等几何分析中的NURBS体造型及算法
发布时间：2018-08-01 18:45
【摘要】：在传统的有限元分析过程中， CAD（几何设计模型）与CAE（分析模型）分别在两个软件平台中实现，，即通过CAD系统建立几何模型，然后将设计模型导入CAE软件平台中产生分析模型。在上述转化过程中，需对几何模型进行细节移除、模型简化、降维等一系列的处理以生成分析模型，进行有限元分析。即从CAD到CAE的过程中没有实现设计模型与分析模型的真正统一。设计者总是希望分析过程尽量简洁和智能，减少人工干预对设计方案的修改和优化。 在现今的CAE分析中，由于上述的设计和分析模型的不统一造成了CAE结果在此过程中作用有限，因此希望能将CAE分析结果智能地反馈到设计系统中以进行自动干预，实现CAE/CAD模型间自动反馈。为解决这个问题，必须使设计模型与分析模型统一，实现CAD和CAE之间的双向映射，即CAD/CAE间的无缝集成。 本文探索性地利用了基于NURBS原理的等几何分析，通过NURBS强大的几何造型功能实现对实体模型的构造。NURBS（非均匀有理B样条）基函数通过线性组合生成精确描述的几何模型，再利用NURBS节点插值和基函数的阶数升降的方法来产生相应的有限元模型，而在此过程中节点插值并不会改变几何模型形状。此种方法彻底摒弃了传统有限元分析中利用网格生成器来生成近似分析模型的方法，实现了真正意义上的设计反馈和模型统一。 本文主要介绍了等几何分析的相关理论，探索了在此理论下NURBS基本算法和体造型算法。本文应用基于三元参数的NURBS造型技术，通过质心参数化，模型中轴线提取等一系列处理过程，生成了高精度的NURBS体网格。在此基础上通过节点插值和对基函数的升阶实现了网格划分与单元生成。生成的模型具有网格质量均匀、单元连续性高的特点。论文最后利用VC++开发了软件系统，实现了上述等几何分析算法及NURBS体造型。
[Abstract]:In the traditional finite element analysis process, the, CAD (geometric design model and the CAE (analysis model) are implemented in two software platforms, namely, the geometric model is built through CAD system, and then the design model is imported into the CAE software platform to produce the analysis model. In the process of transformation, the geometric model should be removed in detail, simplified and dimensionally reduced to generate an analytical model for finite element analysis. That is, the process from CAD to CAE does not realize the real unity of design model and analysis model. The designer always wants the analysis process to be as concise and intelligent as possible, and to reduce the modification and optimization of the design scheme by manual intervention. In today's CAE analysis, due to the disunity of the above design and analysis model, the result of CAE is limited in this process, so it is hoped that the results of CAE analysis can be intelligently fed back to the design system for automatic intervention. Automatic feedback between CAE/CAD models is realized. In order to solve this problem, we must unify the design model with the analysis model, and realize the two-way mapping between CAD and CAE, that is, the seamless integration between CAD/CAE. In this paper, the isometric analysis based on NURBS principle is used to realize the construction of entity model. Nurbs (nonuniform rational B-spline) basis function is constructed by the powerful geometric modeling function of NURBS. The corresponding finite element model is generated by using the NURBS node interpolation and the order rise and fall of the basis function, but in the process the node interpolation does not change the shape of the geometric model. This method completely abandons the traditional method of generating approximate analysis model by using mesh generator in finite element analysis and realizes the design feedback and model unification in real sense. This paper mainly introduces the theory of isometric analysis, and explores the basic algorithm of NURBS and the algorithm of volume modeling under this theory. In this paper, NURBS modeling technology based on ternary parameters is applied to generate a high-precision NURBS volume mesh through a series of processing processes such as centroid parameterization and axis extraction in the model. On this basis, mesh generation and cell generation are realized by node interpolation and raising the order of the basis function. The generated model has the characteristics of uniform mesh quality and high cell continuity. Finally, the software system is developed by using VC, and the above isometric analysis algorithm and NURBS body modeling are realized.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH122;TB115
[Abstract]:In the traditional finite element analysis process, the, CAD (geometric design model and the CAE (analysis model) are implemented in two software platforms, namely, the geometric model is built through CAD system, and then the design model is imported into the CAE software platform to produce the analysis model. In the process of transformation, the geometric model should be removed in detail, simplified and dimensionally reduced to generate an analytical model for finite element analysis. That is, the process from CAD to CAE does not realize the real unity of design model and analysis model. The designer always wants the analysis process to be as concise and intelligent as possible, and to reduce the modification and optimization of the design scheme by manual intervention. In today's CAE analysis, due to the disunity of the above design and analysis model, the result of CAE is limited in this process, so it is hoped that the results of CAE analysis can be intelligently fed back to the design system for automatic intervention. Automatic feedback between CAE/CAD models is realized. In order to solve this problem, we must unify the design model with the analysis model, and realize the two-way mapping between CAD and CAE, that is, the seamless integration between CAD/CAE. In this paper, the isometric analysis based on NURBS principle is used to realize the construction of entity model. Nurbs (nonuniform rational B-spline) basis function is constructed by the powerful geometric modeling function of NURBS. The corresponding finite element model is generated by using the NURBS node interpolation and the order rise and fall of the basis function, but in the process the node interpolation does not change the shape of the geometric model. This method completely abandons the traditional method of generating approximate analysis model by using mesh generator in finite element analysis and realizes the design feedback and model unification in real sense. This paper mainly introduces the theory of isometric analysis, and explores the basic algorithm of NURBS and the algorithm of volume modeling under this theory. In this paper, NURBS modeling technology based on ternary parameters is applied to generate a high-precision NURBS volume mesh through a series of processing processes such as centroid parameterization and axis extraction in the model. On this basis, mesh generation and cell generation are realized by node interpolation and raising the order of the basis function. The generated model has the characteristics of uniform mesh quality and high cell continuity. Finally, the software system is developed by using VC, and the above isometric analysis algorithm and NURBS body modeling are realized.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH122;TB115
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