基于几何造型的参数化有限元建模和曲面网格生成方法及实现

【作者】 隋晓峰；

【导师】 顾元宪； 关振群；

【作者基本信息】 大连理工大学 ， 计算机应用技术， 2002， 硕士

【摘要】 有限元方法是一种求解连续介质力学问题的通用数值方法。它广泛应用于航空、航天、土木、机械、石油、化工、电子等工业部门，已成为结构设计与分析优化的标准方法。有限元分析软件也成为计算机辅助设计系统的重要组成部分。 有限元建模是有限元分析的前置处理过程，它基于CAD平台，是有限元技术与CAD技术的结合点，在有限元方法的工程应用中占有重要的地位。目前的有限元建模方法一般为静态的，建模方式基本为单向建模，模型一旦建立完成便几乎不能作大的修改，这就不能很好地适应现代产品设计的动态特性。另外，在曲面网格划分方面，当前的研究大多是针对单张非闭合曲面进行的，对于闭合曲面和组合曲面的研究甚少，而这些曲面在实际工程中却是经常使用的。 针对有限元建模领域存在的上述问题，本文展开了深入研究并提出了相应解决方法。 在曲面网格划分方面，提出了一种基于映射法的三维组合曲面的有限元网格全自动生成方法。通过引入可移动的虚边界解决了闭合曲面的剖分问题；通过对邻接曲面公共边界的统一处理，保证了组合曲面拼合处网格的相容性；以边界表示数据结构为基础实现了三维组合曲面的全自动网格剖分；采用空间扫描线布点、诊断交换等技术，优化了网格的质量；并以AutoCAD为支撑平台ObjectARX为开发工具，开发了一个基于几何造型的曲面三角形网格全自动生成程序。 针对形状优化领域的应用要求，提出了一种简单而有效的参数化有限元建模方法。通过将几何模型的设计参数作为有限元模型的形状控制参数，实现了有限元模型的参数定义；通过建立几何模型与有限元网格及模型物理描述之间的关联，实现了基于几何造型的有限元模型定义；利用基于几何模型的全自动网格生成方法及物理描述分派方法，实现了有限元模型的自动生成及应参数变化的自动更新；并以参数化造型软件MDT为支撑平台，开发了相应的参数化有限元建模程序。 本文共分六章，前三章为论文的基础部分，主要介绍本文研究工作所倚赖的背景知识；后三章为主体部分，介绍了作者在有限元建模方面的研究成果。第一章主要介绍本文研究涉及的两个领域，通过分析领域中存在的问题，揭示了本文研究的应用背景和意义。第二章介绍本文方法在设计与实现上所依据的一些基本原理和基础知识。第三章介绍本文方法在程序实现过程中所依赖的几个平台。第四章主要介绍作者在曲面网格划分上的研究成果。第五章主要介绍作者在参数化有限元建模方面的工作。在第六章，作者对全文进行了总结，给出了本文研究成果的创新之处，并针对本文方法的缺陷对未来的研究工作进行了展望。更多还原

【Abstract】 Finite element method is a popular numerical analysis method, which is widely applied in many industrial fields such as aviation, architecture, mechanics, electronics and chemistry. It has become the criterion of the analysis and design optimization of structures, and finite element analysis (FEA) software has become the most important part of CAD/CIMS system.Finite element modeling (FEM) is the pre-process of FEA. It is based on CAD system, and ties FEA technique to CAD system. Most of finite element modeling methods are static at present. Once the design engineers finish the finite element model, it will be very difficult to modify the model. This static finite element modeling method doesn’t need the requirement of the dynamic design of product in the modern industry. Otherwise, most work on the surface mesh generation is based on the single trimmed surfaces, and the work to closed surface and combined surface, which are very popular in engineer, is very few.To solve the problems mentioned above, the author studies the problems carefully and gives out some solutions.A method of surface triangulation based on the traditional mapping approach is presented in this thesis. The method has four features: 1) Virtual movable boundaries are given to assist the mesh generation on closed surfaces. 2) For making the meshes consistent on the common boundaries of adjoining surfaces, a new approach of boundary discretization is employed. 3) The boundary-representation structure is adopted to fulfill the mesh generation over combined surfaces. 4) The quality of surface meshes is improved by point creation on 3D scan lines and diagonal swapping procedure. An application to mesh surfaces only depending on geometries is developed. The application is tightly integrate with the CAD package AutoCAD from Autodesk Corporation.A method of parametric finite element modeling for shape optimization is presented in this thesis. The method has three features: 1) The dimensions used in commercial CAD system are selected to be the design variables of shape optimization.2) A mapping between geometry objects and finite element objects such’ as meshes, structure properties is set up to assist in defining finite element models on geometries.3) An automatic mesh generator and a method by which structure properties is assigned from geometry objects to finite element objects automatically are used to update finite element models during the optimization process.更多还原