基于罚函数法和双势能理论的DDA接触理论研究及高阶位移模式理论应用
发布时间：2019-04-01 09:06
【摘要】：不连续变形方法(DDA)是一种基于最小势能原理,可较为准确计算块体系统中块体运动速度和位移的理论。在使用罚函数法处理块体间接触时,块体系统机械能计算精度较低。本文提出变刚度法和冲量法处理块体间的接触,以解决机械能计算不准确的问题,同时结合双势能接触理论和高阶位移模式理论计算块体间的接触力和块体上的变形和应力,以提高计算精度。本文研究的主要内容如下:(1)介绍了 DDA理论并对整体方程组的推导过程和增广拉格朗日乘子法等关键内容做出了解释。(2)从机械能守恒和损耗的角度分析罚函数法接触理论的优缺点,并提出变接触刚度法在无摩擦力作用时解决DDA圆盘在接触和碰撞过程中的机械能不守恒问题,分析结果表明变接触刚度法可以有效阻止碰撞过程中机械能发生突变,但变刚度法在有摩擦力作用时失去效用,同时对移修正公式进行了介绍。(3)在罚函数法处理接触时,块体系统机械能计算精度较低。介绍冲量法以解决上述问题,冲量法是以刚体块体接触前的线速度和角速度为己知量,通过冲量定理建立方程组以计算块体接触分离时的速度。将冲量法编入算例程序中以验证冲量法的有效性,分析发现冲量法可有效的解决块体系统机械能不守恒的问题。(4)将莫尔库仑准则和最大拉应力准则用于判断块体间的接触状态。将悬臂梁离散成紧凑排列的正多边形离散体,设置较大的凝聚力和抗拉强度值以阻止块体间的相对运动。在不同多边形尺寸下使用DDA方法模拟悬臂梁在相同位移载荷作用下的变形,提取梁上边缘多边形的应变与材料力学解进行对比,以此研究多边形块体与梁的相对尺寸对计算精度的影响,分析发现多边形块体相对尺寸越小时,应变计算精度越高。(5)引入双势能理论,计算块体间的接触力。使用高阶位移函数计算块体内部应力和块体上点的位移。将双势能理论和高阶位移模式理论结合起来,编写算例程序,计算块体间接触力和块体变形,发现双势能接触理论可较为准确的计算块体间接触力,高阶位移理论可精确的计算悬臂梁上点的应力和位移。
[Abstract]:Discontinuous deformation method (DDA) is a theory based on the principle of minimum potential energy, which can accurately calculate the velocity and displacement of block motion in a block system. When the penalty function method is used to deal with the contact between blocks, the accuracy of mechanical energy calculation of the block system is lower. In this paper, the variable stiffness method and the impulse method are proposed to deal with the contact between blocks in order to solve the problem of inaccurate calculation of mechanical energy. At the same time, the contact force between blocks and the deformation and stress on the block are calculated by means of the theory of double potential energy contact and the theory of higher order displacement mode. In order to improve the accuracy of calculation. The main contents of this paper are as follows: (1) the DDA theory is introduced and the derivation process of the global equations and the augmented Lagrangian multiplier method are explained. (2) the mechanical energy conservation and loss are divided into two parts. To analyze the advantages and disadvantages of the contact theory of penalty function method, The variable contact stiffness method is proposed to solve the problem of non-conservation of mechanical energy in the process of contact and collision of DDA disc when there is no friction force. The results show that the variable contact stiffness method can effectively prevent the sudden change of mechanical energy in the process of collision. However, the variable stiffness method is ineffective when there is friction, and the displacement correction formula is also introduced. (3) when the penalty function method is used to deal with the contact, the accuracy of mechanical energy calculation of the block system is lower. The impulse method is introduced to solve the above problems. The impulse method is based on the linear velocity and angular velocity before the contact of the rigid block. The equations are set up by the impulse theorem to calculate the velocity of the block contact separation. The impulse method is programmed in a numerical example to verify the validity of the impulse method. It is found that the impulse method can effectively solve the problem of non-conservation of mechanical energy in block system. (4) the Mohr-Coulomb criterion and the maximum tensile stress criterion are used to judge the contact state between blocks. The cantilever is discretized into a compact arrangement of regular polygonal discrete bodies, and a larger cohesion and tensile strength value is set to prevent the relative movement of the blocks. The DDA method is used to simulate the deformation of cantilever beam under the same displacement load under different polygon sizes. The strain of the polygon on the upper edge of the beam is extracted and compared with the mechanical solution of the material. It is found that the smaller the relative size of polygonal block is, the higher the precision of strain calculation is. (5) the theory of double potential energy is introduced to calculate the contact force between blocks. The high-order displacement function is used to calculate the internal stress and displacement of points on the block. By combining the theory of double potential energy with the theory of higher order displacement model, a numerical program is compiled to calculate the indirect contact force and deformation of the block. It is found that the contact theory of double potential energy can accurately calculate the indirect contact force of the block. The higher-order displacement theory can accurately calculate the stress and displacement of the cantilever beam.
【学位授予单位】：西南交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O302
本文编号：2451434
[Abstract]:Discontinuous deformation method (DDA) is a theory based on the principle of minimum potential energy, which can accurately calculate the velocity and displacement of block motion in a block system. When the penalty function method is used to deal with the contact between blocks, the accuracy of mechanical energy calculation of the block system is lower. In this paper, the variable stiffness method and the impulse method are proposed to deal with the contact between blocks in order to solve the problem of inaccurate calculation of mechanical energy. At the same time, the contact force between blocks and the deformation and stress on the block are calculated by means of the theory of double potential energy contact and the theory of higher order displacement mode. In order to improve the accuracy of calculation. The main contents of this paper are as follows: (1) the DDA theory is introduced and the derivation process of the global equations and the augmented Lagrangian multiplier method are explained. (2) the mechanical energy conservation and loss are divided into two parts. To analyze the advantages and disadvantages of the contact theory of penalty function method, The variable contact stiffness method is proposed to solve the problem of non-conservation of mechanical energy in the process of contact and collision of DDA disc when there is no friction force. The results show that the variable contact stiffness method can effectively prevent the sudden change of mechanical energy in the process of collision. However, the variable stiffness method is ineffective when there is friction, and the displacement correction formula is also introduced. (3) when the penalty function method is used to deal with the contact, the accuracy of mechanical energy calculation of the block system is lower. The impulse method is introduced to solve the above problems. The impulse method is based on the linear velocity and angular velocity before the contact of the rigid block. The equations are set up by the impulse theorem to calculate the velocity of the block contact separation. The impulse method is programmed in a numerical example to verify the validity of the impulse method. It is found that the impulse method can effectively solve the problem of non-conservation of mechanical energy in block system. (4) the Mohr-Coulomb criterion and the maximum tensile stress criterion are used to judge the contact state between blocks. The cantilever is discretized into a compact arrangement of regular polygonal discrete bodies, and a larger cohesion and tensile strength value is set to prevent the relative movement of the blocks. The DDA method is used to simulate the deformation of cantilever beam under the same displacement load under different polygon sizes. The strain of the polygon on the upper edge of the beam is extracted and compared with the mechanical solution of the material. It is found that the smaller the relative size of polygonal block is, the higher the precision of strain calculation is. (5) the theory of double potential energy is introduced to calculate the contact force between blocks. The high-order displacement function is used to calculate the internal stress and displacement of points on the block. By combining the theory of double potential energy with the theory of higher order displacement model, a numerical program is compiled to calculate the indirect contact force and deformation of the block. It is found that the contact theory of double potential energy can accurately calculate the indirect contact force of the block. The higher-order displacement theory can accurately calculate the stress and displacement of the cantilever beam.
【学位授予单位】：西南交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O302
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