由粒度空间控制的有限元三角网格剖分算法  

An Algorithm for the Generation of Triangular Finite Element Controlled by the Element-Size Space

作　　者：孔永明[1] 马泽恩[2] 吴建军[2] 

机构地区：[1]北京航空航天大学,北京100083 [2]西北工业大学飞行器制造工程系,陕西西安710072

出　　处：《西北工业大学学报》2000年第3期478-482,共5页Journal of Northwestern Polytechnical University

基　　金：华中理工大学塑性成形模拟及模具技术国家重点实验室研究基金! (0 0 - 4)

摘　　要：提出了一种稳定高效的三角剖分算法 ,根据物理域的离散边界上节点分布 ,可自动地剖分得到形态良好且尺寸过渡连续的三角网格 ,域内插入新节点的位置受相邻节点的影响 ,使得相邻单元间具有较好的协调性。为了改善整个域内单元尺寸分布的连续性 ,引入了单元粒度空间 ,利用粒度值控制新生成的单元尺寸。在新生成的节点处以其粒度值的二分之一为半径建立邻域空间 ,用以搜索可能参与生成新单元的节点 ,从而避免了局部区域畸形单元的产生。The paper presents a steady and efficient automatic mesh generation algorithm, which can generate well shaped elements and evenly size distributed triangular mesh from the initial boundary of a planar physical field. When a new element is generated, the position of the new node inserted into the domain is affected by the adjacent nodes on the boundary. Thus the adjacent elements coordinate well. Element size space is introduced, and the size of the new element is controlled by the element size space. Therefore, the sudden change of the element size in neighbor area can be avoided. Before the grid generation, interpolation triangular mesh will be created first, so that the element size at any position in the domain can be computed. Five cases of the neighborhood at the position where the new node will be inserted were discussed, and the method how to insert the new node was presented. After the new node has been created, its position was adjusted according to the element size at its occupation. To avoid the ill shaped element, neighbour space, the radius of which equals to half of the value of the new node′s element size space, is constructed at the new node. The distribution of some physical variables such as load can be applied to construct the element size space, so the mesh meeting the demand of the distribution can be generated. Through a number of examples, it has been seen that the algorithm is steady and efficient and it can be applied for domains with very complex shape.

关 键 词：有限元 三角单元 粒度空间模型 三角剖分算法 

分 类 号：O241.82[理学—计算数学]