本文選題：向量式固體力學(xué) + 有限質(zhì)點(diǎn)法　； 參考：《浙江大學(xué)》2015年博士論文

【摘要】：薄膜結(jié)構(gòu)是一種典型的柔性張力體系。由于膜材本身幾乎沒(méi)有抗彎、抗剪能力,需要預(yù)應(yīng)力來(lái)提供結(jié)構(gòu)體系的剛度,因此它有著完全不同于傳統(tǒng)剛性結(jié)構(gòu)的力學(xué)性能,其結(jié)構(gòu)行為往往表現(xiàn)出較顯著的非線性特征。鑒于有限質(zhì)點(diǎn)法在結(jié)構(gòu)復(fù)雜非線性問(wèn)題分析中的獨(dú)特優(yōu)勢(shì),本文以課題組現(xiàn)有研究成果為基礎(chǔ),進(jìn)一步發(fā)展了適用于薄膜結(jié)構(gòu)分析求解的有限質(zhì)點(diǎn)法計(jì)算理論,并將其作為基本分析手段,對(duì)當(dāng)前薄膜結(jié)構(gòu)研究中存在的若干共性與難點(diǎn)問(wèn)題及技術(shù)挑戰(zhàn)逐一展開(kāi)研究和探討。 本文詳細(xì)介紹了國(guó)內(nèi)外薄膜結(jié)構(gòu)分析計(jì)算方法的研究現(xiàn)狀以及此類結(jié)構(gòu)在工程界的應(yīng)用情況,總結(jié)歸納了膜材與薄膜結(jié)構(gòu)的基本力學(xué)特點(diǎn)和分析中需要考慮的關(guān)鍵因素,簡(jiǎn)要評(píng)述了有限質(zhì)點(diǎn)法的應(yīng)用優(yōu)勢(shì),明確了本文要做的研究工作。 有限質(zhì)點(diǎn)法以點(diǎn)值描述、途經(jīng)單元和虛擬逆向運(yùn)動(dòng)為基本概念,用清晰的物理模型取代了復(fù)雜的函數(shù)連續(xù)體模型,本質(zhì)上屬于一種幾何非線性動(dòng)力描述方法,在處理結(jié)構(gòu)的幾何大變位、非線性材料本構(gòu)、彈性變形與機(jī)構(gòu)運(yùn)動(dòng)耦合以及不連續(xù)變形等復(fù)雜力學(xué)問(wèn)題時(shí)有獨(dú)特的優(yōu)勢(shì)。文中系統(tǒng)闡述了有限質(zhì)點(diǎn)法的基本概念和原理,詳細(xì)推導(dǎo)了該方法用于薄膜結(jié)構(gòu)分析計(jì)算的基本公式,給出了針對(duì)運(yùn)動(dòng)約束質(zhì)點(diǎn)的特殊處理方法,建立了求解各類靜、動(dòng)力問(wèn)題的基本程序框架,為后文開(kāi)展薄膜結(jié)構(gòu)的各類非線性力學(xué)問(wèn)題研究奠定了基礎(chǔ)。 發(fā)展了以有限質(zhì)點(diǎn)法為核心的薄膜結(jié)構(gòu)初始形態(tài)分析方法。針對(duì)兩類預(yù)應(yīng)力引入方式不同的膜結(jié)構(gòu)形式—張拉膜結(jié)構(gòu)和充氣膜結(jié)構(gòu),分別給出了采用有限質(zhì)點(diǎn)法進(jìn)行初始形態(tài)分析的思路和計(jì)算流程,并改進(jìn)了原有的控制方程求解技術(shù),加快了收斂速度。針對(duì)極小曲面、不等應(yīng)力膜面找形及初始狀態(tài)質(zhì)點(diǎn)分布控制等關(guān)鍵問(wèn)題分別提出了相應(yīng)的分析策略。針對(duì)索桿膜結(jié)構(gòu)的初始形態(tài)協(xié)同分析問(wèn)題,提出了虛設(shè)索桿內(nèi)力和控制索桿位形兩種分析思路；針對(duì)以內(nèi)壓和矢高(或體積)為約束條件的充氣膜結(jié)構(gòu)初始形態(tài)問(wèn)題提出了先找形后找態(tài)的分析思路及相應(yīng)的實(shí)現(xiàn)方式。 發(fā)展了同時(shí)考慮膜材各向異性和非線性拉伸特性的求解薄膜結(jié)構(gòu)大變形問(wèn)題的計(jì)算方法�；诒∧さ牟牧狭W(xué)特性分別建立了正交異性線彈性本構(gòu)模型和各向異性非線性本構(gòu)模型,特別討論了確定彈性主軸坐標(biāo)方向的簡(jiǎn)便計(jì)算方法,實(shí)現(xiàn)了對(duì)薄膜結(jié)構(gòu)幾何與材料大變形過(guò)程的有效模擬。 基于張力場(chǎng)模型,應(yīng)用薄膜非線性計(jì)算理論對(duì)薄膜結(jié)構(gòu)的褶皺問(wèn)題進(jìn)行了模擬和分析,重點(diǎn)研究了膜面狀態(tài)的判定和褶皺區(qū)域的處理。通過(guò)對(duì)膜面平衡條件的分析,建立了區(qū)分三種不同受力狀態(tài)(即張緊、褶皺和松弛)的判定準(zhǔn)則,然后基于Raddeman分析模型并借鑒彈塑性問(wèn)題中塑性修正的概念,建立了一種與有限質(zhì)點(diǎn)法中顯式增量計(jì)算格式相匹配的褶皺分析方法,并給出了在計(jì)算程序中的具體實(shí)現(xiàn)流程。該方法對(duì)材料本構(gòu)關(guān)系沒(méi)有特別限制,線性或非線性、各向同性或各向異性膜材均可適用。 為了進(jìn)一步獲得褶皺的波長(zhǎng)、幅值和數(shù)量等具體構(gòu)形信息,發(fā)展了基于薄殼穩(wěn)定理論的薄膜褶皺精細(xì)化分析技術(shù)。根據(jù)實(shí)際膜材具有少量彎曲剛度的特點(diǎn)以及薄膜褶皺與薄殼屈曲行為的相似性,特別構(gòu)建了能夠同時(shí)考慮面內(nèi)薄膜變形和面外彎剪變形的有限質(zhì)點(diǎn)法薄殼計(jì)算模型。在此基礎(chǔ)上,通過(guò)引入瞬時(shí)擾動(dòng)、位移控制等關(guān)鍵技術(shù)并借助于方法對(duì)非線性問(wèn)題的分析能力,實(shí)現(xiàn)了對(duì)膜面褶皺形態(tài)演化過(guò)程的準(zhǔn)確模擬。 最后,針對(duì)薄膜的碰撞接觸、折疊狀態(tài)展開(kāi)成形、開(kāi)裂破壞等一系列復(fù)雜的強(qiáng)非線性動(dòng)態(tài)行為,以物理過(guò)程的真實(shí)描述為出發(fā)點(diǎn),分別建立了“點(diǎn)-面”接觸模型、多氣室流場(chǎng)模型及質(zhì)點(diǎn)分離與分裂模型,并給出了各個(gè)分析模型在有限質(zhì)點(diǎn)法中的實(shí)現(xiàn)方式和算法流程。綜合運(yùn)用以上各部分的研究成果,對(duì)薄膜結(jié)構(gòu)的各種復(fù)雜動(dòng)態(tài)行為進(jìn)行了仿真計(jì)算,結(jié)合實(shí)例分析驗(yàn)證了算法的有效性。 通過(guò)理論推導(dǎo)、大量數(shù)值模擬及程序模塊的編制表明,本文所發(fā)展的薄膜結(jié)構(gòu)有限質(zhì)點(diǎn)法分析計(jì)算理論是可行且有效的,可以作為工程師和研究者進(jìn)行薄膜結(jié)構(gòu)復(fù)雜行為分析的一種新的技術(shù)手段。同時(shí)論文最后還提出了今后有待解決和完善的若干問(wèn)題。
[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.

【學(xué)位授予單位】：浙江大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2015
【分類號(hào)】：TU383

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