面内预应力功能梯度材料矩形板的横向弯曲

功能梯度材料（FGM)是一类具有广阔应用前景的新型复合材料。本文考虑材料物性参数随坐标和温度变化的特性，研究横向荷载和面内预加荷载作用下FGM矩形板在各种边界条件下的弯曲问题。给出了基于一维微分求积格式的Galerkin技术的半解析方法，并以ZrO2/Ti-6Al-4V板为例考察了材料组分，温度相关性，面内预加荷载，边界约束条件等对FGM板弯曲行为的影响。结果表明，FGM板的弯曲变形介于各向同性陶瓷板与各向同性金属板之间，且随板抗弯刚度的增大而逐步减小，在高温下条件下必须考虑材料物性和温度的相关性。     

功能梯度材料扁锥壳的热弹性大变形分析

研究了功能梯度材料扁薄锥壳在横向非均匀升温场中的几何非线性大变形问题.基于von Kármán几何非线性理论推导出了以中面位移为基本未知量的功能梯度扁薄锥壳在横向非均匀热载荷作用下的轴对称大挠度控制方程.采用打靶法数值求解所得非线性常微分方程边值问题,得到了锥壳的大挠度弯曲变形数值解.给出了锥壳的变形与其形状参数、载荷和材料参数等变化的特征关系曲线,分析和讨论了温度参数和材料梯度变化参数对变形的影响.     

纵横载荷作用下功能梯度梁的弯曲和过屈曲

基于一阶非线性梁理论和物理中面概念,导出了纵横向载荷作用下功能梯度材料(FGM)梁非线性弯曲和过屈曲问题的控制方程,并获得了该问题的精确解;据此解研究了梯度材料性质、外载荷、横向剪切变形以及边界条件等因素对功能梯度材料梁非线性力学行为的影响,分析中假设功能梯度材料性质只沿梁厚度方向,并按成分含量的幂指数函数形式变化。结果表明:纵横载荷共同作用下,功能梯度梁的弯曲构形将有无限多个;随着梯度指数的增大,梁的变形减小,临界载荷升高;随着长高比的增大,横向剪切变形的影响减小。     

径向弹性约束下功能梯度圆板的热过屈曲

研究了周边具有面内径向弹性约束功能梯度圆板在横向非均匀升温下的热过屈曲行为.基于von Karman薄板理论,推导出了横向非均匀加热功能梯度圆板在径向弹性约束作用下的位移形式的轴对称热过屈曲控制方程.假设功能梯度材料性质沿厚度方向按幂函数连续变化,采用打靶法求解得到非线性常微分方程边值问题,获得了周边简支和夹紧条件下功能梯度圆板的热过屈曲响应.定量分析了径向弹性约束对圆板的临界屈曲温度载荷以及热过屈曲变形的影响,给出了不同弹性约束刚度功能梯度圆板的热过屈曲平衡路径和平衡构形.数值结果表明,径向弹性约束对圆板的热过屈曲平衡路径的影响显著,随着约束刚度的减小,临界屈曲温度载荷增大.     

功能梯度中厚圆/环板轴对称弯曲问题的解析解

基于一阶剪切变形板理论，导出了热/机载荷作用下，位移形式的功能梯度 中厚圆/环板轴对称弯曲问题的控制方程，获得了问题的位移和内力的一般解析解. 作为特 例，分别研究了边缘径向固定和可动的夹紧和简支的4种实心功能梯度圆板，给出了它们的 解，并分析了热/机载荷作用下解的形态，讨论了横向剪切变形、材料梯度常数和边界条件， 对板的轴对称弯曲行为的影响.     

考虑横向拉伸影响的FGM夹层板动不稳定性分析

以受多种形式面内载荷作用下的功能梯度夹层矩形板为研究对象,夹层板的功能梯度层组分材料沿厚度方向按幂律分布,考虑组分材料物性参数的温度相关性。研究中所用的位移场在Reddy高阶剪切变形理论基础上考虑了横向拉伸的影响。利用能量原理和Galerkin法得到四边简支功能梯度材料夹层矩形板的动力学模型。运用Bolotin法求得了系统的动不稳定区域。对比结果表明考虑横向拉伸影响时与文献中的对比更接近,并详细研究了几何物理参数、环境温度以及不同分布形式的面内外载荷对系统动不稳定区域的影响,结果表明:随着金属体积分数指数、长宽比、静态载荷参数、载荷比的增加,系统参数激励动不稳定区域的宽度增加;随着温差、长厚比、面内载荷分布系数的增加,系统参数激励动不稳定区域的宽度减小。     

功能梯度与均匀圆板弯曲解的线性转换关系

基于一阶剪切理论, 研究了功能梯度材料圆板与均匀圆板轴对称弯曲解之间 的线性转换关系. 通过理论分析和比较 功能梯度材料圆板和均匀圆板在一阶剪切理论下的位 移形式的轴对称弯曲控制方程, 发现了功能梯度材料圆板的转角与均匀圆板的转角之间 的相似转换关系. 在假设材料性质沿板厚连续变化的情况下, 给出了相似转换系数的解析表 达式. 在此基础上, 进一步导出了一阶剪切理论下功能梯度圆板的挠度与经典理论 下, 均匀圆板的挠度之间的线性关系. 从而, 可将功能梯度材料圆板在一阶剪切理 论下的弯曲问题求解, 转化为相应均匀薄圆板在经典理论下的弯曲问题求解, 以及 转换系数的计算问题. 这一方法为功能梯度非均匀中厚度圆板的求解提供了简捷途 径, 而且更便于工程应用. 作为例子, 采用上述方法分别求得了周边简支和夹紧条 件下, 梯度圆板在均布横向载荷作用下的弯曲解析解, 该解答与Reddy得到的结果 完全吻合.     

功能梯度截顶圆锥壳的热弹性弯曲精确解

研究了功能梯度材料截顶圆锥壳在横向机械载荷与非均匀热载荷同时作用下的变形问题. 基 于经典线性壳体理论推导出了以横向剪力和中面转角为基本未知量的功能梯度薄圆锥壳轴对 称变形的混合型控制方程. 假设功能梯度圆锥壳的材料性质为沿厚度方向按照幂函数 连续变化的形式. 然后采用解析方法求解，得到了问题的精确解. 分别就两端简支和两端固 支边界条件，给出了圆锥壳的变形随其载荷、材料参数等变化的特征关系曲线，重点分析和 讨论了载荷参数与材料梯度变化参数对变形的影响.     

热环境中旋转运动功能梯度圆板的强非线性固有振动

研究热环境中旋转运动功能梯度圆板的非线性固有振动问题．针对金属－陶瓷功能梯度圆板，考虑几何非线性、材料物理属性参数随温度变化以及材料组分沿厚度方向按幂律分布的情况，应用哈密顿原理推得热环境中旋转运动功能梯度圆板的非线性振动微分方程．考虑周边夹支边界条件，利用伽辽金法得到了横向非线性固有振动方程，并确定了静载荷引起的静挠度．用改进的多尺度法求解强非线性方程，得出非线性固有频率表达式．通过算例，分析了旋转运动功能梯度圆板固有频率随转速、温度等参量的变化情况．结果表明，非线性固有频率随金属含量的增加而降低；随转速和圆板厚度的增大而升高；随功能梯度圆板表面温度的升高而降低．     

热环境中旋转运动功能梯度圆板的强非线性固有振动

研究热环境中旋转运动功能梯度圆板的非线性固有振动问题．针对金属－陶瓷功能梯度圆板，考虑几何非线性、材料物理属性参数随温度变化以及材料组分沿厚度方向按幂律分布的情况，应用哈密顿原理推得热环境中旋转运动功能梯度圆板的非线性振动微分方程．考虑周边夹支边界条件，利用伽辽金法得到了横向非线性固有振动方程，并确定了静载荷引起的静挠度．用改进的多尺度法求解强非线性方程，得出非线性固有频率表达式．通过算例，分析了旋转运动功能梯度圆板固有频率随转速、温度等参量的变化情况．结果表明，非线性固有频率随金属含量的增加而降低；随转速和圆板厚度的增大而升高；随功能梯度圆板表面温度的升高而降低．     

Postbuckling of piezoelectric FGM plates subject to thermo-electro-mechanical loading

In this paper, we examine the postbuckling behavior of functionally graded material FGM rectangular plates that are integrated with surface-bonded piezoelectric actuators and are subjected to the combined action of uniform temperature change, in-plane forces, and constant applied actuator voltage. A Galerkin-differential quadrature iteration algorithm is proposed for solution of the non-linear partial differential governing equations. To account for the transverse shear strains, the Reddy higher-order shear deformation plate theory is employed. The bifurcation-type thermo-mechanical buckling of fully clamped plates, and the postbuckling behavior of plates with more general boundary conditions subject to various thermo-electro-mechanical loads, are discussed in detail. Parametric studies are also undertaken, and show the effects of applied actuator voltage, in-plane forces, volume fraction exponents, temperature change, and the character of boundary conditions on the buckling and postbuckling characteristics of the plates.     

功能梯度材料矩形中厚板的受压/热致屈曲

考虑材料组份沿板厚度方向按幂律变化的情形,研究了温度均匀变化时固支功能梯度材料(FGM)矩形中厚板的受压屈曲、热致屈曲和考虑热／机械预应力时的屈曲问题,给出了基于Reddy高阶剪切理论研究板屈曲荷载和屈曲临界温度的半解析数值方法．并以Si3N4／SUS304板为例考虑了材料组份、预加应力、横向剪切变形及面内位移约束条件等对FGM板屈曲承载能力的影响．     

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.     

Thermal buckling of functionally graded circular plates based on higher order shear deformation plate theory

In this research, thermal buckling of circular plates compose of functionally graded material (FGM) is considered. Equilibrium and stability equations of a FGM circular plate under thermal loads are derived, based on the higher order shear deformation plate theory (3rd order plate theory). Assuming that the material properties vary as a power form of the thickness coordinate variable z and using the variational method, the system of fundamental partial differential equations is established. A buckling analysis of a functionally graded circular plate (FGCP) under various types of thermal loads is carried out and the result are given in closed-form solutions. The results are compared with the critical buckling temperature obtained for FGCP based on first order (1st order plate theory) and classical plate theory (0 order plate theory) given in the literature. The study concludes that higher order shear deformation theory accurately predicts the behavior of FGCP, whereas the first order and classical plate theory overestimates buckling temperature.     

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.     

Nonlinear stability and dynamics of composite skew plates under nonuniform loadings using differential quadrature method

The buckling, postbuckling and postbuckled vibration behaviour of composite skew plates subjected to nonuniform inplane loadings are presented here. The skew plate is modelled using first order shear deformation theory accounting for von-Kármán geometric nonlinearity and initial geometric imperfections. The different types of nonuniform loads that have been considered in this study are concentrated load, partial load and parabolic load. The explicit analytical expressions for prebuckling stress distributions within composite skew plate subjected to three different types of nonuniform inplane loadings are developed by solving plane elasticity problem using Airy's stress function approach. It is observed that the inplane normal stress distributions within the skew plate due to above nonuniform loadings do not become uniform even at mid-section. The generalized differential quadrature (GDQ) method is used to solve the nonlinear governing partial differential equations. It is observed that the postbuckled load carrying capacity of skew plate under concentrated loading is the lowest compared to other nonuniform and uniform loadings.     

剪切变形对FGM圆板轴对称屈曲的影响

基于一阶剪切变形板理论，推导了功能梯度材料圆形板在边界面内均布压力作用下的轴对称屈曲方程。在推导过程中，忽略了前屈曲耦合变形。利用一阶板理论与经典板理论屈曲方程之间在数学形式上的相似性，得到了一阶板理论下功能梯度材料圆板与经典板理论下均匀圆板临界屈曲载荷之间的解析关系。利用这个解析关系，可以直接从已有的较为简单的经典理论的结果，获得一阶板理论下功能梯度材料板的临界屈曲载荷。