环形蓄热片相变材料固化时热传导问题的Green函数瞬时解

当环形蓄热片为相变材料所固化时,应用Green函数法分析其瞬时的温度分布.在一个柱形壳体中存储该相变材料(PCM),蓄热片上固体相变材料的厚度随时间而变化,并由Megerlin法求得.找到模型用Bessel方程构成的分析解,讨论了3种不同类型的边界条件,给出了解析解和数值解的比较.结果表明,所有情况下得到的蓄热片温度分布精度是令人满意的.     

双圆柱体结构的热耦合微分方程及其有限元解

针对物体的热耦合问题,给出了内外形式的双圆柱体结构的热耦合分析的基本微分方程,提出了采用有限元进行求解的方法,并给出了具体算例.热耦合是一个复杂的多元微分方程的求解问题.求解得知,热应力分布情况不仅与几何形状有关,也与热载荷与材料物理特性有关,在一定温度变化范围内,物体由于温度变化所产生的等效应力会随温度呈近似线性变化.此外,结构几何尺寸对应力分布变化的影响大于对温度分布变化的影响.     

颗粒增强复合材料热应力分析的双层嵌套模型

建立了一个把增强颗粒球和基体空心球嵌入等效复合介质空腔中的“双层嵌套模型”,研究了颗粒增强材料自高温冷却下来时,不同相中热应力的分布特点。推出了热应力在弹性和弹塑性状态的各种表达式。研究表明,随着温度降低,增强体受到压应力,基体材料中存在的静水应力为拉应力。温度继续下降,将出现自增强颗粒与基体界面向外扩展的屈服区。随增强相体积分数增大,增强颗粒受到的压应力和基体中的静水拉应力减小,增强颗粒与基体界面屈服的起始温差增大,而基体材料全面屈服的温差却减小。     

热荷载作用下薄板的优化设计

板壳结构是一大类广泛使用的结构元件.在热荷载作用下,当热膨胀受到约束时,板壳结构产生内力及挠度,严重时影响结构的正常服役.由于热荷载的特殊性,简单地均匀加大板壳结构的厚度并不能有效地减少热变形和热应力,热结构设计因此特别困难.该文研究在给定材料体积的条件下,通过优化板壳结构的厚度分布来减少弹性薄板结构在热载荷下的变形.以结构的变形能为优化目标,在给定材料体积的条件下,建立了设计板壳结构厚度分布的优化问题列式,并采用变分法,推导出优化准则,给出了修改厚度的迭代公式.应用商用有限元软件的热结构分析功能,对程序进行二次开发,从而实现该优化算法.算例结果表明,采用该方法优化弹性薄板的厚度分布,可以大幅度地减小结构热变形,是一种有效的热结构设计方法.     

高压气体淬火过程中的温度场与相变耦合问题的计算

高压气体淬火技术是一种现代的、有效的材料加工技术．在Cheng所得到的高压气体淬火过程中非线性表面换热系数的基础上,用有限单元法对钢淬火过程的温度场与相变耦合问题进行了模拟计算．在数值计算中,材料的热物性系数被处理为温度和相变体积百分比的函数．为避免数值解的震荡,采用了Norsette有理近似法．     

带相变的铸坯热弹塑性应力分析基本方程

本文讨论了温度、相变、应力间的耦合关系，给出了铸坯在考虑相变时的热弹塑性蠕变的本构关系，以及计算铸坯内应力的有限元迭代公式。     

热环境中粘贴压电层功能梯度材料梁的自由振动

研究了上下表面粘贴压电层的功能梯度材料Euler-Bernoulli梁在升温及电场作用下的屈曲和自由振动行为.在精确考虑轴线伸长基础上,建立了压电功能梯度材料层合梁在热-电-机载荷作用下的几何非线性动力学控制方程.其中,假设功能梯度材料性质沿厚度方向按照幂函数连续变化,上下压电层为各向同性均匀材料.在小振幅和谐振动假设下,上述非线性偏微分方程组被转化为两套相互耦合的常微分方程组,即过屈曲问题的控制方程和过屈曲构形附近的线性振动控制方程.采用打靶法数值求解上述两个耦合的常微分方程边值问题,获得了在均匀电场和横向非均匀升温场作用下两端固定压电.功能梯度材料层合梁在屈曲前和过屈曲构型附近的自由振动响应.绘出了梁的过屈曲平衡路径以及前3阶固有频率随热、电载荷及材料梯度参数变化的特性曲线.结果表明,梁的前3阶频率在屈曲前随着温度升高而减小,在进入过屈曲后它们却随着温度升高而增加.通过施加电压在压电层产生拉应力可有效地提高粱的热屈曲临界载荷,从而提高其固有频率.     

含湿相变粗糙多孔材质的热质耦合分形研究

多孔材质复杂的内部结构和含湿状态对传热和传质特性有着重要意义,其热质耦合传递过程广泛存在于能源开发和工程隔热等领域。不同于在多孔材质理想状态下对传热和传质特性的单方面分析,该文将孔道的分布参数、粗糙表面、含湿状态和相变等因素考虑进去,运用分形理论推导出了含湿相变粗糙表面多孔材质的渗流系数和耦合等效导热系数的表达式。结果表明,渗流系数与面积分形维数、含湿饱和度呈正相关,与相对粗糙度、迂曲分形维数呈负相关;耦合等效导热系数与渗流系数、相变量呈正相关,与相对粗糙度呈负相关。此外,结果还表明,相变量以及相变引起的气体膨胀压强差对热质耦合传递也有着重要影响。     

淬火过程中具有非线性表面系数考虑相变时温度场的有限元分析

温度场的计算对淬火过程中热应力和热应变的分析有较大影响，对淬火后试件的残余应力和微观结构分析也有较大影响·本文以４２ＣｒＭｏ钢圆柱体试件为研究对象，从相变等温动力学ＴＴＴ图，给出了连续冷却相变动力学ＣＣＴ图的数学模拟计算式，计算了钢淬火过程中相变组织成分百分比，将热物性系数处理为温度和相变体积百分比的函数，用有限单元法计算了淬火过程中具有非线性表面系数考虑相变时的温度场·并建立了相应的泛函，为以后计算淬火的热应力和热应变做好准备工作     

异质材料有限长微通道电渗流热效应

采用数值方法,分析有限长PDMS/玻璃微通道电渗流热效应．数值求解双电层的Poisson-Boltzmann方程,液体流动的Navier-Stokes方程和流-固耦合的热输运方程,分析二维微通道电渗流的温度特性．考虑温度变化对流体特性（介电系数、粘度、热和电传导率）的反馈效应．数值结果表明,在通道进口附近有一段热发展长度,这里的流动速度、温度、压强和电场快速变化,然后趋向到一个稳定状态．在高电场和厚芯片的情况下,热发展长度可以占据相当一部分的微通道．电渗流稳定态温度随外加电场和芯片厚度的增加而升高．由于壁面材料的热特性差异,在稳定态时的PDMS壁面温度比玻璃壁面温度高．研究还发现在微通道的纵向和横向截面有温度变化．壁面温升降低双电层电荷密度．微通道纵向温度变化诱发流体压强梯度和改变微通道电场特性．微通道进流温度不改变热稳定态的温度和热发展长度．     

Bifurcation and chaos of thin circular functionally graded plate in thermal environment

A ceramic/metal functionally graded circular plate under one-term and two-term transversal excitations in the thermal environment is investigated, respectively. The effects of geometric nonlinearity and temperature-dependent material properties are both taken into account. The material properties of the functionally graded plate are assumed to vary continuously through the thickness, according to a power law distribution of the volume fraction of the constituents. Using the principle of virtual work, the nonlinear partial differential equations of FGM plate subjected to transverse harmonic forcing excitation and thermal load are derived. For the circular plate with clamped immovable edge, the Duffing nonlinear forced vibration equation is deduced using Galerkin method. The criteria for existence of chaos under one-term and two-term periodic perturbations are given with Melnikov method. Numerical simulations are carried out to plot the bifurcation curves for the homolinic orbits. Effects of the material volume fraction index and temperature on the criterions are discussed and the existences of chaos are validated by plotting phase portraits, Poincare maps. Also, the bifurcation diagrams and corresponding maximum Lyapunov exponents are plotted. It was found that periodic, multiple periodic solutions and chaotic motions exist for the FGM plate under certain conditions.     

The impact of multi-layered porosity distribution on the performance of a lithium ion battery

This study investigates the impact of a multi-layered porosity profile on the electrical and thermal performance of a lithium-ion battery. Consideration is given to key attributes of the battery, namely its specific power and energy and the temperature distribution that may generated throughout the cell under electrical load. The COMSOl Multiphysics software tool has been employed to develop a 3D electrochemical–thermal model of a commercially available 10 Ah lithium iron phosphate cell. Through an extensive simulation study, for a fixed value of active material, the impact of varying the porosity profile across both the thickness and height of the electrode has been studied. For each case study, the distribution of reaction current and the corresponding localised state of charge and temperature profile are quantified for a constant current discharge of 5C. Simulation results highlight that a multi-layered porosity distribution across the thickness of the electrode has the potential to yield superior battery performance compared to when the porosity is varied along the electrode height. Moreover, the total heat generation within the cathode may be reduced by up to 14% compared to a Reference Case, along with 0.33% and 0.44% improvement in the specific energy and power, respectively.     

Analysis of functionally graded plates using higher order shear deformation theory

This work addresses a static analysis of functionally graded material (FGM) plates using higher order shear deformation theory. In the theory the transverse shear stresses are represented as quadratic through the thickness and hence it requires no shear correction factor. The material property gradient is assumed to vary in the thickness direction. Mori and Tanaka theory (1973) [1] is used to represent the material property of FGM plate at any point. The thermal gradient across the plate thickness is represented accurately by utilizing the thermal properties of the constituent materials. Results have been obtained by employing a C° continuous isoparametric Lagrangian finite element with seven degrees of freedom for each node. The convergence and comparison studies are presented and effects of the different material composition and the plate geometry (side-thickness, side–side) on deflection and temperature are investigated. Effect of skew angle on deflection and axial stress of the plate is also studied. Effects of material constant n on deflection and the temperature distribution are also discussed in detail.     

An accurate mathematical study on the free vibration of stepped thickness circular/annular Mindlin functionally graded plates

An analytical solution based on a new exact closed form procedure is presented for free vibration analysis of stepped circular and annular FG plates via first order shear deformation plate theory of Mindlin. The material properties change continuously through the thickness of the plate, which can vary according to a power-law distribution of the volume fraction of the constituents, whereas Poisson’s ratio is set to be constant. Based on the domain decomposition technique, five highly coupled governing partial differential equations of motion for freely vibrating FG plates were exactly solved by introducing the new potential functions as well as using the method of separation of variables. Several comparison studies were presented by those reported in the literature and the FEM analysis, for various thickness values and combinations of stepped thickness variations of circular/annular FG plates to demonstrate highly stability and accuracy of present exact procedure. The effect of the geometrical and material plate parameters such as step thickness ratios, step locations and the power law index on the natural frequencies of FG plates is investigated.     

Nonlinear finite element analysis of functionally graded plates integrated with patches of piezoelectric fiber reinforced composite

In this paper, a nonlinear static finite element analysis of simply supported smart functionally graded (FG) plates in the presence/absence of the thermal environment has been presented. The substrate FG plate is integrated with the patches of piezoelectric fiber reinforced composite (PFRC) material which act as the distributed actuators of the plate. The material properties of the FG substrate plate are assumed to be temperature dependent and graded along the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The derivation of this nonlinear thermo-electro-mechanical coupled finite element model is based on the first order shear deformation theory and the Von Karman type geometric nonlinearity. The numerical solutions of the nonlinear equations of the finite element model are obtained by employing the direct iteration method. The numerical illustrations suggest the potential use of the distributed actuator made of the PFRC material for active control of nonlinear deformations of smart FG structures. The effects of volume fraction index of the FG material of the substrate plates and the locations of the PFRC patches on the control authority of the patches are investigated. Emphasis has also been placed on investigating the effect of variation of piezoelectric fiber orientation angle in the PFRC patches on their actuation capability for counteracting the large deflections of FG plates.     

Thermal Buckling Analysis of FGM Sandwich Circular Plates Under Transverse Nonuniform Temperature Field Actions北大核心CSCD

Based on the von Kármán geometric nonlinear plate theory, the displacement⁃type geometric nonlinear governing equations for FGM sandwich circular plates under transverse nonlinear temperature field actions were derived. With the immovable clamped boundary condition, the analytical formula for dimensional critical buckling temperature differences of the system was obtained from the solution of the linear eigenvalue problem. Moreover, the 2⁃point boundary value problem of ordinary differential equations was solved with the shooting method. The effects of geometric parameters, constituent material properties, gradient indexes, temperature field parameters and layer⁃thickness ratios on the critical buckling temperature differences, the thermal postbuckling equilibrium paths, and the buckling equilibrium configurations of FGM sandwich circular plates, were investigated. The results show that, with the increases of the thickness⁃radius ratio, the relative thickness of the FGM layer and the gradient index, the FGM sandwich circular plate's critical buckling temperature difference will increase monotonically. Given a fixed radius and a fixed total thickness, the postbuckling deformation of the FGM sandwich circular plate will decrease significantly with the relative thickness of the FGM layer. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Wave propagation and transient response of a functionally graded material plate under a point impact load in thermal environments

In this paper, the wave propagation and transient response of an infinite functionally graded plate under a point impact load in thermal environments are studied. The thermal effects and temperature-dependent material properties are taken into account. The temperature field considered is assumed to be a uniform distribution over the plate surface and varies in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Considering the effects of transverse shear deformation and rotary inertia, the governing equations of the wave propagation in the functionally graded plate are derived from Hamilton’s principle. The analytic dispersion relation of the functionally graded plate is obtained by means of integral transforms and a complete discussion of dispersion for the functionally graded plate is given. Using the dispersion relation and integral transforms, exact integral solutions of the functionally graded plate under a point impact load in thermal environments are obtained. The influences of the volume fraction distributions and temperature field on the wave propagation and transient response of functionally graded plates are discussed in detail. The results carried out can be used in the ultrasonic inspection techniques and provide a theoretical basis for engineering applications.     

One-dimensional solidification of pure materials with a time periodically oscillating temperature boundary condition

A finite difference method is used to solve a one-dimensional solidification problem with a periodic boundary condition prescribed at the bottom of the mold of finite thickness. The temperature distributions in the solidified shell and mold, the position of the moving freezing front, and its velocity are evaluated. Analytical results are obtained for the limiting cases and then compared with the numerical predictions to establish the validity of the model and the numerical approach. Interactive effects of the process parameters such as Stefan number of the solidified shell material, the mold thickness, the thermal conductivity and thermal diffusivity between the shell and mold materials on the evolution of the freezing front and its velocity are investigated in detail. The results show that the solidified materials with larger Stefan number grow slower than those with relatively smaller Stefan number. The impact of oscillating mold temperature boundary on the growth of shell thickness is particularly significant at earlier stages of the process and more pronounced for smaller Stefan numbers. Increasing mold thickness or thermal conductivity ratio between the shell and mold materials slows down the evolution of the shell thickness.     

Effect of random system properties on bending response of thermo-mechanically loaded laminated composite plates

In this paper, effect of random variation in system properties on bending response of geometrically linear 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 modeled as basic random variables. The basic formulation is based on higher order shear deformation theory to model the system behavior of the composite plate. A C⁰ finite element method in conjunction with the first order perturbation technique procedure developed earlier by authors for the plate subjected to lateral loading is employed to obtain the second order response statistics (mean and variance) of the transverse deflection of the plate. Typical numerical results for the second order statistics of the transverse central deflection of geometrically linear composite plates with temperature independent and dependent material properties subjected to uniform temperature and combination of uniform and linearly varying temperature distribution are obtained for various combinations of geometric parameters, uniform lateral pressures, staking sequences and boundary conditions. The performance of the stochastic laminated composite model is demonstrated through comparison of mean transverse central deflection with those results available in literature and standard deviation of the deflection with an independent Monte Carlo simulation.     

Quantifying diffusion for an ultrasonic wire bonding process by applying the theory of material forces

Ultrasonic wire bonding is a method applied in electronic packaging to fabricate interconnections between two devices at ambient temperature. In order to investigate the material diffusion during this process, the occurring thermal and mechanical mechanisms at and around the interface of the formed bond were studied by means of coupled thermo-mechanical FE simulations. Within the framework of material forces the local jump of the Eshelby tensor was compared with the thickness of the formed intermetallic phase for various bonding parameters. This allows us to predict an effective diffusion constant which takes temperature and mechanical driving forces into account. After this relation has been established a subsequent objective of our investigations is to optimize the growth of the Au8Al3 intermetallic phase in terms of bonding parameters. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)