theory, a mesh-free Galerkin method for free vibration analysis of stiffened and un-stiffened folded plates and plate structures is presented in this paper. The folded plate or plate structure is modelled as a composite structure that consists of flat plates. The stiffness and mass matrices of the flat plates are derived based on the mesh-free formulation. To avoid the failure of direct superposition, a treatment is introduced to modify the stiffness and mass matrices. The global stiffness and mass matrices of the entire folded plate or plate structure are then obtained by superposing the modified stiffness and mass matrices of the flat plates. The analysis of the stiffened folded plates or plate structures proceeds in a similar fashion, as they are regarded as composite structures of stiffened and un-stiffened flat plates. The stiffness and mass matrices of the stiffened flat plates are also given by the mesh-free method. As no meshes are used in deriving the stiffness and mass matrices, the proposed method is more flexible in studying problems for which remeshing is inevitable with the finite element methods. Several numerical examples are computed with the proposed method to demonstrate its accuracy and convergence. The results show good agreement with the solutions that have been given by other researchers and ANSYS.     

Thermal analysis of carbon-nanotube composites using a rigid-line inclusion model by the boundary integral equation method

The boundary integral equation (BIE) method is applied for the thermal analysis of fiber-reinforced composites, particularly the carbon-nanotube (CNT) composites, based on a rigid-line inclusion model. The steady state heat conduction equation is solved using the BIE in a two-dimensional infinite domain containing line inclusions which are assumed to have a much higher thermal conductivity (like CNTs) than that of the host medium. Thus the temperature along the length of a line inclusion can be assumed constant. In this way, each inclusion can be regarded as a rigid line (the opposite of a crack) in the medium. It is shown that, like the crack case, the hypersingular (derivative) BIE can be applied to model these rigid lines. The boundary element method (BEM), accelerated with the fast multipole method, is used to solve the established hypersingular BIE. Numerical examples with up to 10,000 rigid lines (with 1,000,000 equations), are successfully solved by the BEM code on a laptop computer. Effective thermal conductivity of fiber-reinforced composites are evaluated using the computed temperature and heat flux fields. These numerical results are compared with the analytical solution for a single inclusion case and with the experimental one reported in the literature for carbon-nanotube composites for multiple inclusion cases. Good agreements are observed in both situations, which clearly demonstrates the potential of the developed approach in large-scale modeling of fiber-reinforced composites, particularly that of the emerging carbon-nanotube composites.     

Elasto-plastic element-free Galerkin method

In this paper the element free Galerkin method (EFGM) has been extended to be used in the elastoplastic stress analysis. The developed method has been examined in planar stress analysis around the tip of a crack and in its opening mode of loading. To do this, at the first step by using the incremental relations of plastic deformation a system of elastoplastic EFGM equations has been derived. Since the obtained relations are nonlinear, a nonlinear solution technique has been chosen. To examine the validity of this technique, stress fields in two different plates with and without a crack have been calculated and the results have been compared with other similar analytical works in the literature. In doing so the power law work hardening behavior has been employed and the value of J-integral has been used as a base for comparison of the results.First and second authors wish to express their gratitude to the Office of Research Affairs of Sharif University of Technology for financial support to conduct this research. The second author wishes to appreciate Professor Tom Hyde head of the School of 4 M in the University of Nottingham for his guidance and providing some research facilities.     

A Method for Thermal Diffusivity Determination of Thermal Insulators

A so-called “three-point” (3P) method has been developed for thermal diffusivity measurements of thermal insulating materials. One side of a cylindrical specimen, sandwiched between two thin metal plates, is subjected to intense light from an incandescent lamp to generate a thermal perturbance. The temperature response is measured in three locations along the test specimen. Thermocouples are located at the front and rear faces of the specimen, and the third is placed inside the specimen at a known location. The two outside temperatures are used as boundary conditions, and the unknown thermal diffusivity is calculated from the third temperature versus time curve. The method combines the advantages of rapid transient non-contact heating methods with the well-defined boundary conditions of steady-state methods. The results of the 3P method are compared with those from steady-state methods for a micro-porous insulation material and for a honeycomb structure.     

Computational algorithms and applications of element-free Galerkin methods for nonlocal damage models

In using complex material models, especially the strain-gradient-dependent damage models, the convergence of the finite element computation increasingly becomes a problem. Due to large strains in damaging elements the computation may often result in non-convergence. For the higher-order gradient plasticity the special element formulation would often be necessary, which causes additional difficulties in implementation and computations. In recent years, meshless methods have been developed as an alternative to the finite element method (FEM) and can overcome some known shortcomings of FEM. In the present paper an algorithm of element-free Galerkin (EFG) methods for strain-gradient based nonlocal damage models has been developed and used to simulate ductile material damage. The method provides a reliable and robust results for material failure with large damage zones. The strain gradient-dependent terms can be evaluated from the direct differentiation. The investigation confirms that the nonlocal damage model with element-free Galerkin method is suitable for computing the damage problems and predicting the size effects. With the help of the meshless method, material failure in specimens as well as the size effects are predicted accurately.     

Buckling analysis of corrugated plates using a mesh-free Galerkin method based on the first-order shear deformation theory

This paper deals with elastic buckling analysis of stiffened and un-stiffened corrugated plates via a mesh-free Galerkin method based on the first-order shear deformation theory (FSDT). The corrugated plates are approximated by orthotropic plates of uniform thickness that have different elastic properties along the two perpendicular directions of the plates. The key to the approximation is that the equivalaent elastic properties of the orthotropic plates are derived by applying constant curvature conditions to the corrugated sheet. The stiffened corrugated plates are analyzed as stiffened orthotropic plates. The stiffeners are modelled as beams. The stiffness matrix of the stiffened corrugated plate is obtained by superimposing the strain energy of the equivalent orthotropic plate and the beams after implementing the displacement compatibility conditions between the plate and the beams. The mesh free characteristic of the proposed method guarantee that the stiffeners can be placed anywhere on the plate, and that remeshing is avoided when the stiffener positions change. A few selected examples are studied to demonstrate the accuracy and convergence of the proposed method. The results obtained for these examples, when possible, are compared with the ANSYS solutions or other available solutions in literature. Good agreement is evident for all cases. Some new results for both trapezoidally and sinusoidally corrugated plates are then reported.     

饲喂法制备碳纳米材料改性蚕丝的导热性能

将纳米石墨烯、单壁碳纳米管和纳米石墨粒子这三种碳纳米材料均匀涂覆在桑叶上饲喂四龄蚕,采用简易且绿色经济的饲喂法制备改性蚕丝.利用瞬态电热技术(TET)对蚕丝的导热性能进行研究结果表明:饲喂添加碳纳米材料的桑叶所得到的改性蚕丝的导热性能均有所降低,并且碳纳米材料的添加量越大,改性蚕丝的导热性能越低.导致改性蚕丝导热性能下...     

Thermal conductivity of aligned CNT/polymer composites using mesoscopic simulation

Thermal conductivity of CNT/polymer composites depends on alignment, dispersion, volume fraction and size of CNTs as well as polymer size. By coupling smoothed particle hydrodynamics and dissipative particle dynamics, thermal conductivities of random and aligned composites along with their meso morphologies are studied in detail. Thermal conductivity along the alignment of CNT can be significantly enhanced to 16 times that of polymer by increasing volume fraction, dispersion degree and length of CNT, meanwhile thermal conductivity perpendicular to the alignment of CNT is affected modestly by these factors. Enhancement of thermal conductivity of random composites could only be efficiently achieved by increasing the volume fraction of CNT. Particularly, thermal conductivity $\kappa$ is proportional to the square of volume fraction of CNT v in well dispersed random and aligned composites, i.e. $\kappa \propto v^2$.     

Application of the Three-Omega Method to Measurement of Thermal Conductivity and Thermal Diffusivity of Hydrogen Gas

Preliminary investigations have been conducted to discuss the possibility of measuring the thermal conductivity of hydrogen gas by the three-omega method. A one-dimensional analytical solution for the 3ω component is derived which includes the effect of the wire heat capacity. It is shown that it is very important to take into account the wire heat capacity in the calculation to measure the thermal conductivity of gas by the three-omega method. In contrast, the wire heat capacity is less important for the thermal conductivity of the liquid or solid phase. The importance of the wire heat capacity is found to increase with increasing frequency and decrease if the sample thermal conductivity is high. In order to measure the thermal conductivity of hydrogen gas at atmospheric pressure, a wire of diameter less than 1μm is necessary if the properties of the wire are to be neglected.     

关于测试材料热物性热脉冲法的新探讨

建立起热脉冲法的新理论模型，分析了相应的测试技术问题。利用研制的微机测试系统 种材料的热扩散系数和导热系数进行了测定，得到了满意的结果，表明本文所提出的测试广阔进可信的。     

Meshless analysis of two-dimensional Stokes flows with the Galerkin boundary node method

In this paper, the Galerkin boundary node method (GBNM) is developed for the solution of stationary Stokes problems in two dimensions. The GBNM is a boundary only meshless method that combines a variational form of boundary integral formulations for governing equations with the moving least-squares (MLS) approximations for construction of the trial and test functions. Boundary conditions in this approach are included into the variational form, thus they can be applied directly and easily despite the MLS shape functions lack the property of a delta function. Besides, the GBNM keeps the symmetry and positive definiteness of the variational problems. Convergence analysis results of both the velocity and the pressure are given. Some selected numerical tests are also presented to demonstrate the efficiency of the method.     

瞬态热线法导热系数测量实验数据处理方法的研究

为克服瞬态热线法导热系数测量中实验数据处理一般方法的弊端,将数值模拟引入实验数据处理过程,并通过比较理论计算曲线与实验曲线的符合程度来获得最终的实验结果。通过不同方法对实验数据处理结果的比较分析表明,所使用的方法可以更好地处理瞬态热线法导热系数测量数据,同时,与传统方法相比,采用较少的数据点即可得到正确的结果。研究结果不仅可以改进瞬态热线法导热系数实验数据的分析方法,而且对实验系统的设计与搭建也有借鉴意义。     

Analysis of cylindrical bending thermoelastic deformations of functionally graded plates by a meshless local Petrov–Galerkin method

We analyze plane strain static thermoelastic deformations of a simply supported functionally graded (FG) plate by a meshless local Petrov–Galerkin (MLPG) method. Material moduli are assumed to vary only in the thickness direction. The plate material is made of two isotropic randomly distributed constituents and the macroscopic response is also modeled as isotropic. Displacements and stresses computed with the MLPG method are found to agree very well with those obtained from the analytical solution of the problem. The number of nodes required to obtain an accurate solution for a FG plate is considerably more than that needed for a homogeneous plate.The work was partially supported by the Office of Naval Research grant N00014-98-1-0300 to Virginia Polytechnic Institute and State University with Dr. Y. D. S. Rajapakse as the program manager. L. F. Qian was also supported by the China Scholarship Council.     

反问题法在相变材料热导性能研究中的应用

基于相变导热模型,提出将相界面运动的测试实验与数值计算相结合来求解有效导热系数的反问题法,对几种相变储能材料添加金属介质后导热系数的改善进行了研究。结果表明,金属介质的导热系数越大,则相变材料的有效导热系数也越大;在相同的添加比例下,低热导率相变材料有效导热系数的改善程度要大于高热导率相变材料。该方法的求解结果与相关文献吻合较好。     

热带法测量材料导热系数的实验研究

根据瞬态热带法的基本原理，建立了测量非导电固体材料以及松散材料导热系数的实验装置，采用热电偶直接测量热带的温度变化，整个测量系统更加方便实用、易于实现。对一批试样进行的测试结果表明，本测量装置具有较好的重复性和准确性，可应用于相关的科研部门和工业部门。