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     

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。     

分层递变梯度蜂窝材料的面内冲击性能

提出了一种分层递变梯度蜂窝材料模型,以期控制蜂窝材料的能量动态吸收性能.此模型通过改变胞元的半径来改变蜂窝材料的面内特征参数,以实现蜂窝材料面内动力响应特性的多目标优化设计.计算结果表明,此模型可以在减小初始峰值应力水平的前提下,同时实现材料能量吸收过程的控制,并可以有效控制进入被保护结构的应力水平.此模型可为蜂窝材料...     

功能梯度材料的热/机械耦合分析研究进展

对功能梯度材料结构的热／机械耦合问题的研究现状进行了评述,包括分析方法的进展、热载作用下的裂纹问题、优化设计问题、细观力学问题等,然后提出了需要进一步研究的方向．     

任意梯度分布功能梯度涂层平面裂纹分析

提出可以分析任意梯度功能梯度材料的分层模型,并采用该模型研究功能梯度涂层平面裂纹问题.采用Fourier变换和传递矩阵法将该混合边值问题化为奇异积分方程组,通过数值求解获得应力强度因子.考察了分层模型的有效性,以及材料梯度变化形式、结构几何尺寸和材料梯度参数对裂纹应力强度因子的影响,发现结构几何尺寸、材料梯度变化形式、...     

弥散型核燃料元件热应力的计算模拟

针对弥散型燃料板的具体形状,选择了一种能够反映其实际变形特征的三维代表性体积单元作为研究对象;利用有限元法对其热力耦合行为进行了弹塑性分析,研究了热应力在燃料和基体中的分布特征.     

高承载梯度分层点阵结构的拓扑优化设计方法

随着增材制造技术的迅速发展, 点阵结构由于其高比强度、高比刚度等优异力学性能受到广泛关注, 但其单胞分布设计大多基于均布式假设, 导致其承载能力相对较差. 基于拓扑优化技术提出了一种梯度分层的点阵结构设计方法. 首先, 基于水平集函数建立点阵单胞几何构型的显式描述模型, 引入形状插值技术实现点阵单胞的梯度构型生成; 其次, 构建基于Kriging的梯度点阵单胞宏观等效力学属性预测模型, 建立宏观有限单元密度与微观点阵单胞等效力学属性的内在联系; 然后, 以点阵结构刚度最大为优化目标, 结构材料用量和力学控制方程为约束条件, 构建点阵结构的梯度分层拓扑优化模型, 并采用OC算法进行数值求解. 算例结果表明, 所提方法可实现点阵结构的最优梯度分层设计, 充分提高了点阵结构的承载性能, 同时可保证不同梯度点阵单胞之间的几何连续性. 最后, 开展梯度分层点阵结构与传统均匀点阵结构和线性梯度点阵结构的准静态压缩仿真分析, 仿真结果表明, 与传统均匀点阵结构和线性梯度点阵结构相比, 梯度分层点阵结构的承载能力明显提高. 研究结果可为高承载点阵结构设计提供理论参考.      

梯度半空间梯度覆层中的Love波

对功能梯度弹性半空间上覆盖一层功能梯度材料中的Love波的频散问题进行了研究,给出 了Love波频散方程的一般形式. 对功能梯度弹性半空间和功能梯度覆层的反平面剪切波的运 动控制方程进行了求解,给出了半空间和覆盖层的位移、应力解析解,给出了Love波在该解析 解下的频散方程. 以覆盖层的剪切弹性模量和质量密度均呈指数函数变化,半空间的剪切弹 性模量和质量密度均呈抛物线变化为例,利用迭代方法对频散方程进行了求解,给出了频散 曲线. 结果显示：在最低阶振型频散曲线中出现截止频率.     

材料物性参数识别的梯度正则化方法

本文对梯度正则化方法（Ｇｒａｄｉｅｎｔ－Ｒｅｇｕｌａｒｉｚａｔｉｏｎ Ｍｅｔｈｏｄ）作了进一步的研究,给出一种建立了梯度正则化迭代算法和选择正参数的简明实用方法。文中椭圆算子方程参数识别算例不仅说明了ＧＲ法具有广泛的适应性和一定的抗噪声能力,而且收敛速度较快,具有较大的收敛范围。     

热/机械载荷下功能梯度材料矩形厚板的弯曲行为

采用Reddy高阶剪切板理论,考虑材料物性参数随坐标和温度变化的特性,研究在均匀变化的温度场内功能梯度材料矩形板在面内与横向载荷共同作用下的横向弯曲问题,基于一维DQ法和Galerkin技术,给出了一对边固支、另对边任意约束时板弯曲问题的半解析解.以Si3N4/SUS304板为例考察了材料组份、温度场、面内载荷及边界约束条件等对功能梯度材料板弯曲行为的影响.     

Thermal stress intensity factor for functionally gradient half space with an edge crack under thermal load

Summary The aim of this work is to investigate the thermal stress intensity factor of a functionally gradient half space with an edge crack under a steady heat flux. All material properties of the functionally gradient half space, except for the coefficient of linear thermal expansion, are exponentially dependent on the distance from the boundary of the plate. The coefficient of linear thermal expansion is assumed to be two-dimensionally dependent. The problem is reduced to a singular integral equation by using the Fourier transform. The thermal stress intensity factor versus the nonhomogeneous material parameters is calculated and represented in figures. The numerical results show that thermal stress intensity factor is dramatically decreased when the material nonhomogeneous parameters are appropriately selected.     

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.     

中厚板统计分析的随机边界元法

本文建立了分析含随机材料参数并具厚度不均匀性的中厚板问题的随机边界元法,基于Taylor级数展开技术,分析和到广义位移的均值和一阶偏差的积分方程,其中将材料参数的随机性和厚度的不均匀性作为等效荷载处理,从而得到广义边界位移或面力的均值和协方差,并进一步求出部点广义位移和内力的均值和协方差,最后用本文方法计算了两个数例,并对所得结果进行了分析,探讨。     

Rational finite element method for elastic bending of reissner plates

IntroductionAsawell-establishedandsophisticatednumericalanalysistechniqueforthedifferentialequahons,thefiniteelementmethodwasoriginatedindependentlybythedomesticandtheforeignmechanicalinvestigatorstheyyearsago.ItfoundforthefirsttimewideapplicationsintheelasticstfUctolproblemsandwiththedevelopmentofcomputerextendedinvaryingdegreestOalmostalltheengineeringdisciplinesandmanyscientificandtechnologicalfields.Thisleadstoadramaticbreakthroughforthecurrentcomputationalmathematics.Themathematicalbasis…     

求解不连续中厚板自由振动的微分容积单元法

基于区域叠加原理和微分容积法,发展了一种新型的数值方法——微分容积单元法,用以分析具有不连续几何特征的中厚板的自由振动。根据板的不连续情况将其划分为若干单元,在每个单元内用微分容积法将控制微分方程离散成为一组线性代数方程．在相邻的单元连接处应用位移连续条件和平衡条件,引入边界约束条件后得到一套关于各配点位移的齐次线性代数方程,由此可导出求解系统固有频率的特征方程。本文用子空间迭代法求解特征方程,并以开孔板、混合边界条件板和突变厚度板为例研究了方法的收敛性和计算精度。     

Thermal postbuckling analysis of moderately thick plates

A thermal postbuckling analysis is presented for a moderately thick rectangular plate subjected to (1) uniform and non-uniform tent-like temperature loading; and (2) combined axial compression and uniform temperature loading. The initial geometrical imperfection of plate is taken into account. The formulations are based on the Reissner-Mindlin plate theory considering the effects of rotary inertia and transverse shear deformation. The analysis uses a deflection-type perturbation technique to determine the thermal buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of perfect and imperfect, moderately thick rectangular plates and are compared with the results predicted by the thin plate theory.     

功能梯度材料板件三维分析的半解析梯度有限元法

将半解析有限元与梯度有限元相结合,形成一种半解析梯度有限元来求解功能梯度材料板件问题。该方法兼有有限元法的适应性强、程序统一,半解析有限元法的节省单元与计算工作量,梯度有限元法的适应构件内部材料性能任意梯度分布等特点,并实现用一维数值计算给出构件三维分析结果。算例分析表明了方法的精度、功能与上述特点,充分揭示了功能梯度材料板件力学响应的三维形态。半解析梯度有限元法可推广应用到其他功能梯度材料面结构的各类分析中。     

Dynamic stress concentrations in thick plates with two holes based on refined theory

Based on complex variables and conformal mapping, the elastic wave scat- tering and dynamic stress concentrations in the plates with two holes are studied by the refined dynamic equation of plate bending. The problem to be solved is changed to a set of infinite algebraic equations by an orthogonM function expansion method. As examples, under free boundary conditions, the numerical results of the dynamic moment concen- tration factors in the plates with two circular holes are computed. The results indicate that the parameters such as the incident wave number, the thickness of plates, and the spacing between holes have great effects on the dynamic stress distributions. The results are accurate because the refined equation is derived without any engineering hypothese.     

竖向裂缝对功能梯度板的热响应影响

采用条单元法分析了竖向裂缝对功能梯度板的热响应影响。功能梯度板的材料属性沿板厚方向连续线性变化,温度变化热源作用于带竖向裂缝的功能梯度板上。通过研究得出了裂缝距离热源不同位置、不同长度裂缝及不同频率温度变化热源等状态时,功能梯度板上表面的热响应情况。采用条单元法研究带竖向裂缝的功能梯度板的热响应问题,为带裂缝的功能梯度板的热研究提供了一定的指导。     

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.