【作者】 李云良；

【导师】 谭惠丰；

【作者基本信息】 哈尔滨工业大学 ， 工程力学， 2008， 博士

【摘要】 褶皱作为薄膜的局部屈曲现象,在空间薄膜结构中广泛存在。对于高精度的薄膜结构来说,褶皱是影响其表面精度的主要因素。同时,褶皱产生以后将影响到结构的稳定性,并对结构的动态特性产生一定的影响。目前随着航天领域中高精度薄膜结构应用研究的发展,薄膜褶皱研究已成为热点。张力场理论是较早提出的薄膜褶皱分析理论,通过引入参数对薄膜褶皱区域的本构关系进行修正,以避免薄膜中压应力的出现。基于张力场理论很好的解决了张拉膜结构的褶皱问题。由于基于张力场理论的薄膜褶皱分析不能得到褶皱的面外变形信息,因此不符合高精度空间薄膜结构的褶皱分析要求。为了准确描述薄膜褶皱的面外变形,本文提出了褶皱构形的概念,采用波长,幅度及褶皱方向等参数来描述褶皱构形。根据非线性大挠度方程建立了薄膜褶皱构形参数研究的一般性方法—应力极值法,建立了褶皱半波长与褶皱方向拉应力的关系模型,确定了褶皱构形参数之间的关系。采用应力极值法进行褶皱分析时,避开了褶皱具体变形形式的假定,具有很好的通用性。根据应力极值法,研究了剪切薄膜褶皱和对角张拉矩形薄膜褶皱,得到了褶皱构形参数。将薄膜产生褶皱的过程分为初始屈曲过程和后屈曲过程两个阶段,对两个不同阶段褶皱形成和扩展的机理进行了理论分析。建立了初始屈曲过程剪切薄膜的临界载荷公式,并分析了初始屈曲过程褶皱的形成和扩展规律。对于后屈曲过程的分析,将初始缺陷引入到薄膜褶皱的分析之中,建立了具有初始缺陷的薄膜褶皱的分析模型,分析了褶皱区域的应力分布规律。根据褶皱区域应力分布规律,分析了后屈曲过程褶皱的扩展机理。结合理论分析,讨论了后屈曲过程中可能出现的二次屈曲现象。基于稳定性理论,建立了薄膜褶皱的数值分析方法—直接扰动法,解决了采用常规的非线性屈曲分析引入的初始缺陷无法去除的问题。采用直接扰动法,分析了薄膜初始屈曲过程的临界载荷和褶皱的形成及扩展规律。得到了后屈曲过程薄膜褶皱的构形参数。分析了薄膜屈曲的平衡路径。通过数值方法研究了初始屈曲过程及后屈曲过程中的二次屈曲现象。并将数值分析结果与理论分析结果进行了对比分析,结果符合较好。采用数字摄影测量法进行了剪切薄膜褶皱的实验研究。通过数字摄影测量系统实现了薄膜微小面外变形的非接触式的测量。设计了适合高精度测量要求的剪切薄膜的实验装置,该装置可以实现精确的加载过程控制,便于对薄膜屈曲全过程的分析。采用高精度的数字摄影测量系统获得了褶皱的构形及构形参数,在实验中观测到了二次屈曲现象。通过与数值分析结果进行的对比分析,验证了数值分析方法的合理性。对薄膜屈曲后的动态特性进行了分析。建立了具有褶皱面外变形的薄膜振动的特征值方程,并基于直接扰动法建立了动态分析的数值方法。基于该方法分析剪切褶皱薄膜和对角张拉矩形褶皱薄膜的振动特性。分析了褶皱形成以后薄膜振动的固有频率和主振型的变化规律,及褶皱幅度对于动态特性的影响,研究了褶皱薄膜的振动模态与薄膜褶皱构形的对应关系。本文对薄膜褶皱的形成过程及形成机理进行了研究,研究了薄膜褶皱的变形特性及薄膜屈曲后的动态性能。为空间薄膜结构的形面精度控制、稳定性控制及振动控制的深入研究提供了理论依据。更多还原

【Abstract】 Winkles exist extensively in space membrane structures as a local buckling phenomenon. For high precision membrane structure, wrinkles are the main factors related close to the surface accuracy. At the same time, wrinkles may have significant influences on the stability of the structure and dynamic characteristics of the structure. Nowadays, with the development of high precision membrane structure’s application research, the studies on the wrinkling problem have become a hot topic.Tension field theory is the earlier membrane wrinkle theory. This method introduced parameters to modify the constitutive relation on the membrane wrinkle’s region so as to avoid the compressive stress on the membrane. Winkle problem of tension membrane can be solved by tension field theory very well. Due to that wrinkle analysis based on tension field theory can not achieve the out-of-plane deformation of wrinkles; it is not suit for wrinkle analysis requirement of high-precision space membrane structure.In order to describe the out-of-plane deformation accurately, the concept of wrinkle configuration is proposed in this paper. Parameters such as wavelength, amplitude and direction of the wrinkle are used to describe the wrinkle configuration. According to nonlinear large deflection equation, a general approach Stress Extreme Method(SEM) is established to describe the wrinkle configuration parameters. The relationship between half-wavelength and tensile stress of wrinkle’s direction is established. The relationships between wrinkle configuration parameters are then determined. Shear membrane wrinkle and rectangular membrane under corner load are studied by using stress extreme method, and the wrinkle’s configuration parameters are obtained in the end.The wrinkling process of membrane is divided into two stages: the initial buckling and the post-buckling. The mechanism of wrinkle’s formation and expansion are analyzed in theoretical corresponding to these two different stages. The critical load formula of shear membrane at the initial buckling stage is established and the principle of wrinkle’s formation and expansion are then studied at this stage. For the analysis of post-buckling process, initial imperfections will be introduced into the analysis of the membrane wrinkle. The analytical model of membrane wrinkle within initial imperfections is then established, and the law of stress distribution in wrinkle region is analyzed finally. According to the obtained law, expansion process of wrinkling mechanism in the post-buckling is then researched. Combined with theoretical analysis, the probably second buckling phenomenon is also discussed in the post-buckling.Based on the stability theory, a numerical analysis method Direct Disturbances Method is established to analyze the membrane wrinkle, and this method deals with the problem of unremoved imperfections in the conventional nonlinear buckling analysis. Using the direct disturbance method, the critical load in the initial buckling process and the law of wrinkle’s formation and expansion are analyzed. The configuration parameters of membrane wrinkle at post-buckling process are obtained. The balance path of the membrane buckling is also studied. By using numerical method, the secondary buckling phenomenon is researched both in initial buckling process and post-buckling process. The comparison between numerical analysis and theoretical analysis is done in the end.The experimental study of shear membrane wrinkle is performed by using digital photogrammetry system. Through digital photogrammetry system, non-contact measurement of small out of plane deformation can be obtained. The experimental device of shear membrane is designed for high precision measurement requirements. This device can achieve accurate control of the loading process, which is convenient to analyze the entire membrane buckling process. By using high precision digital photogrammetry system, the configuration and configuration parameters of wrinkles are obtained, and in the experiment the second buckling phenomenon can be observed. The validity of the numerical analysis is verified by the results compared with numerical analysis.Dynamic characteristics of membrane buckling are analyzed. Eigenvalue equation of membrane vibration with out-of-plane deformation is established. Numerical method of dynamic analysis is set up based on direct perturbation method. According to this method, vibration characteristics of shear wrinkle membrane and rectangle wrinkle membrane on corner load are studied. Variation rules of nature frequency and fundamental mode are analyzed after wrinkles appear, and so as to influence of wrinkle amplitude on vibration characteristics. The corresponding relationship between vibration mode of wrinkle membrane and wrinkle membrane configuration is reached.In this paper, the formation process and the formation mechanism of membrane wrinkle are studied. The deformation characteristics of membrane wrinkle and dynamic capability of membrane after buckling are also researched. These results provide a theoretical basis for in-depth study of space membrane structure in surface accuracy control, stability control and vibration control.更多还原