具有不同功能梯度分布函数的板件的三维分析

发展了一种新颖的功能梯度结构分析的细观元法。细观元法对结构的常规有限单元内部设置密集细观单元以反映材料特性梯度变化,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。这种细观元法既能充分反映材料功能梯度变化特性;而其计算单元又和常规有限元一样,是一种针对功能梯度结构分析的有效数值方法。文中通过细观元技术进行计算、分析,给出了具有不同功能梯度分布函数板件的力学量三维分布形态。     

沿板平面材料梯度变化功能材料板件分析

本文发展一种功能梯度构件分析的细观元法.细观元法在构件的常规有限元内部设置密集观细单元以反映材料特性变化,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.这种细观元法既能充分反映材料功能梯度沿各方向任意变化特性;而其计算单元又和常规有限元一样,是一种针对功能梯度结构分析的有效数值方法.现有功能梯度板件分析中无论对不同形状还是不同边界的功能梯度构件,其材料特性均沿板厚度方向梯度变化,本文用细观元法进行计算与分析,给出了目前尚未得到的沿板平面方向功能梯度变化构件的力学量三维分布形态.     

功能梯度材料构件三维分析的细观元模型

提出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特性梯度变化,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。这种细观元法既能充分反映材料功能梯度及组分变化特性,而其计算单元与自由度又与常规有限元一样,是一种针对功能梯度构件分析的有效数值方法。算例表明了细观元法对不同情况下功能梯度构件分析的适应性与精度。     

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。     

各种边界条件平行四边形功能梯度板的动力特性解析解

本文基于斜坐标系,建立起平行四边形功能梯度板的基本微分方程及变分方程,用梁函数组合法对平行四边形及菱形功能梯度板进行动力特性分析,提出了适用于每边任取简支、固定、自由边界之一(包括36种边界)平行四边形功能梯度板固有频率与振型的解析解;在简化情况下,给出了各种边界条件平行四边形功能梯度板各阶固有频率解的统一表达式。     

基于金相图片识别功能梯度材料参数的梯度分布函数

功能梯度材料具有复杂的细观结构.其内部构造远比匀质材料复杂.以目前的实验条件,测量功能梯度材料参数分布函数一般是十分困难的.该文提出一种细观元方法,直接利用功能梯度材料金相图片信息,来进行功能梯度构件宏观响应的跨尺度力学分析.另在功能梯度材料结构静、动力正演分析基础上,根据正演所求得的挠度或固有频率值,采用混和罚函数法来反演识别功能梯度材料参数的宏观梯度分布函数.     

空隙分布对功能梯度板件宏观响应的影响

提出了一种新的功能梯度结构分析的细观元法. 细观元法对结构的常规有限单元内部设置密集细观单元以反映材料细观构造,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. 此方法实现了材料细观结构到构件宏观响应的直接过渡分析. 用细观元法来分析细观构造上空隙存在对宏观响应影响,给出了含有不同分布与形状、位置空隙的功能梯度板件的力学量三维分布形态,实现功能梯度材料结构宏、细观间跨尺度分析.     

功能梯度矩形板的三维弹性分析

将功能梯度三维矩形板的位移变量按双三角级数展开，以弹性力学的平衡方程为基础．导出位移形式的平衡方程。引入状态空间方法，以三个位移分量及位移分量的一阶导数为状态变量，建立状态方程。考虑四边简支的边界条件，由状态方程得到了功能梯度三维矩形板的静力弯曲问题和自由振动问题的精确解。由给出的均匀矩形板自由振动问题的计算结果表明．与已有的理论解以及有限元方法的计算结果相吻合。假设功能梯度三维矩形板的材料常数沿板的厚度方向按照指数函数的规律变化．进一步给出了功能梯度三维矩形板的自由振动问题和静力弯曲问题的算例分析，并讨论了材料性质的梯度变化对板的动力响应和静力响应的影响。     

压电功能梯度板自由振动的三维解

基于三维弹性理论和压电理论,导出了有限长矩形压电功能梯度板的动力学方程及相应的边界条件,并用幂级数展开法进行了求解.得到了压电功能梯度板自由振动的三维精确解公式,求解了自由振动的固有频率,并分析了压电系数的梯度变化对不同电学边界条件下压电板的自由振动频率的影响.结果可用于校核不同的近似理论及理解压电结构的动态行为.     

基于Haar小波方法的功能梯度材料矩形板三维力学分析

利用Haar小波方法对任意材料梯度分布的四边简支功能梯度材料矩形板进行了三维力学分析.由于小波方法在求解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.通过算例得到了矩形板在机械荷载作用下,平板上下表面材料性质差异以及材料不同梯度形式对其结构响应的影响.     

Postbuckling of FGM plates with piezoelectric actuators under thermo-electro-mechanical loadings

A postbuckling analysis is presented for a simply supported, shear deformable functionally graded plate with piezoelectric actuators subjected to the combined action of mechanical, electrical and thermal loads. The temperature field considered is assumed to be of uniform distribution over the plate surface and through the plate thickness and the electric field considered only has non-zero-valued component E_Z. The material properties of functionally graded materials (FGMs) are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and the material properties of both FGM and piezoelectric layers are assumed to be temperature-dependent. The governing equations are based on a higher order shear deformation plate theory that includes thermo-piezoelectric effects. The initial geometric imperfection of the plate is taken into account. Two cases of the in-plane boundary conditions are considered. A two step perturbation technique is employed to determine buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, geometrically mid-plane symmetric FGM plates with fully covered or embedded piezoelectric actuators under different sets of thermal and electric loading conditions. The effects played by temperature rise, volume fraction distribution, applied voltage, the character of in-plane boundary conditions, as well as initial geometric imperfections are studied.     

A finite element study on the large amplitude flexural vibration characteristics of FGM plates under aerodynamic load

The large amplitude flexural vibration characteristics of functionally graded material (FGM) plates are investigated here using a shear flexible finite element approach. Material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of the constituents. The effective material properties are then evaluated based on the rule of mixture. The FGM plate is modeled using the first-order shear deformation theory based on exact neutral surface position and von Kármán’s assumptions for large displacement. The third-order piston theory is employed to evaluate the aerodynamic pressure. The governing equations of motion are solved by harmonic balance method to study the vibration amplitude of FGM plates under supersonic air flow. Thereafter, the non-linear equations of motion are solved using Newmark’s time integration technique to understand the flexural vibration behavior of FGM plates in time domain (simple harmonic or periodic or quasi-periodic). This work is new in the sense that it deals with the non-linear flutter characteristics of FGM plates under high supersonic airflow accounting for both the geometric and aerodynamic non-linearities. Some parametric study is conducted to understand the influence of these non-linearities on the flutter characteristics of FGM plates.     

Thermal buckling and postbuckling of FGM circular plates with in-plane elastic restraints

Based on von Karman's plate theory, the axisymmetric thermal buckling and post-buckling of the functionally graded material(FGM) circular plates with inplane elastic restraints under transversely non-uniform temperature rise are studied. The properties of the FGM media are varied through the thickness based on a simple power law. The governing equations are numerically solved by a shooting method. The results of the critical buckling temperature, post-buckling equilibrium paths, and configurations for the in-plane elastically restrained plates are presented. The effects of the in-plane elastic restraints, material property gradient, and temperature variation on the responses of thermal buckling and post-buckling are examined in detail.     

Nonlinear bending analysis of FGM rectangular plates with various supported boundaries resting on two-parameter elastic foundations

In this paper, model of the FGM plates resting on two-parameter elastic foundations is put forward by using on physical neutral surface and high-order shear deformation theory. Material properties are assumed to be temperature dependent and vary along the thickness, while Poisson’s ratio depends weakly on temperature change and position and is assumed to be a constant. It is worth noting that physical neutral surface will be changed with temperature. The character of physical neutral surface higher-order shear deformation plate theory is that the displacements have special forms, stretching-bending couplings are eliminated in constitutive equations, and governing equations have the simple and similar forms as homogeneous isotropic plates. The validity of physical neutral surface higher-order shear deformation plate theory can be confirmed by comparing with related researchers’ results. Nonlinear bending approximate solutions of FGM rectangular plates with six cases of boundary conditions are given out using Ritz method, and influences played by different supported boundaries, foundation stiffnesses, thermal environmental conditions, and volume fraction index are discussed in detail.     

Influence of corner stresses on the stability characteristics of composite skew plates

Stability characteristics of composite skew plates subjected to in-plane compressive load are investigated here using the shear deformable finite element approach. The influences of high prebuckling stresses at the corner regions of isotropic and composite skew plates on their stability characteristics are emphasized for different load direction, boundary condition and laminate stacking sequence. The non-linear governing equations based on von Kármán's assumptions are solved by Newton-Raphson technique to get the hitherto unreported postbuckling equilibrium paths of composite skew plates loaded between two rigid flat platens. The variation of out-of-plane deformation and end-shortening with compressive in-plane load are examined for simply supported and clamped skew plates made of isotropic, symmetric and unsymmetric laminates. Marguerre's shallow shell theory is employed to study the effect of sinusoidal imperfection on the non-linear behavior of composite skew plates.     

微细三角柱流固耦合动态特性的三维数值研究

在三维双向流固耦合计算基础上使用动网格方法,通过求解不可压缩粘性流体的N-S方程,数值研究了低速流速下(2.5m/s~15m/s)气体绕流微细三角钝体的耦合动态特性及涡激振动特性,得到了运动微细三角柱的升力系数、涡脱频率和振动振幅。观测到了微细三角柱的"锁振"和"拍"现象。接着计算了相同流场条件下的相同尺寸二维三角柱双向流固耦合涡激振动,并将结果与文献及本文中三维模型进行对比发现,三维模型的升力系数的平均幅值、涡脱频率和斯特劳哈尔数较之本文及文献中的二维数值模型较小。     

Influence of rotatory inertia on dynamic stability of the viscoelastic symmetric cross-ply laminated plates

The dynamic stability problem of the symmetrically laminated cross-ply plates made of the viscoelastic Voigt–Kelvin material, compressed by time-dependent stochastic membrane forces, is investigated. The effect of rotatory inertia is included in the present formulation. It is assumed that all elastic moduli have the same retardation times. By using the direct Liapunov method, bounds of the almost sure stability of cross-ply plates as a function of viscous damping coefficient, retardation time, variances of the stochastic forces, ratio of the principal lamina stiffnesses, number of layers, plate aspect ratio, cross-ply ratio and intensity of the deterministic components of axial loading are obtained. Numerical calculations are performed for the Gaussian process with a zero mean, as well as an harmonic process with random phase.     

Closed-form solutions for free vibration of rectangular FGM thin plates resting on elastic foundation

This article presents closed-form solutions for the frequency analysis of rectangular functionally graded material(FGM) thin plates subjected to initially in-plane loads and with an elastic foundation. Based on classical thin plate theory, the governing differential equations are derived using Hamilton's principle. A neutral surface is used to eliminate stretching–bending coupling in FGM plates on the basis of the assumption of constant Poisson's ratio. The resulting governing equation of FGM thin plates has the same form as homogeneous thin plates. The separation-ofvariables method is adopted to obtain solutions for the free vibration problems of rectangular FGM thin plates with separable boundary conditions, including, for example, clamped plates. The obtained normal modes and frequencies are in elegant closed forms, and present formulations and solutions are validated by comparing present results with those in the literature and finite element method results obtained by the authors. A parameter study reveals the effects of the power law index n and aspect ratio a/b on frequencies.