基于混合体分解的高质量六面体网格生成方法研究

Finite element analysis technology plays an important role in product development. As an input to finite element analysis, hexahedral meshes have many advantages over other types of volumetric meshes, so the automatic generation of high-quality hexahedral meshes has been valued by industry and academia. However, for various reasons, the automatic generation of high-quality hexahedral meshes for complex solid models is still a recognized problem. In view of the problem that a lot of manual interaction is needed in order to generate high-quality hexahedral meshes for complex solid models, this project studies the automatic hexahedral mesh generation based on hybrid volume decomposition. It includes four research contents: 1) to investigate the fuzzy clustering based parallel swept volume decomposition method，in which complex models can be decomposed into a set of swept volumes and residual non-sweepable sub-volumes. 2) to investigate the weighted ranking based block decomposition method, in which non-sweepable sub-volumes can be further decomposed into a group of blocks; 3) to investigate a global high-quality hexahedral mesh generation method, in which continuous high-quality hexahedral meshes can be generated; 4) to develop the hexahedral mesh generation prototype system, and verify it by complex product models. Through the research of this project, the theory and key technologies of hexahedral mesh generation are explored, which have important theoretical research significance and extensive engineering application prospects.

有限元分析技术在产品开发中发挥着重要作用。作为有限元分析的输入，六面体网格与其他类型的体网格相比具有诸多优势，因此高质量六面体网格的自动生成一直受到工业界和学术界的重视。然而由于种种原因，目前面向复杂实体模型的高质量六面体网格自动生成仍然是一个公认的难题。针对目前对复杂实体模型生成高质量六面体网格需要大量人工交互的问题，本项目对基于混合体分解的六面体网格自动生成展开研究，共包括四项研究内容：1）研究基于模糊聚类的扫掠体并行分解方法，将复杂模型分解为一组扫掠体和剩余非扫掠子块；2）研究基于加权排序的六面块分解方法，将非扫掠子块进一步分解为一组六面块；3）研究高质量六面体网格全局协调生成方法，生成连续的高质量六面体网格；4）研发六面体网格生成原型系统，并对复杂产品模型进行实例验证。通过本项目的研究，探索六面体网格生成的理论和关键技术，具有重要的理论研究意义和广泛的工程应用前景。

工业界对工程和科学计算的复杂度、精度和效率的要求越来越高，复杂产品模型的六面体网格自动生成这一难题亟待解决。本项目面向高效、高精度工程分析的需要，以复杂产品模型为对象，研究了适应基于模糊聚类扫掠体分解法的模型形式化表征、基于表面奇异结构的潜在扫掠体识别、基于体细分的复杂六面体网格模型交互式构造、大规模六面体网格协调生成等内容，主要取得了以下成果：.•给出了适应基于模糊聚类扫掠体分解法的模型形式化表征，能够预判给定几何模型是否能够有效提取扫掠方向并分解为扫掠体。.•提出了一种基于表面奇异结构的潜在扫掠体识别算法，能够有效识别扫掠路径为自由曲线或扫掠底面为复杂自由曲面的非线性拉伸扫掠体。.•提出了一种基于体细分的复杂六面体网格模型交互式构造方法，能够方便且高效地交互生成六面体网格。.•实现了大规模六面体网格协调生成算法，能够支持对多装配体的工业应用模型生成全六面体网格，并保证网格在连接处的协调拼接。.上述研究成果扩充了六面体网格生成的理论，对实现复杂产品模型的高质量大规模六面体网格自动生成，进而支持高效、高精度工程分析具有重要意义。本项目共发表学术论文6篇，提交了2项国家发明专利申请。