永乐大钟梯形木架稳定性初探

对北京市大钟寺悬挂永乐大钟的梯形木架结构的稳定性进行了初步分析. 根据弹性结构稳定 性理论的能量法和中国古建筑结构``卯榫'接头抗弯性能的简化的本构模型,采用``对比法 '分析了二维梯形木架的结构稳定性;结果表明中国古建筑木架结构的``收分'形状设计对 增大木架稳定性有很大作用, 立柱``侧角'越大,稳定性越好. 收分形式设计凸现 中国古代工程技术人员的聪明智慧.     

短纤维增强三元乙丙橡胶横观各向同性黏-超弹性本构模型

短纤维增强三元乙丙橡胶包覆薄膜,是一种应用于固体火箭发动机缠绕包覆装药的新型复合材料.为了描述其在工作过程中受振动、冲击等载荷作用时的力学行为,基于黏弹性理论和纤维增强连续介质力学理论,提出了一种考虑应变率强化效应的横观各向同性黏-超弹本构模型.模型中应变能函数被分解为超弹性应变能和黏性应变能,其中超弹性应变能包括表征各向同性的橡胶基体应变能和表征各向异性的纤维拉伸应变能,黏性应变能采用表征橡胶和纤维黏性响应的宏观唯象模型.选取表征各应变能的函数形式,经过数学变换、替代、叠加,求解确定最终的应力应变形式,明确模型参数获取的具体步骤,将预测结果与实验结果对比分析,准确性较高.研究表明:该模型能有效预测材料在低应变率下纤维方向为0?～45?的非线性率相关力学特性;模型形式易于实现有限元开发,对固体火箭发动机装药结构完整性分析具有参考价值.     

"疾风吹飞帆，倏忽南与北"—— 帆船航行的力学诗趣

简要介绍了中国传统船帆的常见类型与制作材料,通过对帆船航行时的受力分析,解释了中 国古代诗词中所描述的``帆去如鸟翅'、``欹帆侧柁'、``疾风吹飞帆,倏忽南与北'等力 学现象,并对李白诗句``千里江陵一日还'的可信性问题进行了讨论.     

编织复合材料弹性性能的细观力学模型

提出了编织复合材料弹性性能分析的细观力学模型，这个力学模型考虑了实际编织结构中的纬向和经向纤维束的曲屈，相邻纤维束之间的间隙和纤维束的横截面尺寸对编织复合材料弹性性能的影响，并探讨了在纤维束间纯树脂区内孔隙的含量和两种叠层结构对材料弹性性能的影响．理论计算结果与实测值的比较，表明所提出的细观力学模型是合理的．根据理论分析的结果，提出了优化单层和叠层编织结构的结构参数选择方法     

混凝土SHPB试验数值模拟研究

基于混凝土HJC动态本构模型,分析了该模型方程及参数获得方法,以混凝土材料的基本力学参数确定了HJC模型中各参数值,并运用LS-DYNA软件完成混凝土SHPB试验的三维数值模拟.对比分析数值模拟结果重构所得试样的应力应变曲线与实际试验结果的相似性,研究表明,数值模拟结果可再现试验中混凝土的动态力学行为与破坏特征,而且,数值模拟可很好的反映应力波在波导杆与试件中传播过程,符合一维弹性波理论规律.     

超晶格材料光电性能及其相关力学问题研究进展

超晶格材料是由两种或两种以上性质不同的薄膜交替生长而形成的人工周期性结构材料.超晶格材料中具有连续介质力学``小尺度效应'和量子力学``大尺寸量子效应'并存的现象.阐述了超晶格材料周期结构特征和制备技术,介绍了超晶格材料量子化能带结构及其奇异的光电特性.探讨了超晶格材料微观结构及其变形机理,归纳了超晶格材料量子化电子结构的几种常用计算方法,如紧束缚方法、赝势方法和k$ \cdot $p微扰方法等.重点介绍了外力场和应变对超晶格材料量子化电子结构及其光电性质影响,包括作者所在研究小组近期在端部摩擦、点载荷、有限界面和各向异性等对超晶格微观变形及其量子化电子结构影响的跨尺度一体化研究方面的最新工作进展.      

基于三维细观力学模型的开孔泡沫弹性性能预测

泡沫材料的宏观力学性能主要取决于基体材料的力学特性及其微细观结构特征,基于细观力学模型的分析方法是泡沫材料力学性能研究的重要途径。文中基于Matlab语言和Abaqus软件构建了描述中等孔隙率开孔弹性泡沫材料微结构特征的三维随机分布球形泡孔模型,并采用有限元方法对弹性泡沫压缩变形进行了模拟,并计算给出了不同孔隙率弹性泡沫材料弹性模量、剪切模量、体积模量以及泊松比的分布,建立了相应的唯象表达式。与理论模型及测试结果的比较表明,本文基于三维随机泡孔模型模拟结果构建的唯象表达式能够对弹性泡沫材料的弹性力学性能给出很好的预测。     

各向同性弹性损伤的双标量描述

损伤状态的描述是损伤力学中仍未完善解决的基本问题．我们旨在对此问题就最简单的一种情形——各向同性弹性损伤，进行较为全面的研究．首先，指出了古典各向同性损伤理论中，基于应变等效假设，用单个标量损伤变量描述损伤状态的局限性．然后，建立了一个用两个标量损伤变量描述的各向同性弹性损伤模型．此模型解除了古典理论的局限，能完全描述各向同性弹性损伤，并且得到本文数值实验的验证．最后，将本文模型与现有细观力学结果连接，给出了宏细观损伤变量之间的关系，使得细观量可以通过宏观量来反映，建立了一个用细观损伤材料常数描述细观缺陷特征的损伤本构模型     

短纤维增强EPDM包覆薄膜超弹性本构模型

短纤维增强三元乙丙橡胶(EPDM)包覆薄膜用于一种新型缠绕包覆工艺,主要解决复杂构型自由装填药柱外表面可靠性包覆问题.为了描述其在固体火箭发动机工作过程中产生的大变形、非线性和各向异性等力学行为,根据纤维增强复合材料连续介质力学理论,提出了各向异性超弹性本构模型.该模型中单位体积的应变能函数被解耦成两部分:表征各向同性的橡胶基体应变能和表征各向异性的纤维拉伸应变能,通过引入纤维方向对纤维应变能进行修正,给出了通过单轴拉伸、偏轴拉伸实验数据获取模型参数的具体方法.研究结果表明,该模型能够很好地预测材料在纤维方向0°~45°时的各向异性力学特性,并将预测结果与实验数据对比,误差在5%以下.所建立的各向异性超弹性本构模型准确性高、易于实现数值开发,在一定程度上能够为固体火箭发动机的装药结构完整性分析提供理论依据.     

考虑应变率的广义压电热弹理论及其应用

工程中大量材料的形变介于弹性与黏性之间, 既具有弹性固体特性, 又具有黏性流体特点, 即为黏弹性. 黏弹性使得材料出现很多力学松弛现象, 如应变松弛、滞后损耗等行为. 在研究受热载荷作用的多场耦合问题的瞬态响应时, 考虑此类问题中的热松弛和应变松弛现象, 对准确描述其瞬态响应尤为重要. 针对广义压电热弹问题的瞬态响应, 尽管已有学者建立了考虑热松弛的广义压电热弹模型, 但迄今, 尚未计入应变松弛. 本文中, 考虑到材料变形时的应变松弛, 通过引入应变率, 在Chandrasekharaiah广义压电热弹理论的基础之上, 经拓展, 建立了考虑应变率的广义压电热弹理论. 借助热力学定律, 给出了理论的建立过程并得到了相应的状态方程及控制方程. 在本构方程中, 引入了应变松弛时间与应变率的乘积项, 同时, 分别在本构方程和能量方程中引入了热松弛时间因子. 其后, 该理论被用于研究受移动热源作用的压电热弹一维问题的动态响应问题. 采用拉普拉斯变换及其数值反变换, 对问题进行了求解, 得到了不同应变松弛时间和热源移动速度下的瞬态响应, 即无量纲温度、位移、应力和电势的分布规律, 并重点考察了应变率对各物理量的影响效应, 将结果以图形形式进行了表示. 结果表明: 应变率对温度、位移、应力和电势的分布规律有显著影响.      

Wave propagation in nonlinear and hysteretic media––a numerical study

This paper considers the problem of one dimensional wave propagation in nonlinear, hysteretic media. The constitutive law in the media is prescribed by an integral relationship based on the Duhem model of hysteresis. It is found that the well known nonlinear elastic stress–strain relationship is a special case of this integral relationship. It is also shown that the stress–strain relationship from the McCall and Guyer model of hyesteretic materials can also be derived from this integral stress–strain relationship. The first part of this paper focuses on a material with a quadratic stress–strain relationship, where the initial value problem is formulated into a system of conservation laws. Analytical solutions to the Riemann problem are obtained by solving the corresponding eigenvalue problem and serve as reference for the verification and illustration of the accuracy obtained using the applied numerical scheme proposed by Kurganov and Tadmor. The second part of this research is devoted to wave propagation in hysteretic media. Several types of initial excitations are presented in order to determine special characteristics of the wave propagation due to material nonlinearity and hysteresis. The results of this paper demonstrate the accuracy and the robustness of this numerical scheme to analyze wave propagation in nonlinear materials.     

Discriminating linear from nonlinear elastic damage using a nonlinear time reversal DORT method

The DORT method is a selective detection and focusing technique originally developed to detect defects and damages which induce linear changes of the elastic moduli. It is based on the time reversal (TR) where a signal collected from an array of transducers is time reversed and then back-propagated into the medium to obtain focusing on selected targets. TR is based on the principle of spatial reciprocity. Attenuation, dispersion, multiple scattering, mode conversion, etc. do not break spatial reciprocity. The presence of defects or damage, may cause materials to show nonlinear elastic wave propagation behavior that will break spacial reciprocity. Therefore the DORT method will not allow focusing on nonlinear elastic scatterers. This paper presents a new method for the detection and identification of multiple linear and nonlinear scatterers by combining nonlinear elastic wave spectroscopy, time reversal and DORT method. In the presence of nonlinear hysteretic elastic scatterers, forcing the solid with a harmonic excitation, the time reversal operator can be obtained not only at the fundamental frequency of excitation, but also at the odd harmonics. At the fundamental harmonic, either inhomogeneities and linear damages can be individually selected but only at odd harmonics nonlinear hysteretic elastic damages exist. A procedure was developed where by decomposing the operator at the odd harmonics, it was possible to focus on nonlinear scatterers and to differentiate them from the linear inhomogeneities. A complete mathematical nonlinear DORT formulation for 1 and 2D structures is presented. To model the presence of nonlinear elastic hysteretic scatterers a Preisach–Mayergoyz (PM) material constitutive model was used. Results relative to 1 and 2 dimensional structures are reported showing the capability of the method to focus and discern selectively linear and nonlinear scatterers. Furthermore, an analysis was conducted to study the influence of the number of sources and their location on the imaging process showing that using a higher numbers of sensors does not automatically bring to a minor uncoupled behaviour between the nonlinear targets.     

Wave propagation in an elastic tube: a numerical study

In this paper, a fluid–wall interaction model, called the elastic tube model, is introduced to investigate wave propagation in an elastic tube and the effects of different parameters. The unsteady flow was assumed to be laminar, Newtonian and incompressible, and the vessel wall to be linear-elastic, isotropic and incompressible. A fluid–wall interaction scheme is constructed using a finite element method. The results demonstrate that the elastic tube plays an important role in wave propagation. It is shown that there is a time delay between the velocity waveforms at two different locations and that the peak velocity increases while the low velocity decreases in the elastic tube model, contrary to the rigid tube model where velocity waveforms overlap each other. Compared with the elastic tube model, the increase of the wall thickness makes wave propagation faster and the time delay cannot be observed clearly, however, the velocity amplitude is reduced slightly due to the decrease of the internal radius. The fluid–wall interaction model simulates wave propagation successfully and can be extended to study other mechanical properties considering complicated geometrical and material factors.     

Antiplane elastic wave propagation in pre-stressed periodic structures; tuning,band gap switching and invariance

The effect of nonlinear elastic pre-stress on antiplane elastic wave propagation in a two-dimensional periodic structure is investigated. The medium consists of cylindrical annuli embedded on a periodic square lattice in a uniform host material. An identical inhomogeneous deformation is imposed in each annulus and the theory of small-on-large is used to find the incremental wave equation governing subsequent small-amplitude antiplane waves. The plane-wave-expansion method is employed in order to determine the permissable eigenfrequencies. It is found that pre-stress significantly affects the band gap structure for Mooney–Rivlin and Fung type materials, allowing stop bands to be switched on and off. However, it is also shown that for a specific class of materials, their phononic properties remain invariant under nonlinear deformation, permitting some rather interesting behaviour and leading to the possibility of phononic cloaks.     

基于迭代法的非线性弹性均质化研究

微观结构对复合材料的宏观力学性能具有至关重要的影响, 通过合理设计复合材料微观结构可以得到期望的宏观性能. 均质化方法作为一种有效的设计方法, 它从微观结构的角度出发, 利用均匀化的概念, 实现了对复合材料宏观力学性能的预测和设计. 而当考虑非线性因素, 均质化的实现就非常困难. 本文利用双渐近展开方法, 将位移按照宏观位移和微观位移展开, 推导了非线性弹性均质化方程. 通过直接迭代法, 对非线性弹性均质化方程进行了求解, 并给出了具体的迭代方法和实现步骤. 本文基于迭代步骤和非线性弹性均质化方程编写MATLAB 程序, 对3种典型本构关系的周期性多孔材料平面问题进行了计算, 对比细致模型的应变能、最大位移和等效泊松比, 对程序及迭代方法的准确性进行了验证. 之后对一种三元橡胶基复合材料进行多尺度均质化, 将其分为芯丝尺度和层间尺度. 用线弹性的均质化方法得到了芯丝尺度的等效弹性参数, 并将其作为层间尺度的材料参数. 在层间尺度应用非线性弹性均质化方法对结构进行计算, 得到材料的宏观等效性能, 并以实验结果为基准进行评价.      

非线性变形节理中纵波传播特性的理论研究

基于波前动量守恒理论和位移不连续方法所提出的时域分析新方法,引入岩石非线性法向本构关系,对弹性纵波在岩石非线性节理中的传播特性进行了理论分析。采用节理变形的双曲线模型(BB模型),获得纵波P波斜入射非线性节理的传播波动方程,并通过参数研究分析了在岩石节理中节理非线性系数、节理初始刚度、应力波入射角和入射波幅值等因素对纵波传播规律的影响。结果表明:所推导的应力波传播方程在考虑多种非线性问题时,通过迭代计算即可方便求出透射波和反射波的数值解,避免了复杂的数学运算;当波斜入射节理面时,产生了波型转换,节理变形的非线性对透射波和反射波有较大影响,透射系数和反射系数并非随着非线性参数的变化而单调变化。时域内所推导的波传播方程更有益于波斜入射时非线性参数的广泛研究,为开展该方面的理论研究工作提供了借鉴。     

周期结构后屈曲新算法及其应用

提出了周期结构后屈曲分析的一种新算法。在屈曲点附近,通过加载模型和诱导后屈曲边值问题之间的相互切换,避开屈曲点附近刚度矩阵的奇异性,并诱导结构产生预期的后屈曲变形,避免了以往后屈曲算法中引入几何初始缺陷后对系统带来的可能影响。通过对三种由超弹性材料所构成的周期孔隙结构的后屈曲分析,验证了本文所提出的后屈曲算法的有效性和灵活性。分析了周期孔隙材料多向加载对屈曲模式转换的影响,以及后屈曲变形对弹性波传播带隙的影响,为周期结构中弹性波传播的调控提供良好的基础。     

Nonlinear thermoelasticity,vibration, and stress wave propagation analyses of thick FGM cylinders with temperature-dependent material properties

In the present paper, nonlinear thermoelasticity, vibration, and stress wave propagation analyses of thick-walled cylinders made of functionally graded materials with temperature-dependent properties are performed. In contrast to researches accomplished so far, a third-order Hermitian finite element formulation is employed to guarantee both radial displacement and normal stress continuities, improve the accuracy, and prevent virtual wave source formations at the mutual boundaries of the elements. Stress wave propagation, reflection, and interference under impulsive mechanical loads in thermal environments are also studied. In contrast to the common procedure, the cylinder is not divided into isotropic sub-cylinders. Therefore, artificial wave reflections from the hard interfaces are avoided. Time variations of the temperatures, displacements, and stresses due to the dynamic loads are determined by solving the resulted highly nonlinear governing equations using an updating iterative time integration scheme and over-relaxation and under-relaxation techniques. A comprehensive sensitivity analysis includes effects of the volume fraction indices, dimensions, and temperature-dependency of the material properties is performed. Results reveal the significant effect of the temperature-dependency of the material properties on the transient stress distribution and elastic wave propagation and reflection phenomena. Interesting phenomena are noticed; among them the oblique wave formations during the wave propagation. Since examples of the present field are rare in literature, the extracted results may serve as reference results for future comparisons.     

非均匀损伤介质中波传播的数值解

对弹性波在非均匀损伤介质中的传播理论进行了研究。通过将非均匀损伤区域离散成分层均匀的区域，结合相邻区域交界面处的连续条件，推导出了以右行波、左行波为状态向量的波动方程和传递矩阵。对几种非均匀损伤介质中波的传播进行了实例数值计算，并和其解析解的结果进行了比较，讨论了弹性波在非均匀损伤介质中传播的一般性质。     

梯形应力脉冲在弹性杆中的传播过程和几何弥散

在应力波传播过程中,几何弥散效应往往难以避免.对应力波在弹性杆中传播的几何弥散效应进行解析分析,对于基础波动问题研究以及材料动态力学行为表征等课题,显得至关重要.本文简单说明了弹性杆中考虑横向惯性修正的一维 Rayleigh-Love应力波理论,概述了其波动控制方程的变分法推导过程;针对 Hopkinson杆实验中常用的梯形应力加载脉冲,建立了相应的偏微分方程初边值问题的求解模型,并运用 Laplace变换方法研究了脉冲在杆中传播的几何弥散现象;根据留数定理进行 Laplace反变换,给出了杆中不同位置和时刻的应力波的级数形式解析解,分析了计算项数对结果收敛性的影响;将解析计算结果与采用三维有限元数值模拟的计算结果进行对比,两者吻合程度良好,从而证明 Rayleigh-Love横向惯性修正理论可以有效地表征典型 Hopkinson杆实验中的几何弥散效应.在此基础上围绕梯形加载脉冲的弥散效应进行参数研究,定量描述了传播距离、泊松比、脉冲斜率等参数的影响.本文给出的 Rayleigh-Love杆在梯形加载条件下的解析解,揭示了几何弥散效应的本质规律,可以用于实际实验的弥散修正过程.