在CAE (Computer aided engineering)分析中，使用有限元素(Finite element)技術以模擬產品的設計結果是最為常見的方法，以取代人為的測試或經驗。此技術中網格化是最重要的步驟，但模型的特徵往往由多個面或很小的面所組成，造成網格尺寸勢必縮小與面接近。尤其在於倒圓角(Blend faces)中往往為狹長面，導致網格數增加，不只增加電腦計算時間，也影響網格品質與模擬結果，因此必須要改善狹長型的倒圓角在網格化中的問題。本研究發展一演算法，以B-rep (Boundary representation)資料格式的模型為基礎，將倒圓角進行簡化，方法主要分為：產生幾何曲面資料以取代原本的倒圓角面、刪除原本倒圓角的曲面資料、更新所有B-rep中的拓樸資訊。最後使用數個案例進行測試，當模型經過簡化演算法計算後，會產生所有倒圓角均被簡化的新模型，以驗證此演算法的可行性。

CAE (Computer Aided Engineering) analysis is a common tool to replace physical test. It often employs the Finite Element (FE) method to analyze and simulate the product design. In finite element method of CAE analysis, mesh generation is an indispensable operation. But, one of the problems found in going from CAD to CAE is that CAD models often feature a large number of faces, and many of them are much smaller than the desired finite element size. Specially, the appearing and existing of small blend faces on a CAD model affects the quality of analysis. It not only increases the analysis time but also produces poor simulation results. Hence, small blend face simplification on CAD models for mesh generation is essential to improve the quality of finite elements to analysis. This study develops the algorithms to simplify small blend faces for producing better models for FE based on the understanding the B-rep (Boundary representation) model. It includes the following main operations: generate new geometric data to replace all small blend faces, add new elements into B-rep, delete all elements related to small blend faces and update all topological data of the B-rep. All small blend faces can be suppressed, after the above operations are accomplished, which yields the simplified CAD model without small blend faces. The simplified CAD model without small blend faces will be obtained. In addition, several examples are presented to demonstrate the feasibility of the proposed method for small blend simplification.

[1] S.Venkataraman and M. Sohoni, “Blend Recognition Algorithm and Applications”, The sixth ACM Symposium on Solid Modeling and Applications, pp.99-108, 2001.
[2] J. Li, G. Tong, D. Shi, M. Geng, H. Zhu and I. Hagiwara, “ Automatic Small Blend Recognition from B-rep for Analysis”, Engineering with Computers, pp 279-285, 2009.
[3] X. Cui, S. Gao and G. Zhou, “An Efficient Algorithm for Recognizing and Suppressing Blend Features”, Computer-Aided Design and Applications, Vol. 1, No. 1-4, pp. 421-428, 2004.
[4] H. Zhu and C.H. Menq, “B-Rep Model Simplification by Automatic Fillet/Round Suppressing for Efficient Automatic Feature Recognition”, Computer-Aided Design, Vol. 34, No. 2, pp. 109-123, February 2002.
[5] K.Y. Lee, C.G. Armstrong, M.A. Price and J.H. Lamont, “A Small Feature Suppression/Unsuppression System for Preparing B-rep Models for Analysis”, Computer-Aided Design, ACM 1-59593-015-9/05/0006, 2005.
[6] S. Venkataraman, M. Sohoni and R. Rajadhyaksha, “Removal of Blends from Boundary Representation models”, Proceedings of the seventh ACM symposium on Solid modeling and applications, pp. 83-94, 2002.
[7] N. Joshi and D. Dutta, “Feature Simplification Techniques for Freeform Surface Models”, Journal of Computing and Information Science in Engineering, Vol. 3, No. 3, pp. 177-186, 2003.
[8] H. Mounir, A. Nizar and B. Abdelmajid, “CAD Model Simplification Using a Removing Details and Merging Faces Technique”, Journal of Mechanical Science and Technology, Vol. 26,No. 11, pp. 3539-3548, November 2012.
[9] B. Li and J. Liu, “Detail Feature Recognition and Decomposition in Solid Model”, Computer-Aided Design, Vol. 34, No. 5, pp. 405-414, 2002.
[10] 黃駿, “以B-rep為基礎之圓角特徵簡化技術發展”, 國立中央大學碩士論文, 2014.
[11] 陳星佑, ” CAE應用之混接面辨識技術發展”, 國立中央大學碩士論文, 2014.
[12] Rhino SDK. Available from: http://wiki.mcneel.com/developer/cplusplusplugins
[13] openNURBS. Available from: http://wiki.mcneel.com/developer/opennurbs
[14] B-rep data structure. Available from: http://wiki.mcneel.com/developer/brepstructure
[15] GrabCAD. Available from: https://grabcad.com