功能梯度矩形厚板的三维热弹性分析

直接从三维热弹性力学基本方程出发，通过引入两个位移函数和两个应力函数，导出了一个二阶的齐次状态方程和一个四阶的非齐次状态方程。分析中采用了层合近似模型，即将板划分成厚度足够小的若干薄层，从面可将每一层内的材料常数近似为常数。给出了任意厚度的四边简支横观各向同性功能梯度矩形板的热弹性分析，特别当板较薄时，与薄板理论进行了数值对比，发现两者结果吻合很好。最后研究了材料梯度指标对热弹性场的影响，结果显示梯度指标对热应力和位移都有着显著的作用：在不同的区间，梯度指标对它们有不同的影响；并且在同一区间，梯度指标对两者的影响程度也有所不同。     

梯度功能材料热弹性应变场分析

本文采用显微数字散斑相关方法，对梯度材料在稳态梯度温度场分布状态下应变场进行了实验与理论计算的研究，并对结果进行了比较与分析，从而为研究、设计、制备梯度功能材料提供了实验方法，并可以梯度材料理论研究的发展提供依据。     

复合材料层合板在加工固化后期降温速率对残余热应力的影响

本文采用非线性有限元方法，对材料性质与温度有关的复合材料层合板在加工固化后期降温过程中的温度速场和热应力场进行了分析，对降温度速率对板中固化残余热应力的影响进行了研究，获得一些对层合板固化成型工艺和固化残余热应力分析模型的选取均有意义的结果。     

考虑尺度效应的夹层楔形多孔梁动力学分析

基于修正偶应力理论, 研究了具有大范围旋转中心刚体-功能梯度夹层Euler-Bernoulli楔形多孔柔性微梁系统的动力学特性.楔形梁是中间层为不完全功能梯度层, 两表层为均质材料的功能梯度夹层结构, 它可以减小传统夹层结构由于层与层之间材料属性的不同导致脱粘类型损伤的影响.采用假设模态法描述变形, 考虑具有捕捉动力刚化效应的非线性耦合项, 计及von Kármán几何非线性应变, 运用第二类Lagrange方程, 导出了适用于较大变形的高次刚柔耦合动力学方程.对在平面内做大范围运动的中心刚体-功能梯度夹层Euler-Bernoulli楔形多孔微梁的动力学特性进行了详细研究.研究表明: 功能梯度夹层楔形梁表层结构高度、旋转角速度、功能梯度幂指数、尺度参数、孔隙度以及各层结构的体积分数对系统的动力学特性都有很大的影响; 功能梯度夹层楔形梁综合了功能梯度直梁和楔形梁的特性, 其相对于功能梯度直梁的固有频率增大, 同时使得孔隙度对结构固有频率变化趋势的影响不再与功能梯度直梁相同; 由于柔性梁变形能中具有横向与轴向的耦合势能, 系统在稳态下的平衡位置发生了迁移现象; 系统随着尺度参数的变化发生了频率转向与振型转换.      

磁头/磁盘滑动接触下磁盘温度及热退磁临界条件的研究

采用二维轴对称有限元模型计算磁头/磁盘滑动接触下,铝质磁盘的稳态温度和热应力场以及热退磁临界条件.结果表明:磁盘温度在极短时间内升至摩擦稳态值,然后缓慢线性升高到最终稳态值;经过充分热传导和热交换后磁盘的温度梯度较小,此时磁层内的热应力集中分布于磁盘固定端边缘附近;磁盘的稳态温度和热应力均随速度增大而增大,且载荷越大其值增大越快;热应力小于1.2 GPa时所对应的速度和载荷为安全工况;温升大于373 K时所对应的工况将导致磁盘退磁.     

复合材料层合板在加工固化后期降温速率对残余热应力…

本文采用非线性有限元方法，对材料性质与温度有关的复合材料怪合板在加工固化后期降温过程中的温度速场和热应力场进行了分析，对降温度速率对板中固化残余热应力的影响进行了研究，获得一些对层合板固化成型工艺和固化残余热应力分析模型的选取均有意义的结果。     

耐热梯度功能材料的热应力研究进展

介绍了梯度功能材料的概念和开发背景：回顾了近些年来在梯度功能材料热应力研究方面所取得的研究成果,并对梯度功能材料的发展趋势作一展望．着重论述了梯度功能材料在热应力分析领域的研究现状及其应用前景     

冰载荷下不锈钢复合板挠度特性分析

以复合板中面的挠度响应作为不锈钢复合板抗冲击性能的评价指标,基于能量法和经典层合板理论,考虑层间结构参数设计,通过横向载荷下的弯曲平衡微分方程,建立冰载荷下不锈钢复合板挠度响应简化解析模型。该分析模型将整个动态响应分析过程分为冰载荷计算分析和动力学方程求解两个阶段。分析了冰载荷模型的面倾角、冲击速度和碰撞位置对冰载荷的影响,确定极端工况参数,汇总接触面的节点力数据;分析了层厚比对挠度响应的影响规律;基于LS-DYNA有限元仿真以及数值算例分析,对比挠度响应仿真结果和解析计算值,验证了本文简化解析模型的准确性,研究结果对不锈钢复合板抗冲击性能分析和评估具有一定的参考价值。     

基于细观力学方法的底部充填封装芯片接合层的热应力计算

底部充填是一种用来提高电子产品在恶劣环境下工作的稳定性及可靠性的技术,是电子制造产业的常用方法.本文基于细观力学方法建立了计算底部充填封装芯片热应力的方法.针对底部充填封装芯片焊锡-充填物接合层的结构特点,我们建立了接合层的均一化模型,并从理论上推导了接合层的等效弹性常数、热膨胀系数和导热系数.运用该均一化模型,我们对封装芯片工作产热导致的热传导和热应力问题进行了有限元数值模拟,计算的结果与接合层未均一化的模型具有较好的一致性,而计算效率极大提高,显示了该方法在计算底部充填封装芯片热应力方面的可行性.     

初始和边界不同恒温时二维梯度板瞬态温度场

为了研究二维功能梯度板的平面瞬态温度场及影响因素,假设热导率和容积比热容在板的高和宽方向为同一类型指数函数分布,基于该板的瞬态热传导基本方程,采用分离变量法,导出在初始和边界不同恒温时该板平面瞬态温度场的级数解析解。通过两种方法的对比,验证了本文研究结果的正确性。结果表明：方板内的等温线,在梯度参数ALFA=BETA时,对称于板的450对角线分布,在ALFA=BETA=0时,对称于板的中心分布;在ALFA不等于BETA时,板的等温线不具对称性;随着冷却时间的增加,非均匀板的等温线向左下（或右上）角移动,右上（或左下）角等温线间距变宽,左下（或右上）角等温线间距变窄,且矩形板的冷却过程比方板更快。因此,可选择适合的梯度参数和几何形状来满足设计、应用和热应力分析的需要,该解析解可作为检验其他近似方法的参考标准。     

Optimum material design for functionally gradient material plate

Summary Steady thermal stresses in a plate made of a functionally gradient material (FGM) are analyzed theoretically and calculated numerically. An FGM plate composed of PSZ and Ti-6Al-4V is examined, and the temperature dependence of the material properties is considered. A local safety factor is used for evaluation of the FGM's strength. It is assumed that top and bottom surfaces of the plate are heated and kept at constant thermal boundary conditions. The pairs of the surface temperatures, for which the minimum local safety factor can be of more than one, are obtained as available temperature regions. The temperature dependence of the material properties diminishes, available temperature region as compared with that for an FGM plate without it. The available temperature region of the FGM plate is wider than that of the two-layered plate, especially for the surface temperatures which are high at the ceramic surface and low at the metal side. The influence of different mechanical boundary conditions is examined, and available temperature regions are found to be different, depending on the mechanical boundary conditions. The influence of the intermediate composition on the thermal stress reduction is also investigated in detail for the surface temperatures which are kept at 1300 K at the ceramic surface and 300K at the metal side. Appropriate intermediate composition of the FGM plate can yield the local safety factor of one or more for the four mechanical boundary conditions at once. For the two-layered plate there does not exist, however, any appropriate pair of metal and ceramic thicknesses which would yield the local safety factor of one or more for the four mechanical boundary conditions at once. The influence of the intermediate composition on the maximization of the minimum stress ratio depends on the mechanical boundary conditions. Finally, the optimal FGM plates are determined.     

Self-consistent elastoplastic stress solutions for functionally graded material systems subjected to thermal transients

In this work, a self-consistent constitutive framework is proposed to describe the behaviour of a generic three-layered system containing a functionally graded material (FGM) layer subjected to thermal loading. Analytical and semi-analytical solutions are obtained to describe the thermo-elastic and thermo-elastoplastic behaviour of a three-layered system consisting of a metallic and a ceramic layer joined together by an FGM layer of arbitrary composition profile. Solutions for the stress distributions in a generic FGM system subjected to arbitrary temperature transient conditions are presented. The homogenisation of the local elastoplastic FGM behaviour in terms of the properties of its individual phases is performed using a self-consistent approach. In this work, power-law strain hardening behaviour is assumed for the FGM metallic phase. The stress distributions within the FGM systems are compared with accurate numerical solutions obtained from finite element analyses and good agreement is found throughout. Solutions are also given for the critical temperature transients required for the onset of plastic deformation within the three-layered systems.     

Residual stress analysis of functionally gradient materials

Functionally gradient materials (FGM) are new engineering materials without fully understanding. One important aspect in mechanical analysis of FGM is to determine a gradient distribution that finally results in maximum thermal stress relaxation. In this paper, numerical analysis by finite element method and experimental analysis by Moire interference method were carried out to study the stress distribution in FGM. Much attention was paid on the edge effect stresses in the coating/substrate structures, and their dependence on the different gradient distribution of the new kind of composite materials.     

Thermal stresses in functionally graded materials caused by a laser thermal shock

 Mathematical simulation of a thermal shock method for reliability testing of functionally graded material (FGM) is performed with the end to determine operating parameters of the testing device (power of a laser, laser beam radius, duration of heating) and to investigate the effect of the composition of FGM on a magnitude of thermal stresses in a coating. An analytical method for solution of the thermal elasticity problem is developed whereby the approach of a multilayer plate is used for determining temperature and thermal stresses distributions in a coating. We considered the limiting case of the obtained solution when the thickness of a layer is infinitesimally small and the number of layers tends to infinity. This procedure allowed us to obtain the thermal stresses distribution in a FGM coating. The results for the FGM coating composed of WC (tungsten carbide) ceramics and HS-steel are presented. It is showed that variation of the volume content of ceramics strongly affects thermal stresses in a coating and they decrease significantly in the case of the uniform spatial distribution of ceramics. Received on 21 November 2000 / Published online: 29 November 2001     

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.     

Reduction of thermal stresses by developing two-dimensional functionally graded materials

Modern aerospace shuttles and craft are subjected to super high temperatures, that have variation in two or three directions, which need to introduce new materials that can stand with such applications. Therefore, in the present work a two-dimensional functionally graded materials, 2D-FGM, are introduced to withstand super high temperatures and to give more reduction in thermal stresses. The suitable functions that can represent volume fractions of the introduced 2D-FGM are proposed. Then the rules of mixture of the 2D-FGM are derived based on the volume fractions of the 2D-FGM and the rules of mixture of the conventional FGM. The introduced volume fractions and rules of mixture for 2D-FGM were used to calculate the thermal stresses in 2D-FGM plate. Comparison between 2D-FGM and conventional FGM was carried out and showed that 2D-FGM has high capability to reduce thermal stresses than the conventional FGM.     

Free vibration of functionally graded sandwich plates using four-variable refined plate theory

This paper uses the four-variable refined plate theory (RPT) for the free vibration analysis of functionally graded material (FGM) sandwich rectangular plates. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton’s principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. The validity of the theory is shown by comparing the present results with those of the classical, the first-order, and the other higher-order theories. The proposed theory is accurate and simple in solving the free vibration behavior of the FGM sandwich plates.     

Free vibration of functionally graded sandwich plates using four-variable refined plate theory

This paper uses the four-variable refined plate theory (RPT) for the free vibration analysis of functionally graded material (FGM) sandwich rectangular plates.Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. The validity of the theory is shown by comparing the present results with those of the classical, the first-order, and the other higher-ordex theories. The proposed theory is accurate and simple in solving the free vibration behavior of the FGM sandwich plates.     

Stress intensity factors for three-dimensional cracks in functionally graded materials using enriched finite elements

A three-dimensional enriched finite-element methodology is presented to compute stress intensity factors for three-dimensional cracks contained in functionally graded materials (FGMs). A general-purpose 3D finite-element based fracture analysis program, FRAC3D, is enhanced to include this capability. First, using available solutions from the literature, comparisons have been made in terms of stresses under different loading conditions, such as uniform tensile, bending and thermal loads. Mesh refinement studies are also performed. The fracture solutions are obtained for edge cracks in an FGM strip and surface cracks in a finite-thickness FGM plate and compared with existing solutions in the literature. Further analyses are performed to study the behavior of stress intensity factor near the free surface where crack front terminates. It is shown that three-dimensional enriched finite elements provide accurate and efficient fracture solutions for three-dimensional cracks contained in functionally graded materials.     

Stochastic analysis of a thermoelastic problem in functionally graded plates with uncertain material properties

The statistics (i.e., mean and variance) of temperature and thermal stress are analytically obtained in functionally graded material (FGM) plates with uncertainties in the thermal conductivity and coefficient of linear thermal expansion. These FGM plates are assumed to have arbitrary nonhomogeneous thermal and mechanical properties through the entire thickness of plate and are subjected to deterministic convective heating. The stochastic temperature and thermal stress fields are analysed by assuming the FGM plate is multilayered with distinct, random thermal conductivity and coefficient of linear thermal expansion in each layer. Vodicka’s method, which is a type of integral transform method, and a perturbation method are employed to obtain the analytical solutions for the statistics. The autocorrelation coefficients of each random property and cross-correlation coefficients between different random properties are expressed in exponential function forms as a non-homogeneous Markov random field of discrete space. Numerical calculations are performed for FGM plates composed of partially stabilised zirconia (PSZ) and austenitic stainless steel (SUS304), which have the largest dispersion of the random properties at the place where the volume fractions of the two constituent materials are both 0.5. The effects of the spatial change in material composition, thermal boundary condition and correlation coefficients on the standard deviations of the temperature and thermal stress are discussed.