薄膜结构的有限质点法计算理论与应用研究

发布时间：2018-04-24 21:37

本文选题：向量式固体力学 + 有限质点法　；参考：《浙江大学》2015年博士论文

【摘要】：薄膜结构是一种典型的柔性张力体系。由于膜材本身几乎没有抗弯、抗剪能力,需要预应力来提供结构体系的刚度,因此它有着完全不同于传统刚性结构的力学性能,其结构行为往往表现出较显著的非线性特征。鉴于有限质点法在结构复杂非线性问题分析中的独特优势,本文以课题组现有研究成果为基础,进一步发展了适用于薄膜结构分析求解的有限质点法计算理论,并将其作为基本分析手段,对当前薄膜结构研究中存在的若干共性与难点问题及技术挑战逐一展开研究和探讨。本文详细介绍了国内外薄膜结构分析计算方法的研究现状以及此类结构在工程界的应用情况,总结归纳了膜材与薄膜结构的基本力学特点和分析中需要考虑的关键因素,简要评述了有限质点法的应用优势,明确了本文要做的研究工作。有限质点法以点值描述、途经单元和虚拟逆向运动为基本概念,用清晰的物理模型取代了复杂的函数连续体模型,本质上属于一种几何非线性动力描述方法,在处理结构的几何大变位、非线性材料本构、弹性变形与机构运动耦合以及不连续变形等复杂力学问题时有独特的优势。文中系统阐述了有限质点法的基本概念和原理,详细推导了该方法用于薄膜结构分析计算的基本公式,给出了针对运动约束质点的特殊处理方法,建立了求解各类静、动力问题的基本程序框架,为后文开展薄膜结构的各类非线性力学问题研究奠定了基础。发展了以有限质点法为核心的薄膜结构初始形态分析方法。针对两类预应力引入方式不同的膜结构形式—张拉膜结构和充气膜结构,分别给出了采用有限质点法进行初始形态分析的思路和计算流程,并改进了原有的控制方程求解技术,加快了收敛速度。针对极小曲面、不等应力膜面找形及初始状态质点分布控制等关键问题分别提出了相应的分析策略。针对索杆膜结构的初始形态协同分析问题,提出了虚设索杆内力和控制索杆位形两种分析思路；针对以内压和矢高(或体积)为约束条件的充气膜结构初始形态问题提出了先找形后找态的分析思路及相应的实现方式。发展了同时考虑膜材各向异性和非线性拉伸特性的求解薄膜结构大变形问题的计算方法。基于薄膜的材料力学特性分别建立了正交异性线弹性本构模型和各向异性非线性本构模型,特别讨论了确定弹性主轴坐标方向的简便计算方法,实现了对薄膜结构几何与材料大变形过程的有效模拟。基于张力场模型,应用薄膜非线性计算理论对薄膜结构的褶皱问题进行了模拟和分析,重点研究了膜面状态的判定和褶皱区域的处理。通过对膜面平衡条件的分析,建立了区分三种不同受力状态(即张紧、褶皱和松弛)的判定准则,然后基于Raddeman分析模型并借鉴弹塑性问题中塑性修正的概念,建立了一种与有限质点法中显式增量计算格式相匹配的褶皱分析方法,并给出了在计算程序中的具体实现流程。该方法对材料本构关系没有特别限制,线性或非线性、各向同性或各向异性膜材均可适用。为了进一步获得褶皱的波长、幅值和数量等具体构形信息,发展了基于薄壳稳定理论的薄膜褶皱精细化分析技术。根据实际膜材具有少量弯曲刚度的特点以及薄膜褶皱与薄壳屈曲行为的相似性,特别构建了能够同时考虑面内薄膜变形和面外弯剪变形的有限质点法薄壳计算模型。在此基础上,通过引入瞬时扰动、位移控制等关键技术并借助于方法对非线性问题的分析能力,实现了对膜面褶皱形态演化过程的准确模拟。最后,针对薄膜的碰撞接触、折叠状态展开成形、开裂破坏等一系列复杂的强非线性动态行为,以物理过程的真实描述为出发点,分别建立了“点-面”接触模型、多气室流场模型及质点分离与分裂模型,并给出了各个分析模型在有限质点法中的实现方式和算法流程。综合运用以上各部分的研究成果,对薄膜结构的各种复杂动态行为进行了仿真计算,结合实例分析验证了算法的有效性。通过理论推导、大量数值模拟及程序模块的编制表明,本文所发展的薄膜结构有限质点法分析计算理论是可行且有效的,可以作为工程师和研究者进行薄膜结构复杂行为分析的一种新的技术手段。同时论文最后还提出了今后有待解决和完善的若干问题。
[Abstract]:Thin film structure is a typical flexible tension system. Because the membrane itself has almost no bending and shearing ability, it needs prestress to provide the stiffness of the structural system, so it has the mechanical properties that are completely different from the traditional rigid structure, and its structure behavior often shows a more obvious nonlinear characteristic. On the basis of the existing research results of the project group, this paper further develops the finite particle method calculation theory which is suitable for the analysis and solution of the thin film structure, and uses it as the basic analysis method to solve some common and difficult problems and technical challenges in the research of the current film structure. Study and discuss.
The present situation of the analysis and calculation of thin film structure at home and abroad as well as the application of this kind of structure in the engineering field are described in detail. The basic mechanical characteristics of the membrane and film structure are summarized and the key factors to be considered in the analysis are summarized. The advantages of the finite particle method are briefly reviewed, and the research work to be made in this paper is clarified. Do.
The finite particle method is described by the point value, through the element and the virtual reverse motion as the basic concept. The complex function continuum model is replaced by a clear physical model. In essence, it belongs to a geometric nonlinear dynamic description method, which is used to deal with the large geometric change of the structure, the nonlinear material material constitutive, the elastic deformation and mechanism motion coupling, and the failure. In this paper, the basic concepts and principles of the finite particle method are expounded systematically, and the basic formulas for the analysis and calculation of the thin film structure are derived in detail. The special treatment method for the motion constraint particles is given, and the basic program framework for solving all kinds of static and dynamic problems is established. It lays the foundation for the study of various nonlinear mechanical problems of membrane structures.
The initial morphological analysis method of thin film structure with the finite particle method as the core is developed. Aiming at the different forms of membrane structure and inflatable membrane structure of the two types of prestressing force, the idea and the calculation flow of the initial shape analysis by the finite particle method are given respectively, and the original control equation is improved. The corresponding analysis strategies are proposed for the key problems, such as the minimal surface, the shape finding of the unequal stress film surface and the control of the initial state particle distribution. In view of the problem of the initial form synergistic analysis of the cable rod membrane structure, two kinds of analysis ideas are proposed for the internal force of the cable rod and the control cable position, and the internal pressure and the vector are used for the analysis of the internal pressure and the vector. The initial shape problem of inflatable membrane structure with high (or volume) constraint conditions is put forward.
A calculation method is developed to solve the large deformation problem of thin film structure considering the anisotropy of the membrane and the nonlinear tensile properties. Based on the mechanical properties of the film, the orthotropic linear elastic constitutive model and the anisotropic nonlinear constitutive model are established, and the simple calculation method for determining the direction of the elastic spindle is particularly discussed. The effective simulation of large deformation process of membrane structure and material is realized.
Based on the tension field model, the folds of the thin film structure are simulated and analyzed by the theory of film nonlinear calculation. The determination of the film surface state and the processing of the fold region are emphatically studied. By the analysis of the equilibrium conditions of the membrane surface, the criteria for distinguishing three different stress states (i.e. tensioning, folds and relaxation) are established, and the base is then based on the analysis of the equilibrium conditions of the membrane surface. In the Raddeman analysis model and drawing on the concept of plastic correction in elastoplastic problems, a fold analysis method matching the explicit incremental calculation scheme in the finite particle method is established, and the concrete realization process in the calculation program is given. The method has no special restrictions on the constitutive relation of materials, linear or nonlinear, isotropic or isotropic. Anisotropic membrane materials can be applied.
In order to further obtain the specific configuration information such as the wavelength, amplitude and quantity of the fold, the thin film wrinkle refinement analysis technology based on the thin shell stability theory has been developed. According to the characteristics of a small amount of flexural rigidity and the similarity between the thin film folds and the buckling behavior of the thin shell, the deformation of thin film folds and thin shell is specially constructed to consider the film deformation at the same time. On this basis, on this basis, by introducing the key techniques of instantaneous disturbance, displacement control and the aid of the analytical ability of the nonlinear problem, the accurate simulation of the evolution process of the membrane folds is realized.
Finally, a series of complex strong nonlinear dynamic behaviors, such as the collision contact of the film, the forming of the folding state, the cracking and failure, the point to surface contact model, the flow field model of the multi gas chamber and the separation and splitting model of the particle, and the finite particles are given. By using the results of the above parts, the simulation calculation of various complex dynamic behavior of the film structure is carried out, and the effectiveness of the algorithm is verified by the case analysis.
Through theoretical deduction, a large number of numerical simulation and programming modules have shown that the finite particle method analysis and calculation theory developed in this paper is feasible and effective. It can be used as a new technical means for engineers and researchers to analyze the complex behavior of thin film structure. At the same time, the paper also puts forward to be solved in the future. And a number of problems to be perfected.

【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TU383

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