复杂形状功能梯度板件的三维动力特性分析

从细观力学角度出发根据材料细观组分分布对具有不同复杂形状功能梯度材料构件进行三维动力特性分析,并相应给出其三维固有频率及其基频对应的位移振型和应力振型沿厚度方向的三维分布。结果发现对同样材料细观组分分布的不同功能梯度结构,其固有频率和相应的振型分布均有很大差异。此结果为建立专门的功能梯度板壳理论提供定量的资料依据。     

具有中等组分不同网状结构功能梯度构件的三维动力特性分析

功能梯度材料具有复杂的细部结构,其内部构造远比匀质材料复杂,因此其构件动力分析很难求得其解析解。该文建议一种新颖的功能梯度构件动力分析的细观元法。细观力学研究的目的在于建立材料的宏观性能同其组分材料性能及细观结构之间的定量关系,它可揭示不同的材料组合具有不同的宏观性能的内在机制。此法可实现材料细观结构到构件宏观响应的直接过渡分析,而计算单元与自由度又等同一般常规有限元,却使得组成功能梯度材料构件的各种材料细观构造得到反映。通过细观元技术,对具有中等组分不同网状结构功能梯度构件进行三维动力特性分析,并给出其三维固有频率及振型的三维分布,特别是给出了不同网格结构功能梯度板件应力振型的平面等值线图差异。结果表明:不同细观网格结构对功能梯度材料结构三维动力响应有较明显影响。     

功能梯度材料与构件的静动力识别

功能梯度材料具有复杂的细部结构,其内部构造远比匀质材料复杂.因此,以目前的实验条件,测量功能梯度材料的参数分布是十分困难的.建议一种新颖的功能梯度构件分析的细观元法.细观力学研究的目的在于建立材料的宏观性能同其组分材料性能及细观构造之间的定量关系,它可揭示不同的材料组合及其变异所具有不同的宏观性能的内在机制.利用细观元法探讨功能梯度材料与结构的识别问题,即在已知实验测量的位移或固有频率的情况下,对功能梯度材料的组分分布及组成材料名称进行识别.     

复杂边界条件功能梯度板三维分析的细观元法

发展一种细观分析和宏观计算相结合的计算方法—细观元法。细观元法是使功能梯度构件宏观响应和材料组分的几何、物理、构造参数直接发生关联的分析方法,实现材料细观结构到构件宏观响应的直接过度分析,为解决功能梯度构件宏、细观跨尺度分析提供了一种有力工具。细观元方法不增加结点自由度,却使得功能梯度板件的任意功能梯度变化、各种复杂边界条件得到反映。用细观元法得到了几种具有不同复杂边界条件的功能梯度板件的力学量三维分布形态。     

由材料组分直接计算功能梯度复合材料开孔板宏观响应的跨尺度分析

建议一种新颖的功能梯度构件分析的细观元法, 给出了方法模型、基本算式及特点与功能。细观元法对构件的常规有限单元内部设置密集细观单元以反映材料组分梯度变化, 又通过协调条件将各细观元结点自由度转换为同一常规有限元自由度, 再上机计算。此法可实现材料细观结构到构件宏观响应的直接过渡分析, 而计算单元与自由度又等同于常规有限元, 为解决功能梯度构件宏观、细观跨尺度分析提供了一种有效工具。本文中直接从制备时给定材料组分分布出发计算构件宏观响应, 给出了不同开孔形状与数量功能梯度板的力学量三维分布形态。      

空隙、杂质及组分突变对功能梯度构件动力特性的影响

功能梯度材料具有复杂的细部结构, 其内部构造远比匀质材料复杂, 因此其构件动力分析很难求得其解析解。本文中提出了一种新颖的功能梯度构件动力分析的细观元法, 其目的在于建立材料的宏观性能与其组分材料性能及细观构造之间的定量关系, 以便揭示不同的材料组合及其变异所具有不同的宏观性能的内在机制。利用细观元法对含有空隙、 杂质及组分突变等情况下的功能梯度构件进行动力分析, 求得其三维固有频率及振型的三维分布。从而可知空隙、 杂质及组分突变均对功能梯度材料构件的宏观动力特性有很大的影响。      

功能梯度开孔矩形板的动力特性解

对于功能梯度平板结构,采用与矩形板两对边边界条件相应的梁函数组合级数来求解开孔板动力特性问题,得到板件各阶固有频率与振型解的一般表达式,适用于具有任意孔洞的四边为任意简单（包括36种）边界条件的功能梯度矩形板动力特性分析,为各类功能梯度开孔板件的动力计算与设计打下理论基础。     

热环境中功能梯度圆板的非线性动力响应分析

研究了热环境中功能梯度圆板在横向简谐激励作用下的非线性动力响应和动应力问题。针对陶瓷-金属功能梯度圆板, 考虑几何非线性、材料物理性质参数随温度变化及材料组分沿厚度方向按幂律分布的情况, 应用虚功原理给出了热载荷与横向简谐载荷共同作用下的非线性振动偏微分方程。在固支无滑动的边界条件下, 利用伽辽金法得到了达芬型非线性强迫振动方程。通过数值算例, 给出了关于体积分数指数的分岔图, 相图、Poincare映射等响应图以及动应力变化规律图, 讨论了材料体积分数指数和温度场对功能梯度圆板非线性动力响应的影响。结果表明: 热环境中功能梯度圆板随体积分数指数的变化可使系统出现周期响应、倍周期响应和混沌响应。功能梯度圆板中心处动应力在系统发生分岔或出现混沌响应时出现大幅变化, 而且在混沌响应时具有不可预测性。      

任意梯度分布简支功能梯度板的三维弯曲分析

研究了正交各向异性功能梯度板的三维弯曲问题。假设材料参数沿板厚方向按同一函数规律变化,基于状态空间法,在板的上下表面作用机械载荷的情况下,获得了简支功能梯度平板弯曲问题的Peano-Baker 级数解。通过算例,验证了 Peano-Baker级数解的正确性,同时也分析了材料参数沿板厚方向为余弦函数分布时,不同梯度参数对平板响应的影响。结果表明Peano-Baker 级数解具有很好的收敛性。     

基于Haar小波方法的功能梯度压电材料矩形板三维力学分析

针对任意材料梯度分布形式的四边简支、接地功能梯度压电材料平板,把Haar小波方法引入平板结构的三维分析中。由于小波方法在求解存在局部奇异性问题上的优越性,对于任意材料梯度变化,甚至材料性质存在局部剧烈变化的情况,各分量的Haar小波级数解都有较好的收敛性。通过算例,该文分析了在机械荷载、电荷载分别作用下,材料不同梯度形式、平板上下表面材料性质差异对功能梯度压电平板结构响应的影响。     

Rapid heating of FGM rectangular plates

Thermally induced vibrations of functionally graded material rectangular plates are investigatedin this research. The thermomechanical properties of the plate are assumed to be temperature and positiondependent. Dependency on temperature is expressed based on theTouloukian formula, and position dependencyis written as a power-law function. The ceramic-rich surface of the plate is subjected to temperature rise orheat flux, whereas the metal rich surface is kept at reference temperature or thermally insulated. Temporalevolution of the temperature profile across the plate thickness is obtained by the solution of one-dimensionalheat conduction equation. This equation is originally nonlinear since temperature dependency of thermalconductivity is taken into account. The solution of this equation is obtained by means of the generalizeddifferential quadrature (GDQ) accompanied with the successive Runge–Kutta algorithm in time domain. Themotion equations of the plate are obtained based on the first-order shear deformation theory of plates under smallstrains and small deformations assumptions. Hamilton’s principle is used to establish the motion equations.These equations are discreted in the plate domain bymeans of the two-dimensional GDQ method. The resultingequations are linear time-dependent coupled equations which are traced in time by means of the Newmarktime-marching method. Conducting comparison studies to assure the validity and accuracy of the proposedmodel, parametric studies are carried out to examine the influences of temperature dependency, thermal andmechanical boundary conditions, power-law index, plate geometry and boundary conditions. It is shown thatthermally induced vibrations exist for thin plates.     

Free vibration of FGM plates with in-plane material inhomogeneity

An analysis is presented for the free vibration of a functionally graded isotropic elastic rectangular plate with in-plane material inhomogeneity. A Levy-type solution is obtained for plates with a pair of simply supported edges that are parallel with the material gradient direction. A particular integration method is adopted to solve the fourth-order ordinary differential equation with non-constant coefficients. The efficiency and accuracy of the analysis are demonstrated through numerical examples.     

Vibrations of cracked rectangular FGM thick plates

Accurate first-of-its-kind solutions of the free vibration characteristics of side-cracked rectangular functionally graded material (FGM) thick plates are reported. From a brief review summary of available shear deformable plate theories, the well-established Reddy third-order plate theory apropos to cracked FGM thick plates is utilized. A novel Ritz procedure is developed incorporating special admissible functions – appropriately named in this study as crack functions – that properly account for the stress singularity behaviors in the neighborhood of a crack tip, and that properly account for the discontinuities of displacements and slops across a crack. Material properties of the FGM plates are assumed to vary continuously in the thickness direction according to the Mori–Tanaka scheme or a simple power law. The proposed special admissible functions accelerate the convergence of the extensive non-dimensional frequency solutions summarized. The first known non-dimensional frequencies of simply-supported and cantilevered cracked aluminum (Al) and ceramic (zirconia (ZrO₂)) or alumina (Al₂O₃) FGM thick plates of moderate thickness ratio (side-length to plate thickness, b/h = 10) are accurately determined. The effects of the volume fraction in the modeling of material distribution in the thickness direction and of cracks with different lengths, locations and orientations on the non-dimensional frequencies are investigated.     

功能梯度材料剪切板热屈曲后的非线性振动

基于Reddy高阶剪切变形理论及广义Kármán型方程,对功能梯度材料剪切板热屈曲后的非线性振动进行了分析,分析中考虑了材料热物参数对温度变化的依赖性.数值算例给出两类功能梯度材料剪切板在均匀温度场作用下的热荷载一线性振动频率及热荷载-非线性振动频率比曲线,讨论了材料组分指数变化所带来的影响.     

Paraconductivity along c-axis direction in a plane of a thin film of YBaCuO

Thin films of YBaCuO have been grown using a PrBa₂Cu₃O_7−x template with the caxis aligned in the plane of the films. Conductivity and hence paraconductivity have been measured along the c-axis direction on this plane. Thermal fluctuation studies have been attempted along this direction, and the dimensionality effect was studied for this configuration. As a main characteristic a dimensionality equal to zero is emerged from the data. This dimensionality is consistent with the phenomena of fluctuation along the c-axis.     

Semi-analytical consistent zigzag-elasticity formulations with implicit layerwise shear correction factors for dynamic stress analysis of sandwich circular plates with FGM layers

In the present paper, a consistent power series solution is proposed for dynamic behaviors analysis of circular sandwich plates with functionally graded face sheets/cores, for the first time. The proposed solution is a combination of the finite Taylor’s transform and the fourth-order Runge–Kutta procedure. The extension-bending coupling and the higher-order inertias are considered in the present research. The formulation guarantees continuity of the transverse stress components at the interfaces between layers. Another novelty is proposing a zigzag formulation whose results are corrected on the basis of the dynamic three-dimensional theory of elasticity. An interesting discussion for defining explicit/implicit layerwise shear correction factors is also presented. Furthermore, results reveal that using functionally graded face sheets or cores with transition variations of the material properties may lead to very smooth through-the-thickness stress distributions. Consequently, some of the failure modes may be prevented at the interfaces between the layers.     

Modification of dynamic characteristics of FGM plates with integrated piezoelectric layers using first‐ and second‐order approximations

This paper proposes a method for calculating the required changes in the physical properties of plates made of functionally graded materials (FGM) in order to achieve the desired eigenfrequency shifts in the structure. A finite element formulation based on the classical laminated plate theory (CLPT) is presented for an FGM plate with integrated piezoelectric layers. Using this formulation, an efficient method based on the first‐order and second‐order approximations in Taylor expansion is expressed to calculate the corresponding changes in the plate modal properties due to changes in parameters which characterize the structure's dynamic behaviour. An initial sensitivity analysis is carried out to identify the regions within the structure where modifications are most effective on the structure's dynamic characteristics. The proposed algorithm is applied to a case study with two different boundary conditions and the results are validated against exact solutions. The influence of structural modifications on dynamic response of the plate is also studied using the Newmark‐β method. Copyright © 2006 John Wiley & Sons, Ltd.     

Vibration analyses of FGM plates with in-plane material inhomogeneity by Ritz method

In this study, functionally graded plates which the properties of material varying through the in-plane direction is considered. The analysis is based on a five-degree-of-freedom shear deformable plate theory with different boundary conditions. The vibration solutions are obtained using the Ritz method and assumed displacement functions are in the form of the Chebyshev polynomials. The material properties are assumed to vary as a power form of the in-plane direction. The convergence and comparison studies demonstrate the accuracy and correctness of the present method. Effects of the different material composition, the Poisson ratio and the plate geometry (side-side, side-thickness) on the free vibration frequencies and mode shapes are investigated.