本文選題：泊松比 + 梁模型��； 參考：《中國科學(xué)技術(shù)大學(xué)》2015年碩士論文

【摘要】：泊松比是材料的固有屬性之一,每種各向同性材料都有其固有的泊松比。材料泊松比取決于其本身的內(nèi)部微結(jié)構(gòu),對泊松比變化機(jī)制的研究即為其受到單向拉伸時內(nèi)部結(jié)構(gòu)的變形,而結(jié)構(gòu)的拉伸和旋轉(zhuǎn)為重點研究對象。介紹了梁模型和彈簧網(wǎng)絡(luò)模型兩種模擬網(wǎng)絡(luò)結(jié)構(gòu)受到拉伸變形的方法,從拉伸剛度和彎曲剛度的角度對比了兩種模型,兩者拉伸剛度一致,而彎曲剛度由于不同模型的抵抗彎曲的機(jī)制不同導(dǎo)致對應(yīng)關(guān)系不一致但對應(yīng)的量綱是相同的,故兩種模型模擬結(jié)果的趨勢是一致的,模型的選取不會影響結(jié)論。 從簡單基本單元出發(fā),通過對倒插單元等結(jié)構(gòu)的計算和模擬得到的泊松比的相關(guān)影響因素：結(jié)構(gòu)傾角、材料屬性和連接性等。為了進(jìn)一步探究泊松比變化和各個影響因素的依賴性和相關(guān)機(jī)制,從泊松比的計算公式入手,提出了使用回轉(zhuǎn)半徑的拉格朗日應(yīng)變計算泊松比的方法,驗證了大尺寸網(wǎng)絡(luò)結(jié)構(gòu)下該計算方法和經(jīng)典算法結(jié)果一致,并將該算法和邊界拉格朗日應(yīng)變對比,說明了該算法的優(yōu)勢。使用新的泊松比算法推導(dǎo)出了泊松比與結(jié)構(gòu)拉伸和旋轉(zhuǎn)之間的關(guān)系,發(fā)現(xiàn)泊松比與任意兩點間連線的拉伸和旋轉(zhuǎn)有關(guān),得到了拉伸和旋轉(zhuǎn)具體的修正方法。當(dāng)修正后的拉伸大于旋轉(zhuǎn)時,網(wǎng)絡(luò)結(jié)構(gòu)泊松比為負(fù),反之為正。而材料屬性僅影響實際相連邊的拉伸和旋轉(zhuǎn),故在泊松比變化機(jī)制中,材料屬性首先影響相連變的拉伸和旋轉(zhuǎn)的絕對值,繼而影響了任意兩點連線的拉伸和旋轉(zhuǎn),最終決定了泊松比。 本征模態(tài)作為經(jīng)典的研究變形場的方法被用來研究泊松比的機(jī)制。對梁模型的模擬過程求解網(wǎng)絡(luò)結(jié)構(gòu)的本征模態(tài),將網(wǎng)絡(luò)結(jié)構(gòu)受單向拉伸的變形場映射到各本征模態(tài)。提出了本征模態(tài)變形比的算法,經(jīng)典泊松比算法和回轉(zhuǎn)半徑拉格朗日算法都能推導(dǎo)得到整體泊松比為各本征模態(tài)變形比的加權(quán)求和,權(quán)值為模態(tài)自身對整體變形場貢獻(xiàn)和拉伸方向占整體應(yīng)變比例的乘積,應(yīng)變需要和泊松比計算所采用的相匹配。本征模態(tài)作為一個基本的變形場,泊松比的相關(guān)結(jié)果也能適用,當(dāng)模態(tài)變形場修正后的拉伸大于旋轉(zhuǎn)時,該模態(tài)變形比為負(fù),反之為正。 混亂三角網(wǎng)絡(luò)和Voronoi網(wǎng)絡(luò)被用來驗證相關(guān)結(jié)論,而混亂三角網(wǎng)絡(luò)為最常見的復(fù)雜網(wǎng)絡(luò)結(jié)構(gòu),Voronoi網(wǎng)絡(luò)為在各個領(lǐng)域都具有巨大應(yīng)用前景的復(fù)雜網(wǎng)絡(luò)結(jié)構(gòu)。梁模型和彈簧網(wǎng)絡(luò)模型下,兩種網(wǎng)絡(luò)結(jié)構(gòu)泊松比變化趨勢一致,且經(jīng)典泊松比算法和回轉(zhuǎn)半徑拉格朗日應(yīng)變算法結(jié)果相同。得到了不同材料屬性情況下,修正后拉伸和旋轉(zhuǎn)的分布圖,分布圖被修正后拉伸等于旋轉(zhuǎn)的線劃分為泊松比正負(fù)不同的兩個區(qū)域,而材料屬性在決定相連邊拉伸和旋轉(zhuǎn)絕對值的變化趨勢后,整體修正后拉伸和旋轉(zhuǎn)與相連邊修正拉伸和旋轉(zhuǎn)趨勢一致。展示了網(wǎng)絡(luò)結(jié)構(gòu)受單向拉伸時的模態(tài)映射圖,驗證了整體泊松比和模態(tài)變形比是正確性,并給出了模態(tài)拉伸和旋轉(zhuǎn)的分布圖。
[Abstract]:Poisson's ratio is one of the inherent properties of the material, each kind of Poisson isotropic material has its inherent structure. The Poisson's ratio depends on its own internal micro, research on Poisson's ratio change mechanism is the deformation of the internal structure by uniaxial tension, and the structure of the stretch and rotation as the main object of study. Introduces the method of tensile deformation by spring beam model and network model two simulation network structure, from the tensile stiffness and bending stiffness of the angle of comparison of two kinds of models, both tensile stiffness and bending stiffness, due to the different model of resisting bending mechanism leads to different relationship between inconsistent but the corresponding dimension is the same, so the simulation results of the two models is consistent, selection does not affect the conclusion of the model.
Starting from the basic unit factors obtained by calculation and Simulation of Poisson type unit structure of the impact of the ratio of the structure angle, material property and connectivity. In order to further explore the Poisson's ratio and the change of each dependence and related mechanism factors, Poisson's ratio formula from the start, and puts forward the method of Poisson's ratio the calculation of the Lagrange strain using the radius of gyration, verify the network structure of the large size calculation method and the classical algorithm results, and the algorithm and the boundary of the Lagrange strain comparison, explains the algorithm. The advantages of using the new Poisson's ratio algorithm is derived for the relationship between Poisson's ratio and structure of stretching and rotation, found that stretching the connection between any two Poisson ratio and rotation and, by stretching and rotating the specific correction method. When the tensile modified than rotation, network node The ratio of negative Poisson, and is positive. While the material property only affects the actual tensile connected edge and rotation, so the change in Poisson's ratio mechanism, material properties first effect of tensile and rotation of the variable is the absolute value, then the impact of the tension between arbitrary points and rotation, the final decision of the Poisson's ratio.
As the research method of intrinsic modal deformation of classical field was used to study the mechanism of Poisson's ratio. The intrinsic modal simulation process of solving the network structure of the beam model, the deformation field mapping network structure under tension to the intrinsic modal is proposed. The intrinsic modal strain ratio algorithm, the classical Poisson can be deduced the Poisson's ratio of each intrinsic mode of deformation than the weighted sum than the radius of gyration algorithm and Lagrange algorithm, weight product mode itself on the overall deformation and tensile strain direction of the total contribution ratio, strain and Poisson ratio calculated by matching the intrinsic mode. As a basic deformation field, relevant results of Poisson's ratio can also be applied, when the modified modal tensile deformation field is greater than the rotation, the modal deformation ratio is negative and positive.
Chaos triangle network and Voronoi network are used to verify the relevant conclusions, and chaos triangle network as a complex network of the most common structure, Voronoi network as a complex network structure has great application prospect in various fields. The spring beam model and network model, two kinds of network structure of Poisson's ratio is consistent with the trend, and the classical algorithm and the Poisson's ratio the radius of gyration Lagrange strain algorithm obtained the same results. Under the condition of different material properties, the modified tensile and rotational distribution, distribution is modified after stretching equal to the rotation line is divided into two regions of positive and negative Poisson's ratio of different material properties, and the connecting edge stretching and rotating the absolute value of the change trend in the overall decision, the modified stretch and rotation and connected edge correction stretching and rotating the same trend. Show the modal mapping network structure under tension, verify the overall Poisson The ratio of the ratio and the modal deformation ratio is correct, and the distribution diagram of the mode stretching and rotation is given.

【學(xué)位授予單位】：中國科學(xué)技術(shù)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：TB301

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相關(guān)期刊論文 前1條

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本文編號：1732532