【作者】 宋敏；

【导师】 张见明；

【作者基本信息】 湖南大学 ， 车辆工程， 2010， 硕士

【摘要】 新近提出的边界面法中,边界积分和场变量插值都是在以边界表征的实体边界曲面的参数空间里进行。该法不仅比边界元的计算精度更高,而且避免了计算几何误差。后处理可视化在边界面法的应用中扮演非常重要的作用。虽然有限元的后处理已经发展成熟,但是在边界面法后处理中不能照搬有限元的后处理方法。因此,有必要对边界面法的后处理进行研究。本文对边界面法分析数据的预处理、等值线图和云图的生成算法及程序实现进行了详细研究。具体研究内容如下：1.以边界面法求解势问题为例,分析边界面法的基本原理特点,提出自适应树结构求解任意点场量值。2.在分析等值线生成理论的基础上,对传统的四边形规则网格法进行改进。提出在等值线跟踪过程中,加入基于网格单元的自适应算法,以改进等值线出现折线的缺点。同时,对传统的三角单元不规则网格法进行分析,将等值线的追踪限制在三角单元内,避免了区分边界等值线与内部等值线的问题。3.在分析云图生成理论的基础上,对基于拓扑关系的等值线填充算法和基于三角单元的等值线填充算法进行讨论。基于拓扑关系的等值线填充关键在于等值线间拓扑关系的形成。而对基于三角单元的等值线填充算法进行改进,直接在单元内生成Patch,以Patch为单位完成等值线填充。对比两种方法,后者具有程序实现简单,适应性强的优点。4.在熟悉UG二次开发理论及相关技术的研究基础上,研究了边界面法后处理程序在UG上实现的方法。数值算例表明边界面法后处理可视化取得了很好的视觉效果。更多还原

【Abstract】 In the newly developed boundary face method (BFM), both boundary integration and variable approximation are performed in the 2-D parametric space of the boundary surface of solid represented by the boundary. The proposed approach can not only provide much more accurate results than the boundary element method (BEM), but also avoid geometric error in the BFM. Visualization in post-processing plays an important role in the application of the BFM. Although there are already abundant of matured post-processing tools existing for the finite element method (FEM), these codes can not be directly applied to the BFM. Therefore, it is necessary to investigate new algorithms that are especially suitable for the BFM post-processing.In this paper, the algorithms of the data preparation and isoline generation in the BFM post-processing were studied in detail. Our work involves four aspects as follows:(1) For instance of solving a potential problem by the BFM, according to the speciality of the BFM, an adaptive tree structure for calculating the value of variable at any point is proposed.(2) Based on the theory of isoline generation, the traditional rectangular grid method has been improved. For the shortage that broken line would be created when the linear interpolation was taken, based on the rectangular grid method, some self-adaptive algorithm using grid subdividing was presented. Furthermore, the traditional irregular triangular grid method was analyzed; and the isoline tracking was limited in the traditional element to avoid the problem of distinction between the boundary isoline and internal isoline.(3)Based on the theory of the contour generation, two contour filling algorithms were discussed respectively, one of which is based on the topological relation and the other one of which is based on triangular cell. The formation of the topological relation for isolines is crucial to the contour filling algorithm based on the topology relationship. The contour filling algorithm which is based on the triangular cell has been improved, and patches were directly generates in the cell to fulfill contour filling in the patch. Comparison of two methods showed that the latter algorithm is better than the former in the program implemented and adaptability.(4) After the study on the theory of secondary development of UG and its related technology, the project of post-processing of BFM which is UG-NX oriented has been developed. Numerical examples showed that excellent visualization can be obtained by proposed methods.更多还原