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建立了薄膜褶皱分析的力学模型,并基于张力场理论和稳定性理论分析了褶皱区域的应 力应变关系. 在此基础上提出了褶皱薄膜动态分析的NBA-UM(nonlinear buckling analysis-update matrix)分析方法，分析了褶皱薄膜振动特性. 结 果表明，褶皱使薄膜产生``过度收缩' 现象，并改变了薄膜中的应力分布. 褶皱对薄膜的振动特性有很大的影响，大幅度的褶皱改 变了薄膜振动的固有频率和模态形式. 提出的NBA-UM分析方法可以有效地预报褶皱薄膜 的动态行为.     

基于张力场理论的薄膜褶皱研究评述

张力场理论是较早提出的研究薄膜褶皱的理论，该理论忽略了薄膜的弯曲刚度, 认为在褶皱 区薄膜处于单轴的应力状态，褶皱的方向为大主应力方向，垂直于褶皱方向的小主应力为零. 基于这种方法提出了很多褶皱的分析模型. 这些分析模型通过引入参数对薄膜的本构关系或 变形梯度进行修正，然后通过数值的方法进行求解，可以得到褶皱形成以后的应力分布，及 褶皱的方向. 其主要的缺点是不能得到褶皱的波长、幅度及数量等信息. 基于能量方法的褶 皱分析，首先要假定褶皱的变形模式，然后通过能量关系得到褶皱幅度和波长的表达式. 本 文对比分析薄膜褶皱的不同分析方法，并指出了薄膜褶皱研究的发展趋势.     

空间薄膜结构的褶皱形变预测

空间充气结构技术是一项全新的空间结构构建技术,基于该技术的空间充气结构是未来空间任务的主要需求对象．该结构主要由薄膜构成,因此结构形面精度的保持是关键问题．褶皱是薄膜特有的现象,它的存在会严重影响结构形面精度,因此进行褶皱研究很有必要．根据屈曲理论联合薄膜褶皱的实际构型建立了薄膜结构褶皱的预测模型,分析了矩形平面薄膜受面内水平剪切情况下的褶皱,得到了褶皱幅度和褶皱波长以及薄膜结构产生褶皱时的临界压缩应力,通过与已有文献结果及本文实验结果的比较验证了该分析方法的有效性和结果的正确性．     

基于摄影测量法的薄膜褶皱实验研究

采用非接触式的测试方式摄影测量法对薄膜褶皱进行了实验研究.建立了剪切薄膜褶皱的分析模型,并基于摄影测量法对该模型的褶皱变形模式进行了实验研究.摄影测量法是通过对不同角度上相机拍摄到的同一靶点的图像信息进行处理,可以得到相应靶点的三维坐标,从而实现对微小变形的非接触式的测量.通过摄影测量法得到了剪切薄膜褶皱的变形模式.实验研究表明,在剪切距离增大的情况下薄膜褶皱的数量保持不变,但是褶皱面外变形幅度随着剪切距离的增加而增大.试验结果与数值分析结果具有相关性,摄影测量法适合于薄膜结构微小面外变形的非接触式测量.     

薄膜褶皱的非线性屈曲有限元分析

有限元模拟已经成为目前薄膜褶皱预测的重要工具。本文采用ANSYS SHELL63单元对薄膜受剪情况下的褶皱形变进行了非线性屈曲分析。通过本征屈曲分析得到的模态模拟了薄膜的初始缺陷。利用本文的非线性有限元模型分析得到了薄膜褶皱的波长和幅度,并与理论分析结果进行了比较,结果相近。     

滑动蒙皮变后掠气动力非定常滞回与线性建模

针对低速不可压条件下滑动蒙皮方式变后掠过程中非定常动态气动特 性开展了3方面的研究工作: (1)飞行器变形过程中非定常动态气动特性风洞试验技术研究; (2)变形过程中滞回效应研究和机理分析; (3)基于风洞试验结果开展变形过程中非定常动态 气动力线性建模. 初步研究表明: (1)采用强迫振荡法可以有效地获取变形过程中非定常动态 气动力滞回效应; (2)造成变形过程中气动滞回效应的机理有两个即``动边界效应'和``流场结 构滞回效应', 造成滞回效应的机理可能主要在于后者; (3)引入升力系数和俯仰力 矩系数随后掠角变化率的动导数概念, 可以建立变形过程中非定常动态气动力线性模型.     

对角受拉方膜褶皱变形幅值的理论预测及实验验证

柔性薄膜结构广泛应用于航天飞行器的关键部件.形面平整度是影响薄膜结构性能的主要因素之一.褶皱幅值是评价薄膜反射面天线形面平整度的重要指标.褶皱幅值的大小与垂直于褶皱方向的横向应变密切相关.本文基于薄板稳定性理论,针对对角受拉方形薄膜建立了一个能够准确预测其褶皱变形幅值的理论模型.该模型考虑了横向拉伸力对薄膜变形的影响,将垂直于褶皱方向的位移分解为由泊松效应造成的横向收缩位移、由面外变形造成的褶皱位移以及由横向拉伸力造成的拉伸位移三个部分,重新推导了褶皱幅值的理论公式. 基于数字图像相关技术,对受拉方形薄膜进行了散斑实验测试. 利用双目视觉三维测量系统,测量了方形薄膜的三维位移场, 获得了薄膜的三维变形形貌和褶皱波形图,研究了褶皱幅值与拉伸载荷之间的非线性关系. 与已有理论模型相比,该模型进一步提高了褶皱幅值的计算精度, 与实验结果吻合良好.本文呈现的理论研究可为精确数值模型的建立及算法实现提供有意义的指导.      

薄膜-基体型磁致伸缩微致动器的数值模拟

磁致伸缩薄膜是一种性能优异的微驱动元件。本文针对磁致伸缩薄膜一基体结构中薄膜磁致伸缩系数与层合结构变形之间关系的问题，从经典层合板理论的角度导出了其基本方程，并在此基础上对基体远厚于薄膜的情形采用非层合板理论进行了简化。通过比较非层合板理论和层合板理论下的薄膜一基体结构变形的有限元结果，讨论了有关几何参数和物理参数的影响，给出了用非层合板理论近似处理薄膜一基体型磁致伸缩微致动器的适用条件。     

空间充气展开结构动态分析研究进展

空间充气展开结构是一种以薄膜材料为主构建而成的新型结构, 可用于构建大型的天线、太 阳能集中器、太阳帆等空间结构, 为空间结构的大型化提供了一条有效的解决途径.其动态 特性是充气展开结构设计过程中必须考虑的问题, 动态分析测试技术一直是充气展开结构研 究过程中的关键问题, 由于充气展开结构在材料、结构形式及工作环境等方面的特殊性, 使 得其动态分析和测试技术出现了很多新的问题.目前充气展开结构动态分析的研究方法主要 集中在两个方面：实验研究和数值模拟.实验研究主要是针对充气薄膜结构的特点, 由接触 式的测试手段向非接触式的测试手段发展, 但实验研究在真空和微重力环境的模拟上面临着 很大的问题.数值模拟研究可以有效的模拟结构在真空和微重力环境下的动态行为, 并可分 析重力、空气和褶皱等因素对结构振动特性的耦合影响.本文综述了空间充气展开结构动态 分析的实验研究和数值研究的发展和现状, 并讨论了其中存在的问题, 在此基础上指出了该 项研究的发展趋势.     

"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.     

Numerical simulations for gas-structure interaction in inflated deployment of folded membrane boom

It is very important for gas-structure interaction between compressible ideal gas and elastic structure of space folded membrane booms during the inflatable deployment. In order to study this gas-structure interaction problem, Arbitrary Lagrangian-Eulerian (ALE) finite element method was employed. Gas-structure interaction equation was built based on equilibrium integration relationship, and solved by operator split method. In addition, numerical analysis of V-shape folded membrane booms inflated by gas was given, the variation of inner pressure as well as deployment velocities of inflatable boom at different stage were simulated. Moreover, these results are consistent with the experiment of the same boom, which shows that both ALE method and operator split method are feasible and reliable methods to study gas-structure interaction problem.     

A new model for wrinkling and collapse analysis of membrane inflated beam

A new model is proposed to accurately predict the wrinkling and collapse loads of a membrane inflated beam. In this model, the pressure effects are considered and a modified factor is introduced to obtain an accurate prediction. The former is achieved by modifying the pressure-related structural parameters based on elastic small strain considerations, and the modified factor is determined by our test data. Compared with previous models and our test data, the present model, named as shell-membrane model, can accurately predict the wrinkling and collapse loads of membrane inflated beams.     

In-plane mechanical behaviors of 2D repetitive frameworks with four-coordinate flexible joints and elbowed beam members

The mechanical properties of an open-framework structure constructed of joints and beam members are strongly influenced by both its geometrical configuration and joint flexibility. This paper clarifies the relationship between joint flexibility and Poisson's ratio, which is a mechanical criterion for solid deformation, and discusses two types of in-plane anisotropic structures made up of four-coordinate flexible joints and elbowed beam members. Uniaxial tensile analyses estimate the linear and nonlinear elastic properties of these frameworks by applying straightforward joint modeling with multi-rotational degrees of freedom. The numerical results show that these proposed frameworks produce a variety of deformability dependent on the joint flexibility in auxetic deformation with a negative Poisson's ratio, the folding mechanics under kinematic indeterminacy, and the transition of Poisson's ratio between the positive and negative values. The geometrical and topological aspects of the obtained mechanical behaviors are discussed.     

On the response and stability of an inflated toroidal membrane under radial loading

Two flat annular hyperelastic membranes, stacked and bonded together at both the boundaries (equators), form a closed inflatable structure of toroidal topology. The response and stability of the inflated toroidal structure subjected to a radial line force distribution at the inner boundary are studied. The forcing is considered under constant pressure and constant amount of gas inflation conditions. Two hyperelastic models described by the corresponding relaxed strain energy density functions are considered for the membrane material. The influence of geometry, material and level of inflation on the response and stability of the structure under load has been brought out. The structure exhibits pressure limit points with increasing levels of inflation. The force–deflection (stiffness) behaviour is found to be qualitatively different below and above the pressure limit points. Below the pressure limit point, wrinkling and pull-in under loading are revealed for different inflation conditions, and the stability boundaries are determined. Under certain conditions, a counter-intuitive stretch-softening behaviour is also observed.     

Macroscopic elastic properties of regular lattices

In this paper we study analytically the elastic properties of the 2-D and 3-D regular lattices consisting of bonded particles. The particle-scale stiffnesses are derived from the given macroscopic elastic constants (i.e. Young's modulus and Poisson's ratio). Firstly a bonded lattice model is presented. This model permits six kinds of relative motion and corresponding forces between each bonded particle pair. By comparing the strain energy distributions between the discrete lattices and the continuum, the explicit relationship between the microscopic and macroscopic elastic parameters can be obtained for the 2-D hexagonal lattice and the 3-D hexagonal close-packed and face-centered cubic structures. The results suggest that the normal stiffness is determined by Young's modulus and the particle size (in 3-D), and that the ratio of the shear to normal stiffness is related to Poisson's ratio. Rotational stiffness depends on the normal stiffness, shear stiffness and particle sizes. Numerical tests are carried out to validate the analytical results. The results in this paper have theoretical implications for the calibration of the spring stiffnesses in the Discrete Element Method.     

基于不同板理论的嵌于柔性层中薄膜的皱曲分析

论文对于柔性层-薄膜-柔性层三层结构系统,基于经典板理论、一阶剪切变形理论和高阶剪切变形理论,分别推导给出薄膜皱曲的控制方程。对于两个柔性层,则把它们处理成具有有限厚度的平面应变弹性体。针对上下柔性层固支边界或自由边界条件,利用线性扰动动方法得到柔性层对薄膜的横向压力差,最终获得确定薄膜具有周期性正弦型皱曲的临界载荷方程。同时,对结构系统建立了有限元数值模型,通过模拟结果与三种板理论的结果进行了比较,验证了理论解的精确性和适用性。最后,进行了参数和极限情况分析,阐述了上下层边界条件、薄膜和柔性层的材料和几何参数对临界值的影响。     

A study on wrinkling characteristics and dynamic mechanical behavior of membrane

An eigenvalue method considering the membrane vibration of wrinkling out-of-plane deformation is introduced, and the stress distributing rule in membrane wrinkled area is analyzed. A dynamic analytical model of rectangular shear wrinkled membrane and its numerical analysis approach are also developed. Results indicate that the stress in wrinkled area is not uniform, i.e. it is larger in wrinkling wave peaks along wrinkles and two ends of wrinkle in vertical direction. Vibration modes of wrinkled membrane are strongly correlated with the wrinkling configurations. The rigidity is larger due to the heavier stress in the part of wrinkling wave peaks. Therefore, wave peaks are always located at the node lines of vibration mode. The vibration frequency obviously increases with the vibration of wave peaks.     

Constitutive analysis of thin biological membranes with application to radial stretching of a hollow circular membrane

The constitutive analysis of the mechanical response of thin elastic membranes under inplane deformation is presented by using the multiplicative decomposition of the deformation gradient into its areal and distortional parts. Specific results are obtained for the Evans-Skalak form of the strain energy function. The solution to the problem of radial stretching of a hollow circular membrane obeying this constitutive model is then derived. The stress concentration factor is determined as a function of the relative hole size and the magnitude of the applied tension. The tension boundary is identified above which no compressive stress appears in the membrane. The limit boundary is introduced below which the membrane cannot support the applied loading without unstable wrinkling. For the loading between the tension and the limit boundary, nonuniformly distributed infinitesimal wrinkles appear within the inner portion of the membrane, carrying radial tension but no circumferential stress (tension field). The specific form of the strain energy function is used to describe this behavior, and to calculate the amount of the membrane area absorbed by infinitesimal wrinkles. The wrinkled portion is surrounded by the outer portion of the membrane carrying both radial and circumferential stresses. The limit boundary is reached when wrinkles spread throughout the membrane. It is shown that for a sufficiently large tension at the outer boundary, the wrinkling does not spread throughout the membrane no matter how large the applied tension at the inner boundary of the membrane is, provided that no rupture takes place. The limiting extent of the tension field in such cases is calculated. The linearized version of the analysis is characterized by a closed form solution.     

薄膜结构的几何非线性分析

使用动力松弛法对薄膜结构进行静载分析，并提出一种方法处理皱折单元以确保荷载分析的可靠性。薄膜结构如果在某膜单元的单向应力方向发生皱折，其单元本身仍然能够继续承受荷载，因此提出索松弛单元和膜皱折单元处理薄膜的索松弛和膜皱折问题。就索网结构和薄膜结构分类给出算例进行静载分析，算例表明本文的方法可以有效处理索松弛单元和膜皱折单元，确保荷载分析的准确性。