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。      

沿板平面变异功能梯度板件的三维动力特性

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。文中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。目前功能梯度板件分析只能处理材料特性沿厚度方向梯度变化,而细观元法则直接从制备时给定的材料组分分布出发计算构件宏观三维动力特性,并给出了沿板平面方向材料特性梯度变化的功能梯度板件三维固有频率及振型的三维分布。     

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。     

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。     

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.     

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。      

含椭球夹杂耐热梯度功能材料细观结构优化应力方程

梯度功能材料具有复杂的细观结构组合方式,对其进行细观力学的研究是当前的主要发展方向。本文作者对非均质、耐热、含椭球夹杂梯度功能材料的细观结构与性能进行了分析,研究其细观力学建模和在机械/热载荷下的损伤演化和破坏。结果可应用于多相夹杂梯度功能材料的细观应力分析和细观性能预测,并均以显式给出,以便于工程应用。     

复合材料构件的细观破坏、反演分析

本文探讨一种将材料细观结构与构件宏观响应联系起来的直接算法。该法基于宏观计算，却给出细观力学量，并可反映材料细观结构特征，特别适用于复合材料构件的细观破坏与反演分析。     

非均质梯度功能材料三维本构关系及宏细观结构分析

对非均质耐热梯度功能材料的结构与性能进行了研究。通过对陶瓷-金属梯度功能结构的分析,建立了宏、细观力学模型,并在此基础上导出了反映其宏观力学性能的三维本构关系。      

三维编织复合材料制件的细观单胞元分析

讨论了实现三维编织复合材料细观结构与宏观响应直接相关连的计算方法——细观单胞元法。该方法采用细观结构单胞作为离散单元对三维编织复合材料制件进行宏观网格剖分,在细观结构分析的基础上,将微结构上的物理量转换为细观单胞元的宏观节点变量,建立了细观单胞元刚度矩阵的求解方法。数值结果表明,该方法能反映细观结构参数的变化对材料宏观物理量的影响。     

Sensitivity of Dynamic Response of a Simply Supported Functionally Graded Magneto-electro-elastic Plate to its Elastic Parameters

Dynamic response sensitivity of a simply supported functionally graded magneto-electro-elastic plates have been studied by combining analytical method with finite element method. The functionally graded material parameters are assumed to obey exponential law in the thickness direction. A series solution of double trigonometric function agreed with the simply supported boundary condition is adopted in the plane of the plate and finite element method is used across the thickness of the plate. The finite element model is established based on energy variational principle. The coupled electromagnetic dynamic characteristics of a simply supported functionally graded magneto- electro-elastic plate are decided by its dynamics differential equation into which displacement components, electric potential and magnetic potential as nodal degree of freedom are incorporated. Dynamic response sensitivity is defined as a partial differential of dynamic response with respect to material parameter. Sensitivity of dynamic response of a simply supported functionally graded magneto-electro-elastic plate to its elastic parameters has been studied. The influence of the different exponential factor on dynamic response sensitivity has also been investigated.     

Three-dimensional static and dynamic analysis of functionally graded elliptical plates, employing graded finite elements

On the basis of the three-dimensional theory of elasticity, a graded finite element method capable of modeling static and dynamic behaviors of elliptical plates made of functionally graded materials (FGMs) subjected to uniform pressure is developed. In the present paper, two different material properties distributions are considered. For the dynamic analysis, the effective through-the-thickness continuous material properties distribution of the FGM (which is assumed to be composed of ceramic and metallic constituents) is determined based on Mori–Tanaka homogenization technique. The three-dimensional graded finite element formulation is derived based on the principle of minimum potential energy and Rayleigh Ritz method. To solve the time-dependent equations, Newmark’s direct integration method is employed. To present the efficiency of the present work, several numerical examples are included. Since similar results are not available in the literature, results of the present formulations are verified by comparing them with available ones of a homogenous elliptical plate.     

复杂边界条件功能梯度板三维分析的半解析方法

推导出适应功能梯度材料构件分析的半解析方法基本算式,并针对功能梯度构件的材料参数随空间坐标变化的特点,将材料参数纳入到力学方程中进行整体积分计算,从而编制统一程序计算不同边界条件下的板件问题.该法适应性强而又简洁高效,且不同于一般的半解析法,可采用一维离散,给出三维分析结果,是一种解决功能梯度构件力学性能分析的有效数值方法.文中用半解析法分析几种具有不同复杂边界条件的功能梯度板,给出了板件的力学量三维分布形态.     

复合材料构件性能的细观元分析

本文探讨了实现复合材料细观结构与宏观响应直接联系起来的计算方法——细观元方法。细观元法先进行宏观单元剖分, 然后分析细观结构, 将微结构物理量转化为结点量计算。该方法不增加自由度, 但却使得微结构任意铺设方式和任意微小变化均能在宏观力学量上得到反映。      

Three-dimensional free vibration analysis of functionally graded annular plates using the Chebyshev–Ritz method

The aim of this paper is to investigate three-dimensional free vibration of functionally graded annular plates with different boundary conditions using the Chebyshev–Ritz method, in which a set of duplicate Chebyshev polynomial series multiplied by the boundary function satisfying the boundary conditions are chosen as the trial functions of the displacement components. Two kinds of variations of material properties in the thickness direction of the plates are considered. Convergence of the Chebyshev–Ritz method is checked. Numerical results are given and compared with the previously published solutions.     

Geometrically nonlinear static and free vibration analysis of functionally graded piezoelectric plates

In this paper, nonlinear static and free vibration analysis of functionally graded piezoelectric plates has been carried out using finite element method under different sets of mechanical and electrical loadings. The plate with functionally graded piezoelectric material (FGPM) is assumed to be graded through the thickness by a simple power law distribution in terms of the volume fractions of the constituents. Only the geometrical nonlinearity has been taken into account and electric potential is assumed to be quadratic across the FGPM plate thickness. The governing equations are obtained using potential energy and Hamilton’s principle that includes elastic and piezoelectric effects. The finite element model is derived based on constitutive equation of piezoelectric material accounting for coupling between elasticity and electric effect using higher order plate elements. The present finite element is modeled with displacement components and electric potential as nodal degrees of freedom. Results are presented for two constituent FGPM plate under different mechanical boundary conditions. Numerical results for PZT-4/PZT-5H plate are given in dimensionless graphical forms. Effects of material composition and boundary conditions on nonlinear response are also studied. The numerical results obtained by the present model are in good agreement with the available solutions reported in the literature.