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。     

The effect of initial geometric imperfection on the nonlinear resonance of functionally graded carbon nanotube-reinforced composite rectangular plates

The purpose of the present study is to examine the impact of initial geometric imperfection on the nonlinear dynamical characteristics of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) rectangular plates under a harmonic excitation transverse load. The considered plate is assumed to be made of matrix and single-walled carbon nanotubes (SWCNTs). The rule of mixture is employed to calculate the effective material properties of the plate. Within the framework of the parabolic shear deformation plate theory with taking the influence of transverse shear deformation and rotary inertia into account, Hamilton’s principle is utilized to derive the geometrically nonlinear mathematical formulation including the governing equations and corresponding boundary conditions of initially imperfect FG-CNTRC plates. Afterwards, with the aid of an efficient multistep numerical solution methodology, the frequency-amplitude and forcing-amplitude curves of initially imperfect FG-CNTRC rectangular plates with various edge conditions are provided, demonstrating the influence of initial imperfection, geometrical parameters, and edge conditions. It is displayed that an increase in the initial geometric imperfection intensifies the softening-type behavior of system, while no softening behavior can be found in the frequency-amplitude curve of a perfect plate.     

功能梯度碳纳米管增强复合材料板弯曲和模态的广义有限差分法

由复合材料构成的板结构一直以来受到很大关注,其中功能梯度碳纳米管增强复合材料(functionally graded carbon nanotube-reinforced composite,FG-CNTRC)具有异常优越的力学性能,使得诸多学者展开了对功能梯度碳纳米管增强复合材料板结构力学行为的研究.本文以FG-CN...     

Vibration characteristics of piezoelectric functionally graded carbon nanotube-reinforced composite doubly-curved shells

This paper presents an analytical solution for the free vibration behavior of functionally graded carbon nanotube-reinforced composite(FG-CNTRC) doubly curved shallow shells with integrated piezoelectric layers. Here, the linear distribution of electric potential across the thickness of the piezoelectric layer and five different types of carbon nanotube(CNT) distributions through the thickness direction are considered. Based on the four-variable shear deformation refined shell theory, governing equations are obtained by applying Hamilton's principle. Navier's solution for the shell panels with the simply supported boundary condition at all four edges is derived. Several numerical examples validate the accuracy of the presented solution. New parametric studies regarding the effects of different material properties, shell geometric parameters, and electrical boundary conditions on the free vibration responses of the hybrid panels are investigated and discussed in detail.     

Nonlinear in-plane thermal buckling of rotationally restrained functionally graded carbon nanotube reinforced composite shallow arches under uniform radial loading

The nonlinear in-plane instability of functionally graded carbon nanotube reinforced composite (FG-CNTRC) shallow circular arches with rotational constraints subject to a uniform radial load in a thermal environment is investigated. Assuming arches with thickness-graded material properties, four different distribution patterns of carbon nanotubes (CNTs) are considered. The classical arch theory and Donnell’s shallow shell theory assumptions are used to evaluate the arch displacement field, and the analytical solutions of buckling equilibrium equations and buckling loads are obtained by using the principle of virtual work. The critical geometric parameters are introduced to determine the criteria for buckling mode switching. Parametric studies are carried out to demonstrate the effects of temperature variations, material parameters, geometric parameters, and elastic constraints on the stability of the arch. It is found that increasing the volume fraction of CNTs and distributing CNTs away from the neutral axis significantly enhance the bending stiffness of the arch. In addition, the pretension and initial displacement caused by the temperature field have significant effects on the buckling behavior.     

Nonlinear dynamic response of nanotube-reinforced composite plates resting on elastic foundations in thermal environments

This paper presents an investigation on the nonlinear dynamic response of carbon nanotube-reinforced composite (CNTRC) plates resting on elastic foundations in thermal environments. Two configurations, i.e., single-layer CNTRC plate and three-layer plate that is composed of a homogeneous core layer and two CNTRC surface sheets, are considered. The single-walled carbon nanotube (SWCNT) reinforcement is either uniformly distributed (UD) or functionally graded (FG) in the thickness direction. The material properties of FG-CNTRC plates are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The motion equations are based on a higher-order shear deformation theory with a von Kármán-type of kinematic nonlinearity. The thermal effects are also included and the material properties of CNTRCs are assumed to be temperature-dependent. The equations of motion that includes plate-foundation interaction are solved by a two-step perturbation technique. Two cases of the in-plane boundary conditions are considered. Initial stresses caused by thermal loads or in-plane edge loads are introduced. The effects of material property gradient, the volume fraction distribution, the foundation stiffness, the temperature change, the initial stress, and the core-to-face sheet thickness ratio on the dynamic response of CNTRC plates are discussed in detail through a parametric study.     

ANALYSIS OF GROUND VIBRATION CONTROL BY GRADED WAVE IMPEDING BLOCK

波阻板（wave impeding block,WIB）隔振体系是一种有效的振动污染治理措施,虽逐渐被应用在工程实际中,但以往的研究多集中于单相固体均质材料的情形,而对材料特性沿空间连续变化的非均匀固体材料的波阻板隔振性能的研究相对较少.基于功能梯度材料（functionally graded material,FGM）特点,本文提出了以功能梯度波阻板作为隔振屏障的一类新型的地基振动控制体系.考虑在弹性地基内部设置梯度波阻板,基于线弹性理论,利用傅里叶积分变换,根据Helmholtz矢量分解原理,建立了弹性地基在动载荷作用下的回传射线矩阵法（reverberation ray matrix method,RRMM）计算列式.假设梯度波阻板的物理力学性质沿深度方向按幂函数连续变化,采用数值傅里叶逆变换获得了弹性地基的位移和应力等物理量的数值解.通过数值算例,与单相固体均质波阻板进行了对比,并分析讨论了梯度波阻板的材料梯度因子、埋深以及梯度波阻板厚度等物理力学参数对地基隔振性能的影响规律.结果表明,梯度波阻板能有效降低振动的振幅,与单相固体均质波阻板相比,梯度波阻板具有更好的减振隔振效果.地基的位移幅值和应力幅值随着梯度因子的增大而减小.梯度波阻板的隔振效果随着波阻板厚度的增大而提高,而随着梯度波阻板埋深的增大而降低.     

GAS WAVE IN FUNCTIONALLY GRADED MAGNETO-ELECTRO-ELASTIC COUPLED STRUCTURE

研究了由均匀磁电弹半空间和功能梯度磁电弹层组成的耦合结构中间隙波的传播特性.假定功能梯度层的材料性能沿厚度方向呈指数变化,且其表面机械自由,但承受两种电磁边界条件.首先推导了频散方程,然后结合数值算例分析了功能梯度层材料性能的梯度变化、厚度及电磁边界条件对相速度的影响,结果对功能梯度磁电弹材料在声波器件中的应用具有参考价值.     

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。     

由组份材料性能计算复合材料强度的理论与实践简

强度是结构材料最重要的一项性能指标,但如何预报纤维增强复合材料的极限承载能力却依然还是一个世界性难题. 经作者及其团队多年来的不懈努力,使得实现由原始组份性能计算复合材料强度的目标不再遥不可及. 本文围绕如何达到这一目标进行简要介绍. 也许不久之后,一旦纤维和基体材料的性能数据库建立起来,任何一个复合材料结构的设计与开发将不再依赖于甚至无需任何实验. 这不仅能节省大笔实验费用,而且能大幅缩短复合材料新产品的问世周期,促进复合材料更加广泛和更为有效地应用.     

任意加载模式下含裂纹超弹性体的能量释放率

能量释放率是表征断裂性能的一个重要指标, 在经典的断裂力学中, 只给出在恒力或恒位移加载情形下通过柔度标定来确定材料能量释放率的公式, 而且仅限于线弹性材料. 但是近年来生物材料和高分子材料(如橡胶) 等超弹性材料的断裂韧性和增韧机理越来越受到研究人员的关注, 该文旨在导出一个更加通用的柔度标定公式, 从而可以确定非线性弹性材料在任意加载模式下的能量释放率, 并能判断裂纹扩展的稳定性. 在推导的过程中, 对一些重要而容易被错误理解的概念做了进一步论述.     

能量有限元预示复合材料结构动响应研究进展

复合材料结构高频动响应预示是飞行器等结构设计中的重要研究内容之一.为了探讨精确预示复合材料结构高频动响应方法,分析比较了目前较为通用的3种动力学响应预示方法,指出能量有限元法最适合求解具有各向异性特征的复合材料结构高频动响应问题.紧接着概述了国内外关于能量有限元方法和该方法在复合材料结构高频动响应预示方面的研究进展.在此基础上分析了能量有限元法在预示复合材料结构高频动响应问题中尚待深入研究的问题.     

钢--混凝土组合结构抗震性能研究进展简

钢-混凝土组合结构的抗震性能受到了工程研究领域的广泛关注. 本文总结了国内外研究者在组合梁、组合柱、组合节点及组合框架结构抗震性能方面的试验研究概况,分析了组合构件的作用机理及地震损伤演化累积效应,讨论了钢-混凝土组合结构地震反应分析的数值模型,包括微观模型、宏观模型以及近年来迅速发展的多尺度模型,并阐述了组合结构抗震性能评价指标及抗震性能水平的确立方法.     

金属材料的强度与应力-应变关系的球压入测试方法

压入法获取材料单轴应力-应变关系和抗拉强度对服役结构完整性评价有重要的基础意义.假定材料均匀连续、各向同性、应力应变关系符合Hollomon律,基于能量等效假定,即代表性体积单元(representativevolume element, RVE)的vonMises等效和有效变形域内能量中值等效假定,本文提出了关联材料载荷、深度、球压头直径和Hollomon律的四参数半解析球压入(semi-analyticalspherical indentation,SSI)模型.通过球压入载荷-深度试验关系获得材料的应力-应变关系和抗拉强度.考虑压入过程中的损伤效应,针对金属材料提出了用于球压入测试的材料弹性模量修正模型.对11种延性金属材料完成了球压入试验,采用本文提出的球压入试验方法测到的弹性模量、应力-应变关系和抗拉强度与单轴拉伸试验结果吻合良好.      

The mesoscopic structures of dense granular materials

密集颗粒物质由大量颗粒组成的多体相互作用体系,在一定条件下,颗粒互相连接,形成相对稳定的介观尺度结构,其几何和动力学性质较大程度上决定了颗粒体系的宏观物理和力学性质,因此开展颗粒的介观结构研究具有重要的理论价值,是科学的前沿之一.自然界的堆石坝、堰塞体和碎屑流,以及工程中的高温气冷堆堆芯颗粒流和先进核裂变能系统（ADS嬗变）的颗粒散裂靶等都是典型的颗粒体系,研究颗粒体系宏观力学性质是灾害预测和调控技术的关键.本文首先介绍颗粒接触力理论和简化模型的研究进展,接着介绍介观尺度结构分析方法与测量技术,颗粒体系Jamming转变、软点和颗粒微位移测量技术等,最后列举了几个关键的科学问题.颗粒介质中很多基本力学问题的解决需要借鉴物理和数学等学科的最新成果,建立新的概念和范式,从新的角度、思路、理念去认识颗粒介质的基本问题.同时,颗粒介质的基础研究还要紧密结合工程应用领域的大量相关的核心技术,与工程领域专家共同合作,使得颗粒介质的研究有的放矢,更具生命力.     

Thermal loading in multi-layered and/or functionally graded materials: Residual stress field,delamination, fatigue and related size effects

The stress field and fracture propagation due to thermal loading in multi-layered and/or functionally graded composite materials are extensively analysed. Regarding fracture, we have focused the attention on delamination between the layers due to brittle or fatigue thermally induced crack propagations. The statically indeterminate stress analysis is solved coupling equilibrium, compatibility and constitutive equations. Fracture analysis is based on the classical Griffith’s criterion rewritten for composite structures under thermal loading. As an example, a two-layer prismatic structure is considered, each layer being composed by a different functionally graded material. The solution is particularized for the case of a linear grading. The size and shape effects are discussed and an optimization procedure is proposed. A numerical application of the findings to hard metal and diamond based cutters concludes the paper.     

THREE-DIMENSIONAL STATIC ANALYSES FOR FGM PLATES WITH MEDIUM COMPONENTS AND DIFFERENT NET STRUCTURES

A new microelement method for the analyses of functionally graded structures was proposed. The key of this method is the maneuverable combination of two kinds of elements. Firstly, the macro elements are divided from the functionally graded material structures by the normal finite elements. In order to reflect the functionally graded distributions of materials and the microconstitutions in each macro-element, the microelement method sets up the dense microelements in every macro-element, and translates nodes to the same as the normal finite elements by the degrees of freedom of all microelemental the compatibility conditions. This microelement method can fully reflect the micro constitutions and different components of materials, and its computational elements are the same as the normal finite elements, so it is an effective numerical method for the analyses of the functionally graded material structures. The three-dimensional analyses of functionally graded plates with medium components and different micro net structures are given by using the microelement method in this paper. The differences of the stress contour in the plane of functionally graded plates with different net microstructures are especially given in this paper.     

Raman spectroscopy investigations of functionally graded materials and inter-granular mechanics

The recent evolution of micro-Raman spectroscopy as micro-mechanical experimental technique had a profound effect on the field of solid mechanics. Micro-Raman spectroscopy (MRS) is the only technique capable of measuring local stress in a wide range of materials with a spatial resolution of 1 μm. With the current trend of near-field Raman, such spatial resolution is expected to increase down to few tens of nanometers. In addition, the technique is capable of interrogating chemical and structural changes in the materials, hence, for the first time, direct correlation can be identified in-situ by means of the same technique. Such capabilities have been previously utilized in the field of fibrous composites to provide accurate measurements of axial and interfacial stress distributions along individual fibers and at fiber/matrix interface. Such experimental measurements shed light on and strengthened our understanding of crucial events taking place during composite loading such as damage initiation, propagation, and resulted in more accurate models capable of predicting composite behavior and lifetime. In this paper we demonstrate the power of MRS in investigating functionally graded joints for carbon–carbon composites and its ability to provide the necessary data for the correlation of chemical changes with mechanics of the joint. In addition, our recent demonstration of the ability of the technique to measure inter-granular stress fields in polycrystalline materials will be reviewed.     

The method of fundamental solutions for nonlinear functionally graded materials

In this paper, we investigate the application of the method of fundamental solutions (MFS) to two-dimensional steady-state heat conduction problems for both isotropic and anisotropic, single and composite (bi-materials), nonlinear functionally graded materials (FGMs). In the composite case, the interface continuity conditions are approximated in the same manner as the boundary conditions. The method is tested on several examples and its relative merits and disadvantages are discussed.