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功能梯度矩形厚板的三维热弹性分析 总被引:6,自引:1,他引:6
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。 相似文献
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功能梯度材料作为一种新型材料在众多领域中有着重要的应用价值,其断裂问题是固体力学与材料科学共同关注的课题. 目前,功能梯度材料断裂力学研究工作主要集中在理论分析和数值模拟两方面,实验研究相对较少,其中的大部分实验工作只关注功能梯度材料的宏观断裂性能,而缺乏对其微观断裂机理的研究.本文对近10年来功能梯度材料断裂行为的实验研究的进展予以介绍和评述.首先介绍了可应用于功能梯度材料断裂行为研究的实验方法,然后介绍了相关实验工作的进展和取得的成果,最后分析了实验工作的不足之处,从实验研究角度提出了下一阶段功能梯度材料断裂行为的研究重点. 相似文献
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机械传动关键活动零部件接触副往往受到力载荷和摩擦热载荷的耦合作用,使得接触界面间的接触力学行为的分析变得极其复杂. 利用基于等效夹杂方法建立的考虑热对流非均质材料热弹接触力学分析模型研究不同摩擦系数、夹杂位置和材料属性等参数对材料表面及内部温升及热应力分布影响规律. 此外,进一步分析了接触副材料中含分布球形夹杂时摩擦热造成的影响. 结果表明:接触副表面温升梯度受热对流系数的影响较大;下表面温升和热应力随摩擦系数增大而增大;分布夹杂则将接触副材料下表面温升及热应力分布变得更为复杂. 相似文献
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当材料中存在不连续性缺陷的时候,传统的基于连续介质理论的方法在研究热传导问题时存在诸多不便.我们基于近场动力学方法(Peridynamics)建立了功能梯度材料的热传导模型,并且研究了在温度荷载作用下功能梯度材料的温度场的变化表现.该文概述了PD方法应用于热传导问题时的详细理论基础,描述了其建模思路以及计算体系,给出了使用PD方法模拟结构承受温度荷载时的计算格式,讨论了不同梯度形式对功能梯度材料内热传导的影响.算例结果表明:通过PD模型所得到的温度场与解析解吻合较好,证明了PD方法在分析功能梯度材料热传导行为等问题时的可行性. 相似文献
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功能梯度简支矩形板的非线性动力响应 总被引:1,自引:0,他引:1
研究了功能梯度简支矩形板在横向简谐激励作用下的非线性动力响应问题.采用幂律分布规律描述功能梯度材料的等效材料参数,基于Galerkin法建立了系统广义坐标的常微分控制方程.利用平均法得到了系统的幅频响应特性,分析了功能梯度矩形薄板的非线性主共振特性.数值算例验证了平均化方法的正确性,揭示了功能梯度平板主共振响应中的多值性和跳跃现象;同时分析发现初始条件会改变功能梯度平板主共振的响应幅值.最后讨论了功能梯度材料的梯度指数对系统幅值响应的影响. 相似文献
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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. 相似文献
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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. 相似文献
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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. 相似文献
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Yuezhong Feng Zhihe Jin 《Acta Mechanica Solida Sinica》2009,22(5):453-464
This work examines the fracture behavior of a functionally graded material (FGM) plate containing parallel surface cracks with alternating lengths subjected to a thermal shock. The thermal stress intensity factors (TSIFs) at the tips of long and short cracks are calculated using a singular integral equation technique. The critical thermal shock △Tc that causes crack initiation is calculated using a stress intensity factor criterion. Numerical examples of TSIFs and △Tc for an Al2O3/Si3N4 FGM plate are presented to illustrate the effects of thermal property gradation, crack spacing and crack length ratio on the TSIFs and △Tc. It is found that for a given crack length ratio, the TSIFs at the tips of both long and short cracks can be reduced significantly and △Tc can be enhanced by introducing appropriate material gradation. The TSIFs also decrease dramatically with a decrease in crack spacing. The TSIF at the tips of short cracks may be higher than that for the long cracks under certain crack geometry conditions. Hence, the short cracks instead of long cracks may first start to grow under the thermal shock loading. 相似文献
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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. 相似文献
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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. 相似文献
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为研究金属-FGM-陶瓷 EFBF
复合板的稳态热应力,从热传导规律出发,结合热应力计算公式,建立了该复合板稳态热应
力的研究模型,用有限元和辛普生法分析了T_a=500K和T_b=1800K时,该
复合板的稳态热应力分布并与无梯度两层复合板的结果进行了比较.
结果表明:FGM梯度层的厚度、组分和孔隙率对该EFBF复合板的热应力有不同程度的影响,
此外,有梯度三层复合板的热应力比较缓和,最大拉应力减小29.18%.
此结果为该复合板的设计和应用提供了准确的计算依据. 相似文献
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IntroductionCeramic/metalfunctionalygradientmaterial(FGM)hasgradientingredientdistribution,soitspropertiesoftheheattransferan... 相似文献
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Anastasia H. Muliana 《International Journal of Solids and Structures》2009,46(9):1911-1924
This study introduces a micromechanical model for predicting effective thermo-viscoelastic behaviors of a functionally graded material (FGM). The studied FGM consists of two constituents with varying compositions through the thickness. The microstructure of the FGM is idealized as solid spherical particles spatially distributed in a homogeneous matrix. The mechanical properties of each constituent can vary with temperature and time, while the thermal properties are allowed to change with temperature. The FGM model includes a transition zone where the inclusion and matrix constituents are not well defined. At the transition zone, an interchange between the two constituents as inclusion and matrix takes place such that the maximum inclusion volume contents before and after the transition zone are less than 50%. A micromechanical model is used to determine through-thickness effective thermal conductivity, coefficient of thermal expansion, and time-dependent compliance/stiffness of the FGM. The material properties at the transition zone are assumed to vary linearly between the two properties at the bounds of the transition zone. The micromechanical model is designed to be compatible with finite element (FE) scheme and used to analyze heat conduction and thermo-viscoelastic responses of FGMs. Available experimental data and analytical solutions in the literature are used to verify the thermo-mechanical properties of FGMs. The effects of time and temperature dependent constituent properties on the overall temperature, stress, and displacement fields in the FGM are also examined. 相似文献