基于图像八叉树的三维比例边界有限元多面体网格生成算法  

Study on mesh generation algorithm of polyhedron in 3D scaled boundary finite element method based on image octree

作　　者：章鹏 杜成斌[2] 赵文虎 ZHANG Peng;DU Chengbin;ZHAO Wenhu(Institute of Civil Engineering and Intelligent Management,Nanjing Institute of Technology,Nanjing 211167,China;College of Mechanics and Materials,Hohai University,Nanjing 211100,China;School of Infrastructure Engineering,Nanchang University,Nanchang 330031,China)

机构地区：[1]南京工程学院土木工程与智慧管理研究所,江苏南京211167 [2]河海大学力学与材料学院,江苏南京211100 [3]南昌大学工程建设学院,江西南昌330031

出　　处：《河海大学学报（自然科学版）》2024年第1期46-54,共9页Journal of Hohai University(Natural Sciences)

基　　金：国家重点研发计划项目(2018YFE0122400);国家自然科学基金项目(52109152,12202179);江西省自然科学基金项目(20232BAB214086)。

摘　　要：基于图像八叉树方法,提出了平衡八叉树和多面体网格修剪相结合的三维比例边界有限元多面体网格算法,该算法根据结构尺寸建立恰好完全包含整个结构的立方体网格,再建立结构图像像素信息,根据像素信息,按照2∶1的平衡分割原则递归地进行等分,完成平衡八叉树网格生成。结构内单元网格完全保留,结构外单元网格删除,对于结构边界单元网格,提出采用面-立方体相交判断方法进行边界单元与结构边界相交面的筛选,搜寻结构单元与结构边界表面相交点,通过有序连接相交点形成边界单元切割面,再结合边界单元其他几个面,构成裁剪后的多面体单元。数值算例结果表明,基于本文算法生成的比例边界有限元网格计算结果具有较好的精度和边界适应性。The paper combines the balanced octree with polyhedron mesh trimming based on the image octree method,and proposes a mesh generation algorithm of polyhedron in the 3D scaled boundary finite element method.According to the size of the structure,a cube grid is built to exactly include the whole structure,and then the pixel information of the structure image is formed.Then,according to the principle of 2∶1 balanced partition,the grid is divided recursively to realize the fast transition of mesh,and the balanced octree mesh can be generated.The internal elements are completely preserved while the external elements are removed.For the mesh of the boundary element,the surface-cube intersection method is proposed to screen the intersection surfaces of boundary element and structural boundary,and the intersection points between boundary element and structural boundary surface are searched to form a new element surface.The cut surface of the boundary element is formed by connecting the intersection points in order,and then combined with other surfaces of the boundary element to form the cut polyhedron element.Two numerical examples show that the calculated results of the scaled boundary finite element mesh generated by the proposed method have good accuracy and boundary adaptability.

关 键 词：平衡八叉树 多面体网格修剪 三维比例边界有限元 网格生成算法 图像像素 

分 类 号：O346.1[理学—固体力学]