一类界面元建模与分析方法及其在装备设计中的应用研究

发布时间：2018-05-29 02:56

本文选题：离散元 + 有限元　；参考：《浙江大学》2013年博士论文

【摘要】：界面元是指两种连续结构或连续结构与离散介质在接触界面一定范围内的有限单元集或有限单元/粒子单元集。界面元方法是研究界面元区域内单元之间的力作用和结点属性等效传递的一种数字化模拟方法。本文提出界面元方法来模拟和分析装备工作过程中连续结构与离散介质、连续结构与连续结构在相互作用界面的作用力计算、单元结点属性的等效传递问题,研究工作主要体现在以下五个方面： 1针对界面元方法预处理阶段需要快速生成离散颗粒集问题,提出一种几何和物理相结合的颗粒集生成算法,充分利用离散介质颗粒单元的几何特性和颗粒下落时的物理特性,构建了几何与物理特性相结合的颗粒堆积移动模型,快速生成二维域圆形颗粒集和三维域球形颗粒集,生成颗粒集的时间与颗粒数量成线性关系,且颗粒集密度高,生成时间短。 2为了模拟和计算连续结构与离散介质之间的相互作用力,提出基于单元/粒子接触的界面元方法,根据有限单元与粒子单元之间的几何接触情形,采用线弹性模型直接计算单个离散颗粒与有限元面片间的作用力,再将计算得到的作用力等效至有限元节点,进一步计算有限元节点的受力和位移,可视化显示了离散介质的受力、变化状况和连续结构的受力、应变状况。 3针对大规模粒子集在机械结构作用下的应力、应变分析问题,提出基于单元／粒子交迭的界面元模型,将直接受结构作用的区域及其近邻区域用离散元表示,较远区域则用六面体有限单元表示,两种单元区域在它们的相互作用界面有一定程度的交迭。在交迭区,将有限单元内离散粒子的质量、受力等效传递至有限元节点,得有限元节点加速度,将有限元节点的速度、加速度等参插值至离散单元,得离散粒子所在位置的应变和应力,同时以交迭区有限单元的受力作为边界条件求解整个区域的受力和变形状况。 4为了解决多个有限元网格在接触界面的节点不匹配而导致节点属性不能光滑传递的问题,提出异构网格界面元方法,构建了二维异构的四边形单元节点及其错位节点形函数,实现异构四边形单元网格在接触界面属性的光滑传递,将该方法进一步延伸至四边形网格与三角形网格之间的界面元分析；同时研究了三维异构的六面体单元网格之间结点属性的光滑传递方法。通过一个异构网格接触实例验证了方法的正确性,并将方法应用于齿轮的接触分析。 5提出了主/辅网格节点属性等效集成方法，，以解决异构有限元网格多场信息难以集成显示的问题。将多个有限元网格模型中的一个作为主网格,其它作为辅网格,将辅网格单元节点信息向主网格节点等效转移,最终在主网格单元节点中实现多场信息的集成显示。研究结果分析了盾构刀盘掘进过程中刀具和刀盘受到的应力场和温度场综合作用分布和多场作用的最强区域,为刀具和刀盘设计提供了依据。
[Abstract]:The interface element refers to the finite element set or the finite element / particle unit set of two continuous structures or continuous structures and discrete media within a certain range of contact interfaces. The interface element method is a digital simulation method to study the force action and the equivalent transfer of node properties between the elements in the interface element region. The simulation and analysis of the continuous structure and the discrete medium, the calculation of the interaction force of the continuous structure and the continuous structure in the interaction interface and the equivalent transfer of the attribute of the unit node in the process of equipment work are mainly reflected in the following five aspects:
1 in view of the need to quickly generate the discrete particle set problem in the preprocessing phase of the interface element method, a particle collection algorithm combining geometry and physics is proposed, which makes full use of the geometric characteristics of the granular element and the physical characteristics of the particle falling, and constructs a particle accumulation moving model combining geometric and physical properties. Two dimensional circular particles and three dimensional spherical particle sets are formed. The time of generating particle sets is linearly related to the number of particles, and the particle density is high and the generation time is short.
2 in order to simulate and calculate the interaction force between the continuous structure and the discrete medium, an interface element method based on the element / particle contact is proposed. According to the geometric contact between the finite element and the particle element, the linear elastic model is used to calculate the force between the single discrete particle and the finite element face, and then the calculated effect is obtained. The force is equivalent to the finite element node, and the force and displacement of the finite element node are further calculated. The visualization of the force, the change state of the discrete medium and the stress of the continuous structure and the strain state are visualized.
3 in view of the stress and strain analysis of large-scale particle sets under the action of mechanical structure, an interface meta model based on the overlapping of elements / particles is proposed, which will be expressed directly by the discrete element in the region and adjacent area of the structure, and the far region is expressed with the hexahedral finite element, and the two element regions are in their interaction interfaces. A certain degree of overlap. In the overlapping area, the mass of discrete particles in the finite element is transferred to the finite element node, and the finite element node acceleration is obtained. The velocity and acceleration of the finite element nodes are interpolated to the discrete element, and the strain and stress of the position of the discrete particle are obtained, while the force of the finite element in the overlapping area is taken as the edge. Boundary conditions are used to solve the stress and deformation conditions of the whole area.
4 in order to solve the problem that the node properties of multiple finite element grids are not matched at the contact interface, the heterogeneous grid interface element method is proposed. The two-dimensional heterogeneous quadrilateral element node and its misplaced node shape function are constructed to realize the smooth transfer of the heterogeneous quadrilateral single grid in the contact interface properties. The method is further extended to the interface element analysis between the quadrilateral mesh and the triangular mesh, and the smooth transfer method of the node properties between the three dimensional heterogeneous hexahedral meshes is studied. The method is verified by a heterogeneous grid contact case, and the method is applied to the contact analysis of the gear.
5 the equivalent integration method of the main / auxiliary grid node attribute is proposed to solve the problem that the multi field information of the heterogeneous finite element mesh is difficult to integrate. One of the multiple finite element mesh models is used as the main grid and the other is used as the auxiliary grid. The node information of the auxiliary grid unit is transferred to the node of the main grid equivalent, and finally in the main grid unit node. The integrated display of multi field information is realized. The research results are made to analyze the distribution of the stress field and the temperature field and the strongest area of the multi field effect on the cutting tool and the cutter disk during the tunneling of the shield cutter disk, and provide the basis for the design of the cutter and the cutter disk.
【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：TH122

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