功能梯度碳纳米管增强复合材料结构建模与分析研究进展

功能梯度碳纳米管增强复合材料是一种新一代的先进复合材料.在这种材料中,碳纳米管作为增强体在空间位置上梯度排布.功能梯度碳纳米管增强复合材料的力学行为已成为近年来材料科学与工程科学的研究热点.本文对功能梯度碳纳米管增强复合材料结构的建模与分析的研究进展进行评述,集中讨论功能梯度碳纳米管增强复合材料梁、板、壳在各种载荷条件下,边界条件下和环境条件下的线性和非线性弯曲、屈曲和后屈曲、振动和动力响应.文中所列成果可以看作是进一步研究的基石.最后,提出需要进一步研究的方向.     

Modeling and analysis of functionally graded carbon nanotube reinforced composite structures: A review

功能梯度碳纳米管增强复合材料是一种新一代的先进复合材料.在这种材料中,碳纳米管作为增强体在空间位置上梯度排布.功能梯度碳纳米管增强复合材料的力学行为已成为近年来材料科学与工程科学的研究热点.本文对功能梯度碳纳米管增强复合材料结构的建模与分析的研究进展进行评述,集中讨论功能梯度碳纳米管增强复合材料梁、板、壳在各种载荷条件下,边界条件下和环境条件下的线性和非线性弯曲、屈曲和后屈曲、振动和动力响应.文中所列成果可以看作是进一步研究的基石.最后,提出需要进一步研究的方向.     

功能梯度碳纳米管增强复合材料结构建模与分析研究进展

功能梯度碳纳米管增强复合材料是一种新一代的先进复合材料。在这种材料中，碳纳米管作为增强体在空间位置上梯度排布。功能梯度碳纳米管增强复合材料的力学行为已成为近年来材料科学与工程科学的研究热点。本文对功能梯度碳纳米管增强复合材料结构的建模与分析的研究进展进行评述，集中讨论功能梯度碳纳米管增强复合材料梁、板、壳在各种载荷条件下，边界条件下和环境条件下的线性和非线性弯曲、屈曲和后屈曲、振动和动力响应。文中所列成果可以看作是进一步研究的基石。最后，提出需要进一步研究的方向。     

Hamilton体系下功能梯度梁的热冲击动力屈曲分析

在Hamilton体系下，基于Euler梁理论研究了功能梯度材料梁受热冲击载荷作用时的动力屈曲问题；将非均匀功能梯度复合材料的物性参数假设为厚度坐标的幂函数形式，采用Laplace变换法和幂级数法解析求得热冲击下功能梯度梁内的动态温度场:首先将功能梯度梁的屈曲问题归结为辛空间中系统的零本征值问题，梁的屈曲载荷与屈曲模态分别对应于Hamilton体系下的辛本征值和本征解问题，由分叉条件求得屈曲模态和屈曲热轴力，根据屈曲热轴力求解临界屈曲升温载荷。给出了热冲击载荷作用下一类非均匀梯度材料梁屈曲特性的辛方法研究过程，讨论了材料的梯度特性、结构几何参数和热冲击载荷参数对临界温度的影响。     

夹层FGM圆柱壳在扭转载荷作用下的弹性稳定性

采用半解析方法研究了两端简支的功能梯度夹层圆柱壳在端部扭转载荷作用下的弹性稳定性.考虑圆柱壳的里外表层为均匀材料,中间层为材料性质沿厚度方向连续变化的功能梯度材料,并且在界面处的材料性质保持连续.基于Flügge薄壳理论,建立了位移形式的结构静态屈曲控制方程.根据边界条件将位移表示为三角级数形式,获得包含柱壳端部扭转载荷参数的近似线性代数特征值问题,并通过数值方法求得了表征结构失稳特征的临界载荷.数值结果表明,临界载荷随着半径与厚度比的增加而减小,随着功能梯度中间层的弹性模量的平均值的增加而增加.     

热环境下功能梯度夹层双曲壳自由振动分析

功能梯度夹层双曲壳结构广泛应用在航空航天、海洋工程等领域中,对于该类结构的动力学特性研究非常重要.论文以热环境下功能梯度夹层双曲壳为研究对象,在三阶剪切变形理论的基础上,考虑横向拉伸作用的影响提出了一种新的位移场,假设材料的物性参数与温度有关,且沿厚度方向表示为幂律函数.利用Hamilton原理得到简支边界条件下功能梯度夹层双曲壳三维振动系统动力学方程,利用Navier法求得两种不同夹层类型的系统固有频率.研究了几何物理参数和温度场对功能梯度夹层双曲壳自由振动固有频率的影响.     

一种特殊梯度分布的功能梯度圆柱壳的二维分析

功能梯度材料是一种新型材料,其结构分析已成为当今力学研究的热点。本文对一种特殊梯度分布的功能梯度材料圆柱壳进行了二维精确分析。从弹性力学平面应变问题的基本方程出发,引入应力函数,导出功能梯度材料圆柱壳受静载作用下的控制微分方程。假设材料的杨氏模量沿半径方向呈幂函数分布,泊松比为常数,利用分离变量法,导出了简支边界情况下功能梯度圆柱壳的精确解。通过算例分析了不同梯度变化时,功能梯度圆柱壳内的应力和位移变化规律。计算结果表明不同梯度分布的圆柱壳结构中的应力、位移沿厚度方向的变化规律是不同的,有时甚至差别很大。因此对于材料性质梯度变化的功能梯度材料圆柱壳,必须针对其自身特点,建立相应的理论分析模型。     

热过屈曲功能梯度壁板的气动弹性颤振

功能梯度材料的宏观物理性能随空间位置连续变化,能充分减少不同组份材料结合部位界面性能的不匹配因素.功能梯度壁板用作高速飞行器的热防护结构,能有效消除气动加热带来的壁板内部热应力集中.本文考虑热过屈曲变形引入的结构几何非线性,分析功能梯度壁板的气动弹性颤振边界.基于幂函数材料分布假设,采用混合定律计算功能梯度材料的等效力学性能.根据一阶剪切变形板理论、冯·卡门应变-位移关系和一阶活塞理论,基于虚功原理建立超声速气流中受热功能梯度壁板的非线性气动弹性有限元方程.采用牛顿-拉弗森迭代法数值求解壁板的热屈曲变形,分析超声速气流对热屈曲变形的影响机理.在壁板热过屈曲的静力平衡位置分析动态稳定性,确定了壁板的颤振边界.研究表明,当陶瓷-金属功能梯度壁板的组份材料沿厚度方向梯度分布时,会破坏结构的对称性导致壁板在面内热应力作用下发生指向金属侧的热屈曲变形.超声速气流中壁板热屈曲变形最大的位置随气流速压增大向下游推移,并伴随屈曲变形量的减小.热过屈曲壁板的几何非线性效应会提高壁板的颤振边界,这种影响在高温、低无量纲速压且壁板发生大挠度热屈曲变形时表现显著.较高无量纲气流速压下由于壁板的热屈曲变形被气动力限定在小挠度范围,几何非线性效应不明显.     

功能梯度材料与结构的若干力学问题研究进展

功能梯度材料的宏观材料特性在空间上是连续变化的,因此即使在线弹性理论范围内,由于控制偏微分方程是变系数的,相应的力学分析具有很大的挑战性.综述了功能梯度材料与结构若干力学问题的最新研究进展,包括功能梯度材料梁、板、壳结构的解析解与半解析解以及简化理论的研究、功能梯度材料结构的数值计算方法研究、功能梯度材料的断裂力学研究.最后对未来功能梯度材料与结构的力学研究进行了展望.     

热环境下功能梯度夹层双曲壳三维自由振动分析

功能梯度夹层双曲壳结构广泛应用在航空航天、海洋工程等领域中，对于该类结构的动力学特性研究非常重要。本文以热环境下功能梯度夹层双曲壳为研究对象，在三阶剪切变形理论的基础上，考虑横向拉伸作用的影响提出了一种新的位移场，假设材料的物性参数与温度有关，且沿厚度方向表示为幂律函数。利用Hamilton原理得到简支边界条件下功能梯度夹层双曲壳三维振动系统动力学方程，利用Navier法求得两种不同夹层类型的系统固有频率。研究了几何物理参数和温度场对功能梯度夹层双曲壳自由振动固有频率的影响。     

Nonlinear axisymmetric thermomechanical response of piezo-FGM shallow spherical shells

Thermomechanical instability of shallow spherical shells made of functionally graded material (FGM) and surface-bonded piezoelectric actuators is studied in this paper. The governing equations are based on the classical shell theory of shells and the Sanders nonlinear kinematics equations. It is assumed that the property of the FGMs varies continuously through the thickness of the shell according to a power law distribution of the volume fraction of the constituent materials. The constituent materials of the functionally graded shell are assumed to be mixture of ceramic and metal. The analytical solutions are obtained for uniform external pressure, thermal loading, and constant applied actuator voltage.     

Torsional buckling and postbuckling of FGM cylindrical shells in thermal environments

A postbuckling analysis is presented for a functionally graded cylindrical shell subjected to torsion in thermal environments. Heat conduction and temperature-dependent material properties are both taken into account. The temperature field considered is assumed to be a uniform distribution over the shell surface and varied in the thickness direction. 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 are assumed to be temperature-dependent. The governing equations are based on a higher order shear deformation theory with a von Kármán–Donnell-type of kinematic non-linearity. The non-linear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling load and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of twist, perfect and imperfect, FGM cylindrical shells under different sets of thermal fields. The results reveal that the volume fraction distribution of FGMs has a significant effect on the buckling load and postbuckling behavior of FGM cylindrical shells subjected to torsion. They also confirm that the torsional postbuckling equilibrium path is weakly unstable and the shell structure is virtually imperfection–insensitive.     

Mechanical and thermal postbuckling of FGM thick circular cylindrical shells reinforced by FGM stiffener system using higher-order shear deformation theory

The postbuckling of the eccentrically stiffened circular cylindrical shells made of functionally graded materials(FGMs),subjected to the axial compressive load and external uniform pressure and filled inside by the elastic foundations in the thermal environments,is investigated with an analytical method.The shells are reinforced by FGM stringers and rings.The thermal elements of the shells and stiffeners in the fundamental equations are considered.The equilibrium and nonlinear stability equations in terms of the displacement components for the stiffened shells are derived with the third-order shear deformation theory and Leckhniskii smeared stiffener technique.The closed-form expressions for determining the buckling load and postbuckling load-deflection curves are obtained with the Galerkin method.The effects of the stiffeners,the foundations,the material and dimensional parameters,and the pre-existent axial compressive and thermal load are considered.     

Postbuckling of internal pressure loaded FGM cylindrical shells surrounded by an elastic medium

This paper presents a study on the postbuckling response of a functionally graded cylindrical shell of finite length embedded in a large outer elastic medium and subjected to internal pressure in thermal environments. The surrounding elastic medium is modeled as a tensionless Pasternak foundation that reacts in compression only. The postbuckling analysis is based on a higher order shear deformation shell theory with von Kármán–Donnell-type of kinematic nonlinearity. The thermal effects due to heat conduction are also included and the material properties of functionally graded materials (FGMs) are assumed to be temperature-dependent. The nonlinear prebuckling deformations and the initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the postbuckling response of the shells and an iterative scheme is developed to obtain numerical results without using any assumption on the shape of the contact region between the shell and the elastic medium. Numerical solutions are presented in tabular and graphical forms to study the postbuckling behavior of FGM shells surrounded by an elastic medium of tensionless elastic foundation of the Pasternak-type, from which results for conventional elastic foundations are obtained as comparators. The results reveal that the unilateral constraint has a significant effect on the postbuckling response of shells subjected to internal pressure in thermal environments when the foundation stiffness is sufficiently large.     

Second-order homogenisation of functionally graded materials

The homogenisation theory for periodic composites is generalised to the case of quasi-periodic composites. In quasi-periodic composites, the unit cell does not repeat throughout the medium but gradually changes along one or more directions of periodicity (grading directions). Quasi-periodic composites are thus to functionally graded materials (FGMs) what periodic composites are to statistically uniform composite materials. Contrarily to most of the homogenisation methods applied to FGMs, the proposed second-order homogenisation theory takes explicitly into account the grading at the micro-level. The derived equivalent material happens to be a particular second gradient material in which few components of the strain gradient (second gradient of the displacement) should be taken into account in addition to the classical strains (first gradient of displacement). The second gradient theory therefore appears as the natural framework to appropriately handle functionally graded materials at the macro-level. It is worth mentioning that the presented second-order homogenisation procedure is somehow analogous to the one developed for periodic composite materials submitted to rapidly varying macroscopic strain fields as in regions of high gradients. In fact, both are a generalisation of the first-order homogenisation theory for periodic media and lead to a second gradient equivalent material. However, besides their different domains of application, they exhibit further substantial differences, which are highlighted in the paper.     

Thermoviscoelastic deformations of functionally graded thin plates

By considering the influence of the mid-plane strains due to the inhomogeneous property of FGMs across the thickness, a constitutive equation of thermoviscoelastic functionally graded thin plates is reduced on the basis of the Kirchhoff's hypothesis for the classical plate theory. The corresponding simplified Gurtin's type variational principle of functionally graded thin plates is presented by means of the modern convolution bilinear forms. By using the Navier analytic method or combining the Ritz method in the spatial domain and the Legendre interpolation method in the temporal domain, the static thermoelastic deformations or quasi-static thermoviscoelastic deformations of functionally graded thin plates under mechanical or thermal loads are studied.     

Dynamic curving cracks in functionally graded materials under thermo-mechanical loading

Mixed-mode dynamic crack growth along an arbitrarily smoothly varying path in functionally graded materials (FGMs) under thermo-mechanical loading is studied. The property gradation in FGMs is considered by varying shear-modulus, mass density, thermal conductivity and coefficient of thermal expansion exponentially along the gradation direction. Asymptotic analysis in conjunction with displacement potentials is used to develop the stress fields around propagating cracks in FGMs. Asymptotic temperature fields are developed first for the exponential variation of thermal conductivity and later these temperature fields are used to derive thermo-mechanical stress fields for a curving crack in FGMs. Using these thermo-mechanical stress fields, various components of the stresses are developed and the effect of curvature parameters, temperature and gradation on these stresses are discussed. Finally, using the minimum strain energy density criterion, the effect of curvature parameters, crack-tip speeds, non-homogeneity values and temperature gradients on crack growth directions are determined and discussed.     

Non-linear buckling behavior of FGM truncated conical shells subjected to axial load

In this study, the non-linear buckling behavior of truncated conical shells made of functionally graded materials (FGMs), subject to a uniform axial compressive load, has been investigated using the large deformation theory with von the Karman-Donnell-type of kinematic non-linearity. The material properties of functionally graded shells are assumed to vary continuously through the thickness of the shell. The variation of properties followed an arbitrary distribution in terms of the volume fractions of the constituents. The fundamental relations, the modified Donnell type non-linear stability and compatibility equations of functionally graded truncated conical shells are obtained and are solved by superposition and Galerkin methods and the upper and lower critical axial loads have been found analytically. Finally, the influences of the compositional profile variations and the variation of the shell geometry on the upper and lower critical axial loads are investigated. Comparing the results of this study with those in the literature validates the present analysis.     

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.