The fixed grid technique avoids the complicated meshing process along the boundary of the structure, showing great advantages in the analysis of complex geometric structure. Modeling accuracy and analysis accuracy are two major problems in structural analysis using the fixed grid. To enhance the modeling accuracy in the fixed grid, a fast transformation method from the CAD model to the analytic model is proposed. Firstly, the CAD model is described by the boundary representation, and then the ray intersection method is developed to distinguish the elements in the fixed grid. The boundary elements are subdivided by the quatree/octree technique. Finally, the weighted B-spline finite cell method is used to guarantee the analysis accuracy of the CAD model. In this paper, a new design flow from the structural CAD model to simulation analysis in the fixed grid is established. Numerical examples demonstrate the validity and efficiency of the proposed method.
LI Xinyao
,
ZHANG Weihong
,
CHEN Liang
. A fast analytic method for CAD model based on boundary representation in fixed grid[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019
, 40(6)
: 222693
-222693
.
DOI: 10.7527/S1000-6893.2018.22693
[1] GARCÍA-RUÍZ M J, STEVEN G P. Fixed grid finite elements in elasticity problems[J]. Engineering Computations, 1999, 16(2):145-164.
[2] GARCÍA-RUÍZ M J. Fixed grid finite element analysis in structural design and optimization[D]. Sydney:The university of Sydney, 1999:4-9.
[3] CAI S Y, ZHANG W H, ZHU J H, et al. Stress constrained shape and topology optimization with fixed mesh:A B-spline finite cell method combined with level set function[J]. Computer Methods in Applied Mechanics and Engineering, 2014, 278:361-387.
[4] CAI S Y, ZHANG W H. Stress constrained topology optimization with free-form design domains[J]. Computer Methods in Applied Mechanics Engineering, 2015(289):267-290.
[5] 赵林英. 基于固定网格的形状/拓扑优化新方法[D]. 西安:西北工业大学,2017:17-20. ZHAO L Y. Study on the new method in shape and topology optimization with fixed grid[D]. Xi'an:Northwestern Polytechnical University, 2017:17-20(in Chinese).
[6] 罗雅文. 基于固定网格的三维结构应力分析和形状优化[D]. 西安:西北工业大学,2015:24-28. LUO Y W. Stress analysis and shape optimization of 3D structure with fixed mesh[D]. Xi'an:Northwestern Polytechnical University, 2015:24-28(in Chinese).
[7] WENISCH P, WENISCH O. Fast octree-based voxelization of 3D boundary representation-objects[R]. Technische Universitāt München, 2014.
[8] DVSTER A, PARVIZIAN J, YANG Z, et al. The finite cell method for three-dimensional problems of solid mechanics[J]. Computer Methods in Applied Mechanics and Engineering, 2008,197:3768-3782.
[9] RANK E, RUESS M, KOLLMANNSBERGER S, et al. Geometric modeling, isogeometric analysis and the finite cell method[J]. Computer Methods in Applied Mechanics and Engineering, 2012, 249:104-115.
[10] 孙家广, 杨长贵. 计算机图形学(新版)[M]. 北京:清华大学出版社, 1995. SUN J G, YANG C G. Computer graphics (new edition)[M]. Beijing:Tsinghua University Press, 1995(in Chinese).
[11] WANG W C, LI J, WU E H. 2D point-in-polygon test by classifying edges into layers[J]. Computer & Graphics, 2005, 29:427-439.
[12] 张宁宁, 张树有,谭建荣. 映射相关边概念的多边形内外点判别算法[J]. 计算机辅助设计与图形学学报, 2004, 16(7):935-938. ZHANG N N, ZHANG S Y, TAN J R. Point inclusion test for simple polygons by the nearest relevant edge[J]. Journal of Computer-aided Design & Computer Graphics, 2004, 16(7):935-938(in Chinese).
[13] 陈瑞卿, 周健, 虞烈. 一种快速判断点与多边形关系的快速算法[J]. 西安交通大学学报, 2007, 41(1):59-63. CHEN R Q, ZHOU J, YU L. Fast method to determine spatial relationship between point and polygon[J]. Journal of Xi'an Jiao Tong University, 2007, 41(1):59-63(in Chinese).
[14] KALAY Y E. Determining the spatial containment of a point in general polyhedra[J]. Computer Graphics and Image Processing, 1982, 19(1):203-334.
[15] LANE J, MAGEDSON B, RARICK M N. An efficient point in polyhedron algorithm[J]. Computer Vision, Graphics and Image Processing, 1984, 26:118-125.
[16] HORN W, TAYLOR D L. A theorem to determine the spatial containment of a point in a planar polyhedron[J]. Computer Vision, Graphics and Image Processing, 1989, 45:106-116.
[17] MŌLLER T, HAINES E. Real-time rending[M]. 2nd ed. Wellesley:A K Peters Ltd, 2002:349-353, 583-586, 596-597.
[18] WATT A. 3D computer graphics[M]. 3rd ed. New Jersey:Addison-Wesley, 2000:51-54.
[19] GORDON D, SHULONG C. Front-to-back display or BSP trees[J]. IEEE Computer Graphics and Application, 1991, 11(5):79-86.
[20] O'ROURQUE J. Computational geometry in C[M]. Cambridge:Cambridge University, 1994:2.
[21] FEITO F, TORRES J, URENA A. Orientation, simplicity and inclusion test for planar polygons[J]. Computer & Graphics, 1995, 19:595-600.
[22] FEITO F R, TORRES J C. Inclusion test for general polyhedra[J]. Computers & Graphics, 1997, 21(1):23-30.
[23] CARLOS J O, RAFAEL J S, FRANCISCO R F. Point in solid strategies[J]. Computers & Graphics, 2005, 29:616-624.
[24] PARVIZIAN J, DVSTER A, RANK E. Finite cell method[J]. Computatinal Mechanics, 2007(41):121-133.
[25] SCHILLINGER D, RUESS M. The finite cell method:A review in the context of higher-order structural analysis of CAD and image-based geometric models[J]. Archives of Computational Methods in Engineering, 2015(22):391-455.
[26] PIEGL L, TILLER W. The NURBS book[M]. Berlin:Springer Science & Business Media, 2012.
[27] HOLLIG K, REIF U, WIPPER J. Weighted extended B-spline approximation of Dirichlet problems[J]. Siam Journal on Numerical Analysis, 2001, 39(2):442-462.
[28] HOLLIG K, APPRICH C, STREIT A. Introduction to the Web-method and its application[J]. Advances in Computational Mathematics, 2005, 23(1-2):215-237.
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