石墨烯增强功能梯度材料板条的热弹性响应

研究了石墨烯增强功能梯度复合材料板条的热弹性问题。基于推广后的Mian和Spencer功能梯度板理论,在板厚度方向上考虑热传导引起的稳态温度场,沿板厚方向考虑了三种石墨烯纳米片的分布形式,最终给出了不同边界条件下石墨烯增强功能梯度板条在温度场作用下的解析解。通过算例分析验证了本文方法的有效性,并讨论了边界条件和石墨烯的分布形式等因素对板条热弹性响应的影响。计算结果表明:石墨烯增强功能梯度材料板条在温度场作用下的热响应与在机械力作用下的弹性响应有较大不同。     

轴对称自由振动功能梯度材料微圆板中的热弹性阻尼

基于经典弹性薄板理论和单向耦合热传导理论,研究了材料性质沿厚度连续变化的功能梯度微圆板的热弹性阻尼特性．首先,考虑热力耦合效应,建立了功能梯度微圆板轴对称横向自由振动微分方程．然后,忽略温度梯度在面内的变化,建立了单向耦合变系数一维热传导方程．采用分层均匀化近似方法,将变系数热传导方程转化为一系列常系数的微分方程,利用上下表面的热边界条件和层间连续性条件获得了微圆板温度场解析解．将所得温度场代入微圆板的自由振动微分方程,得到了包含热弹性阻尼的复频率,从而获得了反映热弹性阻尼水平的逆品质因子．最后,针对材料性质沿板厚按幂函数变化的陶瓷-金属功能梯度微圆板,定量地分析材料梯度指数、几何尺寸、边界条件、温度环境等对微圆板热弹性阻尼的影响．     

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.     

功能梯度材料明德林矩形微板的热弹性阻尼

功能梯度材料微板谐振器热弹性阻尼的建模和预测是此类新型谐振器热?弹耦合振动响应的新课题. 本文采用数学分析方法研究了四边简支功能梯度材料中厚度矩形微板的热弹性阻尼. 基于明德林中厚板理论和单向耦合热传导理论建立了材料性质沿着厚度连续变化的功能梯度微板热弹性自由振动控制微分方程. 在上下表面绝热边界条件下采用分层均匀化方法求解变系数热传导方程, 获得了用变形几何量表示的变温场的解析解. 从而将包含热弯曲内力的结构振动方程转化为只包含挠度振幅的偏微分方程. 然后,利用特征值问题在数学上的相似性,求得了四边简支条件下功能梯度材料明德林矩形微板的复频率解析解, 进而利用复频率法获得了反映谐振器热弹性阻尼水平的逆品质因子. 最后, 给出了材料性质沿板厚按幂函数变化的陶瓷?金属组分功能梯度矩形微板的热弹性阻尼数值结果. 定量地分析了横向剪切变形、材料梯度变化以及几何参数对热弹性阻尼的影响规律. 结果表明, 采用明德林板理论预测的热弹性阻尼值小于基尔霍夫板理论的预测结果, 而且两者的差别随着相对厚度的增大而变得显著.      

功能梯度旋转圆板的热弹性固有振动

在考虑热因素及旋转运动条件下,针对金属－陶瓷功能梯度圆板的固有振动问题进行研究．给出随温度变化且材料组分沿厚度方向按幂律分布的材料物性参数,依据热弹性理论得到圆板的能量关系式．基于哈密顿原理建立旋转金属－陶瓷功能梯度圆板热弹性动力学方程．采用伽辽金法得到边界约束下圆板的自由振动方程,确定了静挠度及固有振动频率．基于数值计算,得到系统固有频率值随体积分数指数、转速和温度等参量的变化曲线,讨论了静挠度变化规律及动力系统的奇点稳定性问题．结果表明,固有频率随体积分数指数、材料表面温度以及转速的增加而减小．     

功能梯度平板的二维热弹性分析

本文研究正交各向异性功能梯度平板的二维热弹性问题.该平板在y方向无限长,x方向对边简支且温度恒定.从热弹性力学的基本方程出发,假设材料参数沿板厚方向(z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荷载和热荷 载的情况下,获得了功能梯度平板二维热弹性问题的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不同的幂函数分布对平板响应的影响.     

基于混合数值法的功能梯度材料板瞬态热响应分析

采用混合数值法分析了功能梯度材料板中瞬态热响应问题．功能梯度材料板的材料特性沿板厚方向连续变化,在梯度板中心作用温度变化的热源,此热源沿板厚方向连续分布．得出了温度变化对梯度板的影响,观测点处的位移响应与应力变化随时间分布的曲线以及瞬态的位移响应．研究表明,温度变化对板的作用效果与外载作用对板的作用效果是相当的．此研究是对混合数值法的在热领域应用的延伸与开拓,对热响应问题的研究具有一定的指导意义．     

功能梯度热释电材料矩形板的三维精确分析

对四边简支、接地、等温的功能梯度热释电材料矩形板进行精确三维分析．根据正交各向异性热释电材料基本方程，导出了功能梯度热释电材料的状态方程．假定材料的机械、电学和热学性质沿板厚方向按统一的指数函数形式梯度分布，获得了四边简支、接地和等温的矩形板，在上下表面作用任意的机械荷载、电荷载和热荷载情况下的三维精确解．通过算例，分析了在机械荷载、电荷载和热荷载分别作用下，材料性质的不同梯度变化对平板结构响应的影响．所获得的精确结果可作为评价其他近似方法的标准解答或者作为建立简化的功能梯度热释电材料平板理论的基础。     

正交各向异性厚层压板的热弹性响应分析

对受温度场作用的正交各向异性厚层压板建立了单层的热弹性状态方程，运用现代控制理论传递求解得到温度场作用的层压板的精确热弹性响应。对典型的受沿面内正弦分布沿厚度方向线性分布的温度场作用的四边简支矩形板的精确热弹性响应进行了详细分析和求解，与国内外相关理论结果比较，令人满意。     

热载荷作用下对称S型功能梯度圆板的非线性力学行为

本文研究了热环境中陶瓷-金属-陶瓷功能梯度圆板（S-FGM）的过屈曲和弯曲行为。圆板材料组分的体积分数符合Sigmoid定律,并承受沿圆板厚度方向变化的温度场作用。基于经典板理论,用能量法导出了对称S-FGM圆板静态问题的非线性平衡方程。用打靶法对所得方程进行了数值求解,并利用数值结果研究了不同边界条件、材料的组分、热载荷等因素对对称S-FGM圆板力学行为的影响。数值结果表明：对称S-FGM圆板相较于普通FGM圆板,其力学行为存在一些不同之处,且板的上下表面温升比对S型功能梯度圆板的力学行为有着显著的影响。     

3D thermally induced analysis of annular plates of functionally graded materials

Within the framework of three-dimensional elasticity theory, this paper investigates the thermal response of functionally graded annular plates in which the material can be transversely isotropic and vary along the thickness direction in an arbitrary manner. The generalized Mian and Spencer method is utilized to obtain the analytical solutions of annular plates under a through-thickness steady temperature field. The present analytical solutions are validated through comparisons against those available in open literature. A parametric study is conducted to examine the effects of gradient distribution, different temperature fields, different diameter ratio and boundary conditions on the deformation and stress fields of the plate. The results show that these factors can have obvious effects on the thermo-elastic behavior of functionally gradient materials(FGM)annular plates.     

Elasticity solutions for functionally graded plates in cylindrical bending

The plate theory of functionally graded materials suggested by Mian and Spencer is extended to analyze the cylindrical bending problem of a functionally graded rectangular plate subject to uniform load. The expansion formula for displacements is adopted. While keeping the assumption that the material parameters can vary along the thickness direction in an arbitrary fashion, this paper considers orthotropic materials rather than isotropic materials. In addition, the traction-free condition on the top surface is replaced with the condition of uniform load applied on the top surface. The plate theory for the particular case Of cylindrical bending is presented by considering an infinite extent in the y-direction. Effects of boundary conditions and material inhomogeneity on the static response of functionally graded plates are investigated through a numerical example.     

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.     

Thermal buckling of imperfect functionally graded plates

Thermal buckling analysis of rectangular functionally graded plates (FGPs) with geometrical imperfections is presented in this paper. The equilibrium, stability, and compatibility equations of an imperfect functionally graded plate are derived using the classical plate theory. It is assumed that the nonhomogeneous mechanical properties of the plate, graded through thickness, are described by a power function of the thickness variable. The plate is assumed to be under three types of thermal loading as uniform temperature rise, nonlinear temperature rise through the thickness, and axial temperature rise. Resulting equations are employed to obtain the closed-form solutions for the critical buckling temperature change of an imperfect FGP. The results are reduced and compared with the results of perfect functionally graded and imperfect isotropic plates.     

弹性地基加肋功能梯度板自由振动分析的无网格法

基于一阶剪切变形理论和移动最小二乘近似研究Winkler弹性地基上加肋功能梯度板的固有频率。假设功能梯度板的材料性质沿厚度方向按幂函数连续变化,基于物理中面和移动最小二乘近似分别推导功能梯度板和肋条的动能和势能,再通过引入位移协调条件,建立板和肋条节点参数转换关系,叠加两者的总能量,然后利用Hamilton原理推导加肋功能梯度板自由振动控制方程。采用完全转换法施加边界条件。通过将本文的计算结果与有限元以及文献的结果对比,验证方法的收敛性以及准确性。     

The transient piezothermoelastic problem of a thick functionally graded thermopiezoelectric strip due to nonuniform heat supply

This paper is concerned with the theoretical treatment of the transient piezothermoelastic problem involving a thick functionally graded thermopiezoelectric strip due to nonuniform heat supply in the width direction. The thermal, thermoelastic and piezoelectric constants of the strip are assumed to vary exponentially in the thickness direction. The transient two-dimensional temperature is analyzed by the methods of Laplace and finite sine transformations. We obtain the exact solution for a simply supported strip under the state of plane strain. Some numerical results for the temperature change, the displacement, the stress and electric potential distributions are presented in figures and table. Furthermore, the influence of the nonhomogeneity of the material and that of the electric boundary conditions are investigated.     

Mode III fracture problem of an arbitrarily oriented crack in an FGPM strip bonded to a homogeneous piezoelectric half plane

This paper studies the Mode III electric-elastic field of a cracked functionally graded piezoelectric strip bonded to a homogeneous piezoelectric half plane. The crack is oriented in arbitrary direction. The material properties of the strip vary along the strip thickness in exponential forms. By using the Fourier transform, the problem can be formulated to a system of singular integral equations and solved by applying the Gauss-Chebyshev integration formula. The effects come from the edge, crack orientations and the nonhomogeneous material parameter on intensity factors are discussed graphically.     

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.     

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.     

Static analysis for functionally graded piezoelectric actuators or sensors under a combined electro-thermal load

Based on the theory of piezoelasticity, a functionally graded piezoelectric sandwich cantilever under an applied electric field and/or a heat load is studied. All materials may be arbitrary functional gradients in the thickness direction. The static solution for the mentioned problems is presented by the Airy stress function method. As a special case, assuming that the material composition varies continuously in the direction of the thickness according to a power law distribution, a comprehensive parametric study is conducted to show the influence of electromechanical coupling (EMC), functionally graded index, temperature change and thickness ratio on the bending behavior of actuators or sensors. The distribution of electric field or normal stress in present FGPM actuators is continuous along the thickness, which overcomes the problem in traditional layered actuators. The solution facilitates the design optimization for different piezoelectric actuators and has another potential application for material parameter identification.