基于八叉树的三维有限元网格快速生成算法

FAST THREE-DIMENSIONAL FINITE ELEMENT MESH GENERATION ALGORITHM BASED ON OCTREE

  • 摘要: 针对有限元网格划分依赖人工干预、效率低的问题,本文基于八叉树方法,提出了一种由几何模型快速生成有限元网格的算法。该算法首先依据几何模型确定计算域并提取边界面信息,设置初始尺寸参数构建初始网格模型,通过边界面的几何特征约束网格模型尺寸分布,按照平衡八叉树的2∶1分割原则递归等分,完成平衡八叉树网格自动划分。设置相对容差参数,当平衡八叉树网格与几何模型的交点处于容差范围内时,以网格节点替换交点,完成切割拓扑计算后初步生成有限元网格。然后采用拉普拉斯法优化边界网格,得到与几何模型高度贴合的有限元网格模型。本文以某地下洞室建筑信息模型(BIM)为例,采用本文算法与人工有限元建模方法对其进行网格划分,生成两套有限元网格。网格质量检查结果表明,本文算法生成的网格质量满足工程实践要求。对两套网格分别进行全过程开挖数值模拟,结果表明两者的位移、应力的大小与分布规律基本一致。

     

    Abstract: In view of the issues of the dependence on manual intervention and of the low efficiency in finite element mesh generation, an algorithm for rapid generation of finite element meshes from geometric models is proposed by the base of the octree method. Firstly, the computational domain is determined according to the geometric model and the boundary face information is extracted, and the initial size parameters are set to construct the initial mesh model. The size distribution of the mesh model is constrained by the geometric characteristics of the boundary face, and the octree is divided recursively and equally according to the 2∶1 division principle to complete the automatic mesh division of the balanced octree. Then, the relative tolerance parameter is set. When the intersection point between the balanced octree mesh and the geometric model is within the tolerance range, the intersection point is replaced by the mesh node, and the finite element mesh is initially generated after the cut topology calculation is completed. Finally, the Laplacian method is used to optimize the boundary mesh, and the finite element mesh model is highly consistent with the geometric model. This study takes the Building Information Modeling (BIM) of underground caverns as an example, and uses the algorithm and the manual finite element modeling method to mesh it, generating two finite element meshes. The simulation results of the mesh quality inspection show that the mesh quality generated by the algorithm meets the requirements of engineering practice. Numerical simulations of the entire excavation process were conducted on the two meshes, respectively. The results show that the magnitudes and distribution patterns of the displacements and stresses of the two are basically identical.

     

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