【作者】 方锡武；

【导师】 谭建荣； 刘振宇；

【作者基本信息】 浙江大学 ， 机械设计与理论， 2013， 博士

【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。更多还原

【Abstract】 The interface element(IE) is the finite elements within a certain range of the contact interface between two kinds of continuous structures, or finite/discrete elements between continuous structure and discrete media. The interface element method(IEM) is a numerical simulation method of researching the interaction and the equivalent transition of node property between elements within IE region. This paper puts forward the IEM to simulate and analyze the interaction and the equivalent transition of node property on the interactive interface between continuous mechanical structures and between continuous mechanical structure and discrete media in the working process of mechanical equipment. This research work can be reflected in the following five aspects:First, for a discrete particle assembly should being generated quickly in the preprocessing stage of IEM, an algorithm by considering geometric and physical factors is put forward, this algorithm constructs the moving model of particle packing by making best use of the geometrical and physical properties of discrete element. It can quickly generate circular particle assembly in2D region and sphere particle assembly in3D region. The time to create the granular particles set is linear with the particle number and this process is completed in a comparatively short time with high-density particles set.Second, a IE model on the direct contact interface of the finite/discrete element is proposed for simulating and computing the interaction between continuous structure and discrete media. According to the geometrical touch type between finite and discrete element, the interaction force between discrete element and finite element patch is calculated with linear elastic model. Then the contact force is equivalent to the finite element nodes and the force and displacement on the nodes can be computed, so the force and the change of displacement of discrete media can be visualized ideally, and it is the same case with the force and the strain of continuous structure.Third, aiming at the analysis of stress and strain of discrete media composed of a great number of particles acted by mechanical structure, a IE model is proposed in the overlap region presented by finite and discrete element in one kind of media, The region acted by mechanical structure directly and its near region is presented by discrete element, the far region by finite element with hexahedron, and the regions of these two kind of elements have an overlapping level on their interface. In the overlapping region, first, with the particle-in-cell method, the mass of the discrete particle which lies in the finite element and the force acting on the particle are equivalent to the nodes of the finite elements. Then the velocity and acceleration of the node of the finite element is obtained. Last, the velocity and acceleration are isoparametric interpolated to the discrete element, so the strain and stress on the position of discrete particle can also be obtained. At the same time, the force and strain of the whole region can be solved with the boundary condition of the force of the finite element in the overlapping region.Fourth, in order to solve the problem that the node property can’t transit smoothly on the interface of two or many contact heterogeneous meshes with non-matching nodes, the model and the analysis method of interface element between heterogeneous finite element meshes is put forward, the shape functions of the nodes and the non-matching nodes of2-D heterogeneous quadrilateral element are constructed, the smooth connection of the attributes at the contact face for heterogeneous quadrilateral element is realized, and the method is extended to the analysis of the interface element between the quadrilateral mesh and the triangular mesh. In the meanwhile, the method for the smooth connection of the nodal attributes of the heterogeneous hexahedron elements in3D is studied. For the proposed method, its correctness is verified by one example of heterogeneous interface mesh, and it is applied to the contact analysis of the gears.Fifth, a primary-secondary-mesh method is put forward which focuses on how to integrate the properties of the multiple physical fields on heterogeneous finite element meshes. That is, one of the heterogeneous meshes is taken as primary mesh and the other the secondary one. The properties of the secondary mesh are equivalent to that of the primary mesh by the inverse isoparametric mapping method, thus, all the different fields on different meshes are integrated and visualized on the primary mesh. This method has already been used to integrate and visualize the stress field and the temperature field on the cutters and cutter head of the shield machine, the strongest effect aera of multi-physical fields is got, and some advice on the structural design of the cutters and the cutter head is given by the finite element analysis.更多还原