泊松比与拉伸和旋转的内在联系

发布时间：2018-04-10 19:11

本文选题：泊松比 + 梁模型　；参考：《中国科学技术大学》2015年硕士论文

【摘要】：泊松比是材料的固有属性之一,每种各向同性材料都有其固有的泊松比。材料泊松比取决于其本身的内部微结构,对泊松比变化机制的研究即为其受到单向拉伸时内部结构的变形,而结构的拉伸和旋转为重点研究对象。介绍了梁模型和弹簧网络模型两种模拟网络结构受到拉伸变形的方法,从拉伸刚度和弯曲刚度的角度对比了两种模型,两者拉伸刚度一致,而弯曲刚度由于不同模型的抵抗弯曲的机制不同导致对应关系不一致但对应的量纲是相同的,故两种模型模拟结果的趋势是一致的,模型的选取不会影响结论。从简单基本单元出发,通过对倒插单元等结构的计算和模拟得到的泊松比的相关影响因素：结构倾角、材料属性和连接性等。为了进一步探究泊松比变化和各个影响因素的依赖性和相关机制,从泊松比的计算公式入手,提出了使用回转半径的拉格朗日应变计算泊松比的方法,验证了大尺寸网络结构下该计算方法和经典算法结果一致,并将该算法和边界拉格朗日应变对比,说明了该算法的优势。使用新的泊松比算法推导出了泊松比与结构拉伸和旋转之间的关系,发现泊松比与任意两点间连线的拉伸和旋转有关,得到了拉伸和旋转具体的修正方法。当修正后的拉伸大于旋转时,网络结构泊松比为负,反之为正。而材料属性仅影响实际相连边的拉伸和旋转,故在泊松比变化机制中,材料属性首先影响相连变的拉伸和旋转的绝对值,继而影响了任意两点连线的拉伸和旋转,最终决定了泊松比。本征模态作为经典的研究变形场的方法被用来研究泊松比的机制。对梁模型的模拟过程求解网络结构的本征模态,将网络结构受单向拉伸的变形场映射到各本征模态。提出了本征模态变形比的算法,经典泊松比算法和回转半径拉格朗日算法都能推导得到整体泊松比为各本征模态变形比的加权求和,权值为模态自身对整体变形场贡献和拉伸方向占整体应变比例的乘积,应变需要和泊松比计算所采用的相匹配。本征模态作为一个基本的变形场,泊松比的相关结果也能适用,当模态变形场修正后的拉伸大于旋转时,该模态变形比为负,反之为正。混乱三角网络和Voronoi网络被用来验证相关结论,而混乱三角网络为最常见的复杂网络结构,Voronoi网络为在各个领域都具有巨大应用前景的复杂网络结构。梁模型和弹簧网络模型下,两种网络结构泊松比变化趋势一致,且经典泊松比算法和回转半径拉格朗日应变算法结果相同。得到了不同材料属性情况下,修正后拉伸和旋转的分布图,分布图被修正后拉伸等于旋转的线划分为泊松比正负不同的两个区域,而材料属性在决定相连边拉伸和旋转绝对值的变化趋势后,整体修正后拉伸和旋转与相连边修正拉伸和旋转趋势一致。展示了网络结构受单向拉伸时的模态映射图,验证了整体泊松比和模态变形比是正确性,并给出了模态拉伸和旋转的分布图。
[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.

【学位授予单位】：中国科学技术大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TB301

【参考文献】