等幾何分析中的NURBS體造型及算法
發(fā)布時間：2018-08-01 18:45
【摘要】：在傳統(tǒng)的有限元分析過程中， CAD（幾何設(shè)計模型）與CAE（分析模型）分別在兩個軟件平臺中實現(xiàn)，，即通過CAD系統(tǒng)建立幾何模型，然后將設(shè)計模型導入CAE軟件平臺中產(chǎn)生分析模型。在上述轉(zhuǎn)化過程中，需對幾何模型進行細節(jié)移除、模型簡化、降維等一系列的處理以生成分析模型，進行有限元分析。即從CAD到CAE的過程中沒有實現(xiàn)設(shè)計模型與分析模型的真正統(tǒng)一。設(shè)計者總是希望分析過程盡量簡潔和智能，減少人工干預對設(shè)計方案的修改和優(yōu)化。 在現(xiàn)今的CAE分析中，由于上述的設(shè)計和分析模型的不統(tǒng)一造成了CAE結(jié)果在此過程中作用有限，因此希望能將CAE分析結(jié)果智能地反饋到設(shè)計系統(tǒng)中以進行自動干預，實現(xiàn)CAE/CAD模型間自動反饋。為解決這個問題，必須使設(shè)計模型與分析模型統(tǒng)一，實現(xiàn)CAD和CAE之間的雙向映射，即CAD/CAE間的無縫集成。 本文探索性地利用了基于NURBS原理的等幾何分析，通過NURBS強大的幾何造型功能實現(xiàn)對實體模型的構(gòu)造。NURBS（非均勻有理B樣條）基函數(shù)通過線性組合生成精確描述的幾何模型，再利用NURBS節(jié)點插值和基函數(shù)的階數(shù)升降的方法來產(chǎn)生相應的有限元模型，而在此過程中節(jié)點插值并不會改變幾何模型形狀。此種方法徹底摒棄了傳統(tǒng)有限元分析中利用網(wǎng)格生成器來生成近似分析模型的方法，實現(xiàn)了真正意義上的設(shè)計反饋和模型統(tǒng)一。 本文主要介紹了等幾何分析的相關(guān)理論，探索了在此理論下NURBS基本算法和體造型算法。本文應用基于三元參數(shù)的NURBS造型技術(shù)，通過質(zhì)心參數(shù)化，模型中軸線提取等一系列處理過程，生成了高精度的NURBS體網(wǎng)格。在此基礎(chǔ)上通過節(jié)點插值和對基函數(shù)的升階實現(xiàn)了網(wǎng)格劃分與單元生成。生成的模型具有網(wǎng)格質(zhì)量均勻、單元連續(xù)性高的特點。論文最后利用VC++開發(fā)了軟件系統(tǒng)，實現(xiàn)了上述等幾何分析算法及NURBS體造型。
[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.
【學位授予單位】：電子科技大學
【學位級別】：碩士
【學位授予年份】：2012
【分類號】：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.
【學位授予單位】：電子科技大學
【學位級別】：碩士
【學位授予年份】：2012
【分類號】：TH122;TB115
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