基于离散单元法的简单结构静动力响应数值模拟研究

发布时间：2018-05-31 21:41

本文选题：三维粱(杆)系结构 + 离散单元法　；参考：《东南大学》2015年硕士论文

【摘要】：离散单元法(Discrete Element Method,DEM)是主要模拟非连续介质力学行为的数值分析方法。该方法的基本思想是将研究区域划分成离散的、独立运动的单元,单元间允许发生相对运动和碰撞,无需刻意满足变形协调条件和连续条件。离散单元法利用显示的动态松弛法按时步迭代求解各个单元的运动状态,无需集成结构刚度矩阵,避免了由于刚度矩阵奇异造成的计算不收敛。本文利用改进的DEM单元模型,实现了分析过程由连续体到非连续体的顺利过渡。同时,详细讨论了模型各参数的取值方法及其对计算结果的影响。最后,运用本文改进的DEM模型对结构倒塌全过程包含的线弹性、几何非线性、材料非线性、断裂、碰撞等多个问题进行了数值模拟分析。主要内容和结论如下：(1)基于颗粒流连结模型和接触型模型建立了连续介质的离散单元模型,通过杆端力和杆端位移关系推导了适用于多种截面形式的二维离散元接触刚度系数。为选取合理的离散元模型参数,对单元形状和数量、单元排列形式、单元接触模型、模型边界条件的处理、实际荷载等效方式、时间步长以及阻尼系数等参数的取值进行了系统研究。改进颗粒流模型,将DEM模型由二维扩展到三维。通过杆端力和杆端位移关系推导了三维DEM模型的接触刚度系数,并利用等效质量和等效刚度修正单元质量和转动惯量,以确保分析过程正确有效。(2)利用离散单元法对不同结构形式进行几何非线性静/动力响应、材料非线性数值模拟。本文基于Mises屈服准则确立了广义应力(单元内力)屈服条件,进而建立了DEM弹塑性接触本构关系。利用塑性铰模型和考虑截面塑性发展的模型推导了简单内力状态下的DEM塑性接触刚度系数,同时,利用广义应力屈服面的正交性推导了复杂内力状态下的离散单元塑性刚度系数矩阵。通过多个算例验证了改进的DEM模型求解连续介质非线性问题的可行性。(3)建立了构件断裂、单元碰撞模型,编写程序检测单元间接触关系,更新单元连结,计算碰撞接触力。利用本文各部分研究成果模拟分析了K6型单层球面网壳振动台倒塌过程和框架结构爆炸倒塌过程,并将计算结果与试验结果进行了比较,验证了接触检测程序的正确性以及DEM法在分析结构由连续介质过渡到非连续介质问题的可行性。(4)本文采用Fortran语言编写了二维、三维DEM法计算程序,并将弹塑性分析、单元断裂、碰撞检测、碰撞接触力计算等分别编写为独立模块,需要时调用即可。通过对不同结构形式(包括简单机构、框架、桁架、网壳等)的力学行为进行模拟,并将其计算结果与其它方法得到的结果进行了对比,验证了本文DEM方法在分析结构动静力响应、弹塑性大变形及断裂碰撞等问题中的适用性。
[Abstract]:Discrete Element method (DEM) is a numerical method for simulating the mechanical behavior of discontinuous media. The basic idea of this method is to divide the study area into discrete and independent moving units. The relative motion and collision are allowed between the elements without the need to satisfy the deformation coordination condition and the continuous condition. The discrete element method uses the displayed dynamic relaxation method to solve the motion state of each element step by step on time without the need to integrate the stiffness matrix of the structure so as to avoid the non-convergence of the calculation caused by the singularity of the stiffness matrix. In this paper, the improved DEM element model is used to realize the smooth transition from continuum to discontinuum. At the same time, the method of choosing each parameter of the model and its influence on the calculation results are discussed in detail. Finally, the improved DEM model is used to simulate the linear elasticity, geometric nonlinearity, material nonlinearity, fracture, collision and so on. The main contents and conclusions are as follows: (1) based on the particle flow connection model and the contact model, the discrete element model of continuous medium is established, and the contact stiffness coefficients of two-dimensional discrete elements suitable for various cross-section forms are derived by means of rod end force and pole end displacement relationship. In order to select reasonable parameters of discrete element model, to deal with the shape and quantity of element, the form of arrangement of element, the contact model of element, the boundary condition of model, the equivalent mode of actual load, The time step and damping coefficient are studied systematically. The particle flow model is improved and the DEM model is extended from two to three dimensions. The contact stiffness coefficient of the three-dimensional DEM model is derived by the relationship between the end force and the displacement of the rod, and the mass and moment of inertia of the element are corrected by using the equivalent mass and the equivalent stiffness. In order to ensure that the analysis process is correct and effective, the discrete element method is used to simulate the geometric nonlinear static / dynamic responses of different structures and the material nonlinear numerical simulation. In this paper, the generalized stress (internal force) yield condition is established based on the Mises yield criterion, and then the DEM elastoplastic contact constitutive relation is established. The plastic contact stiffness coefficient of DEM under simple internal force is derived by using the plastic hinge model and the model considering the plastic development of section. By using the orthogonality of the generalized stress yield surface, the plastic stiffness coefficient matrix of discrete elements under complex internal forces is derived. The feasibility of the improved DEM model for solving the nonlinear problem of continuum medium is verified by several examples.) the component fracture, the element collision model, the program to check the contact relationship between the elements, the renewal of the element connection, and the calculation of the collision contact force are established. The collapse process of K6 single-layer spherical reticulated shell vibration table and the explosion collapse process of frame structure are simulated and analyzed by using the research results of each part of this paper, and the calculated results are compared with the experimental results. The correctness of the contact detection program and the feasibility of DEM method in analyzing the transition of structure from continuous medium to discontinuous medium are verified. In this paper, the two-dimensional and three-dimensional DEM program is compiled by Fortran language, and the elastic-plastic analysis and element fracture are carried out. Collision detection, collision contact force calculation and so on are written as independent modules, which can be called when needed. The mechanical behavior of different structural forms (including simple mechanism, frame, truss, latticed shell, etc.) is simulated, and the calculated results are compared with those obtained by other methods. The applicability of the DEM method in the analysis of structural dynamic and dynamic responses, large elastic-plastic deformation and fracture collisions is verified.
【学位授予单位】：东南大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TU311

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