基于混合Trefftz有限梯度元法的功能梯度材料热传导数值模拟

针对功能梯度材料物性参数随坐标变化的特点,基于Trefftz完备解提出了求解功能梯度材料热传导问题的有限梯度元方法。首先,利用变量代换推导出指数型、二次型和三角型功能梯度材料稳态热传导问题的Trefftz完备解;然后,利用Trefftz完备解对单元内部的温度场进行插值,构造出可自然模拟材料梯度属性的梯度单元,在该基础上建立混合Trefftz有限梯度元法求解功能梯度材料的稳态热传导方程;最后,采用混合Trefftz有限梯度元法对典型功能梯度材料板的温度分布进行数值模拟,以验证该方法的正确性和有效性。     

二维耦合热弹性动力学问题的无网格自然邻接点Petrov-Galerkin法

为了更有效地求解二维耦合热弹性动力学问题,对无网格自然邻接点Petrov-Galerkin法在此类问题中的应用进行了研究,并发展了相应的计算方法。该方法建立试函数时可以只依赖于一组离散的节点,有效地避免了复杂的网格划分和网格畸变的影响。相对于常用的移动最小二乘而言,自然邻接点插值不涉及复杂的矩阵求逆运算,更不需要任何人为参数。由于运动方程和瞬态热传导方程相互影响,这些方程必须联立求解。采用Newmark法求解空间离散后得到的二阶常微分方程组,进而可直接获得温度场和位移场的数值结果。     

径向基函数配点法分析三维功能梯度材料板的静力和动力问题

传统配点法在求解动力学问题时会存在误差随时间累积的问题,而无网格径向基函数配点法在全域内采用具有无限连续性的径向基函数作为近似函数,结合配点法构建方程,通过最小二乘法进行求解。无网格径向基函数配点法不仅在数值计算过程中不需要任何网格,是真正的无网格法,而且易于离散,精度高,不需要积分,计算效率高;径向基函数的近似函数仅与距中心点的距离有关,非常适宜于求解三维问题。对于这种方法,本文先离散空间域,然后再离散时间域,并在每一时间步内施加边界条件,来分析三维功能梯度材料板的静力和动力问题,据此可解决传统配点方法在求解动力问题时误差随时间累积的问题。数值分析表明,材料性能呈梯度分布会导致其力学性能在梯度方向呈现非线性变化,不同的梯度分布模式会导致力学性能非线性变化的幅度不同。     

基于格构模型的水泥浆体离子稳态扩散模拟

首先采用数值模型得到水泥浆体的模拟微观结构,然后将其离散化为像素.根据该离散化微观结构建立具有扩散性能的格构单元组成的三维格构网络,求解固定离子浓度边界条件下通过水泥浆体的离子流量和内部离子浓度分布,并预测材料的扩散系数.在求解离子浓度分布的过程中,比较了差分法和共轭梯度法的优缺点,发现采用共轭梯度法更快捷.最后用稳态氯离子扩散试验验证了该模拟方法的可靠性,并预测了水泥浆体的氯离子有效扩散系数随水胶比和养护龄期的变化关系.     

有限单元法在解三维轴对称静电场中的应用

用有限单元法求解三维轴对称静电场问题来确定系统的电场分布是具有一定的普遍意义的。文中介绍了有限单元法的基本思想和运算步骤,边界条件和介质的处理,以及对110千伏油纸电容式变压器套管尾部电场的计算实例。     

基于ANSYS的空间轴对称分析

结合轴对称问题的特点和实质,通过对一个轴对称实例的求解与分析,对比得出采用二维平面单元求解轴对称问题比采用三维实体单元具有更好的精度,且可以显著节省建模及求解计算时间。     

横观各向同性功能梯度圆板弯曲问题的精确解

对周边为弹性支承边界条件下的横观各向同性功能梯度材料圆板轴对称弯曲问题进行了分析.将位移函数写成傅里叶-贝塞尔级数的形式,根据横观各向同性功能梯度材料基本方程,并针对指数函数形式的梯度分布情况,对功能梯度圆板轴对称弯曲问题的位移和应力进行了精确分析.并通过具体算例,分析了在圆板上、下表面荷载作用下,材料性质的不同梯度变化对圆板结构响应的影响.分析结果表明,材料性质的梯度变化对圆板的力学性能有显著影响.     

玻璃幕墙传热系数计算方法及工程应用

在研究玻璃幕墙热传递特点的基础上,基于一维稳态热传导理论,以中空玻璃为例建立了玻璃系统传热系数计算模型;基于二维稳态热传导理论和有限单元法,采用三节点三角形单元对二维温度场进行了离散,推导了单元热传导矩阵和温度载荷列阵,并推导了热对流、热流密度、辐射以及各种边界条件耦合作用下对单元热传导矩阵和温度载荷列阵的修正公式,建立了玻璃幕墙框及附加线传热系数计算模型。利用Visual C++和ObjectARX对AutoCAD进行了二次开发,研发了玻璃幕墙传热系数计算软件TJCW,并通过算例与LBNL系列软件计算结果进行比较,验证了所编软件的正确性和有效性。最后对某工程实例中玻璃幕墙传热系数进行了节能验算。研究结果表明：建立的传热系数计算模型能够正确的计算玻璃幕墙传热系数,基于该计算模型开发出的软件能够应用于实际工程的节能分析和计算中。     

利用人工神经网络求解混凝土板瞬态温度场

阐述了混凝土板温度场的热传导微分方程和差分解析方法以及BP网络的算法步骤。在此基础上，提出了利用人工神经网络技术求解混凝土板瞬态温度场的方法。     

小波单元在热传导问题中的应用

利用 Daubechies小波尺度函数 ,构造了适用于热传导问题分析的小波单元 ,对不同边界条件的热传导问题进行了分析 .将分析结果与理论解及商用软件 ANSYS的分析结果比较 ,可以看出 ,构造的小波单元是收敛的 ,并具有较高的分析精度 ,特别是对于大梯度问题的分析具有独到的优势     

Response of functionally graded cylindrical shells under moving thermo-mechanical loads

The transient thermoelastic analysis of functionally graded (FG) cylindrical shells under moving boundary pressure and heat flux is presented. The material properties are assumed to be temperature-dependent and graded in the radial direction. The hyperbolic heat conduction equations are used to include the influence of finite heat wave speed (i.e., the non-Fourier effect). To benefit from the high accuracy and low computational efforts of the differential quadrature method (DQM) in conjunction with the effectiveness of the finite element method (FEM) in general geometry, loading and systematic boundary treatment, a combination of these methods is employed to discretize the governing equations in the spatial domain. The resulting system of differential equations is solved using Newmark's time integration scheme in the temporal domain. The presented formulation and method of solution are validated by showing their fast rate of convergence and by comparing the results, in the limit cases, with those obtained using the commercial finite element package ANSYS and some other available solutions in the literature. Then, the effects of different geometrical, material and load parameters on the transient thermoelastic behavior of the FG cylinders under moving mechanical and thermal loads are studied.     

Free vibration analysis of laminated FG-CNT reinforced composite beams using finite element method

In the present study, the free vibration of laminated functionally graded carbon nanotube reinforced composite beams is analyzed. The laminated beam is made of perfectly bonded carbon nanotubes reinforced composite (CNTRC) layers. In each layer, single-walled carbon nanotubes are assumed to be uniformly distributed (UD) or functionally graded (FG) distributed along the thickness direction. Effective material properties of the two-phase composites, a mixture of carbon nanotubes (CNTs) and an isotropic polymer, are calculated using the extended rule of mixture. The first-order shear deformation theory is used to formulate a governing equation for predicting free vibration of laminated functionally graded carbon nanotubes reinforced composite (FG-CNTRC) beams. The governing equation is solved by the finite element method with various boundary conditions. Several numerical tests are performed to investigate the influence of the CNTs volume fractions, CNTs distributions, CNTs orientation angles, boundary conditions, length-to-thickness ratios and the numbers of layers on the frequencies of the laminated FG-CNTRC beams. Moreover, a laminated composite beam combined by various distribution types of CNTs is also studied.     

Dynamic analysis of functionally graded truncated conical shells subjected to asymmetric moving loads

The dynamic behavior of functionally graded (FG) truncated conical shells subjected to asymmetric internal ring-shaped moving loads is studied. The material properties are assumed to have continuous variations in the shell thickness direction. The equations of motion are derived based on the first-order shear deformation theory (FSDT) using Hamilton׳s principle. The finite element method (FEM) together with Newmark׳s time integration scheme is employed to discretize the equations of motion in the spatial and temporal domain, respectively. The formulation and method of solution are validated by studying their convergence behavior and carrying out the comparison studies in the limit cases with existing solutions in the literature. Then, the influences of material graded index, radius-to-length ratio, semi-vertex angle, thickness, boundary conditions and moving load velocity on the dynamic behavior of the FG truncated conical shells are studied. In addition, the difference between the responses of the FG shells under symmetric and asymmetric loadings is compared.     

A second degree approximation for the calculation of the transfer function coefficients for heat conduction through walls

Calculation of the conduction transfer function coefficients using a state space representation requires the transient governing differential equation to be discretized in space by the use of finite difference or finite element methods, in order to obtain a set of first order differential equations. The use of FEM to discretize the media gives an additional advantage due to it is possible to use a higher order approximation of the dependent variable, which gives us a better accuracy with less elements. In this paper, the transient heat flow problem is tackled using a quadratic finite element. The variational formulation for the governing differential equation is developed, the Ritz approximation to construct the finite element formulation is used and the approximation functions are presented using a normalized local coordinate system for elements with three equally spaced nodes for the one-dimensional problem. The 2D transient problem is presented using a rectangular 8 node element. Results with 1, 2 and 3 three-node elements are compared with the ASHRAE conduction transfer functions for the 3, 5, 6, 8 and 32 wall groups and a 2D-example is given.     

高墩日照温差效应耦合场分析

采用三维瞬态热-结构耦合场方法分析了高墩的日照温差效应,引入地形系数概念,并结合规范方法采用等效温度边界条件,可较好地考虑高墩沿墩高方向的温度变化以及墩顶和墩底交界面上复杂的热传导.计算表明高墩中一般为竖向温度应力起控制作用,内壁拉应力可达到2 MPa左右.同时,日照温差还使得墩顶横向变位达到20 mm.高墩的日照温差效应在设计中必须给予充分的重视.所采用的方法和得出的规律均可为类似分析作参考.     

Thermoelastic dynamic stability of thin-walled beams with graded material properties

The dynamic stability of functionally graded thin-walled beams allowing for shear deformability is investigated in this article. The analysis is based on a model that has small strains and moderate rotations which are formulated through the adoption of a second-order non-linear displacement field. The beam is subjected to axial external dynamic loading. The model takes into account thermoelastic effects. The heat conduction equation is solved in order to characterize the temperature in the cross-sectional domain. Galerkin's and Bolotin's methods are employed with the scope to discretize the governing equations and to determine the regions of dynamic stability, respectively. Regions of stability are evaluated and expressed in non-dimensional form. The influence of the longitudinal vibration on the unstable regions is investigated. The numerical results show the importance of this effect when the forcing frequency approaches to the natural longitudinal frequency, obtaining substantially wider parametric stability regions. The effects of temperature gradients, shear flexibility and axial inertia, in beams with different cross-sections and different types of graded material are analyzed as well.     

Spatial homogenization algorithm for bridging disparities in scale between the fire and solid domains

The analysis of structures exposed to non-uniform heating from localized fires is a challenging task due to the spatially varying boundary conditions and the differences in scale between the fire simulation and solid heat transfer model. This paper presents a spatial homogenization algorithm for capturing non-uniform boundary conditions from a high-resolution fire simulation in a low-resolution finite element heat transfer model of a structure. The homogenization algorithm uses numerical integration by the trapezoid rule to calculate the equivalent thermal flux vector in the finite element heat transfer model for a spatially varying surface flux. The proposed method is compared to other approximating techniques, including averaging, sampling, and least squares methods, for a 2D heat transfer problem. The results demonstrate that the proposed homogenization algorithm converges rapidly due to the energy-equivalent representation of the thermal boundary condition. The homogenization algorithm is then implemented in a 3D heat transfer model that uses macro-level plate elements. For an application involving a horizontal plate exposed to a localized fire, the model is shown to converge to the results obtained by a solid finite element model. The homogenization algorithm combined with the plate heat transfer element proves to be an accurate and highly efficient means for analyzing structures with spatially varying thermal boundary conditions calculated by computational fluid dynamics.     

Sensitivity study of time delay coefficient of heat transfer formulations for insulated steel members exposed to fire

Heat transfer analysis for an insulated steel member exposed to fire conditions, in general, involves solving a 2D transient conduction equation with well-posed conditions. For design purpose, the current Eurocode 3 provisions adopt a closed-form solution from the SP approach which employs a simplified 1D characteristic heat transfer model. A virtual “time delay” has been incorporated in the analytical solution based on the assumption that the heat capacitance of insulation material is small compared to that of steel section. A sensitivity study is presented in this paper to assess the validity of the time delay coefficient. Results of the study indicate that for insulation with large heat capacitance, the time delay estimation in the SP approach yields significant discrepancy compared against exact solution. An exact formulation of time delay is recommended, which gives accurate results for insulation material with either small or large heat capacitance.     

大挠度功能梯度压杆的后屈曲分析

对一端固定一端自由功能梯度压杆的后屈曲问题进行了分析。依据组份材料的体积含量,假设材料的物性参数沿杆件的厚度按幂函数变化。基于Kirchhoff大变形理论,推导了大挠度功能梯度压杆后屈曲分析的控制微分方程和边界条件。采用微分求积法对所得控制微分方程和边界条件进行数值计算,得到压杆后屈曲时的自由端转角和自由端位移。分析了载荷、梯度指数和截面边长比对杆件后屈曲平衡路径的影响。     

建筑墙体的延时与削弱作用

本文采用数值方法分析了建筑墙体的材料与厚度对墙体延时与削弱作用的影响。基于这个目的,考虑了一维墙体带第三类周期性边界条件的非稳态导热。通过分析墙体材料的导热系数七、热容C和墙体厚度对墙体延时与削弱作用的影响,发现热容C和导热系数k对墙体延时与削弱作用影响明显。墙体达到一定厚度则具有比较好的延时与削弱效果。