基于弹簧质点模型的自由曲面四边形网格平面化研究
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摘要
为实现对自由曲面的平面四边形网格划分,提出了一种基于力学模拟的网格优化算法,建立了包含杆件长度的约束力、边界固定质点约束力、曲面对质点的吸附力、网格平面化作用力的弹簧质点计算模型.首先,采用映射法或其他方法对曲面进行初始四边形网格划分,在获得曲面的初始网格划分的基础上根据不同网格性能的侧重要求,计算出相应的弹性系数k_(ij)、边界约束刚度k_c、对网格点的吸附刚度k_m、平面化控制系数p_c,建立以平面化为目标的网格弹簧质点模型,通过动力松弛法,经多次迭代得到平面化网格;然后结合四边形平面化指标,以流畅性指标和均匀性指标对网格进行质量综合评价,同时引入网格偏离指标对网格的形状进行控制;最后,进行了算例验证,算例表明,弹簧质点平面化网格计算方法可以很好地适应自由曲面,通过调整参数,在一定条件下可使网格平面化的许允误差限制达到合理范围,同时可以兼顾流畅性和均匀性的要求.
In order to obtain the planar quadrangle architectural mesh of free-form surfaces,a mesh optimization algorithm based on mechanical simulation was proposed.The spring-mass model comprised of restraint force for rod length,the restraint force for boundary fixed particle,the adsorption force for surface to particle and the force for mesh planarization,was established.First,according to the designer,mapping method or other methods were used for the initial quadrangle grid generation.Then,considering the requirements of different performance,the elastic coefficient k_(ij),boundary constraint stiffness k_c,adsorption stiffness k_m,and planarity coefficient p_c were calculated.The mesh spring particle model with coplanar target was established,and the coplanar mesh was obtained by multiple iterations through dynamic relaxation method.Then,combined with the quadrilateral planarization index,the quality of the grid was evaluated comprehensively by fluency index and uniformity index,and the grid deviation index was introduced to control the shape of the grid.Finally,examples were given to verify the results.Examples show that the planarity optimization algorithm can be well adapted to free-form surfaces.By adjusting the parameters,the allowable error limits of planarization can reach a reasonable range with fluent and uniform architectural grids under certain conditions.
In order to obtain the planar quadrangle architectural mesh of free-form surfaces,a mesh optimization algorithm based on mechanical simulation was proposed.The spring-mass model comprised of restraint force for rod length,the restraint force for boundary fixed particle,the adsorption force for surface to particle and the force for mesh planarization,was established.First,according to the designer,mapping method or other methods were used for the initial quadrangle grid generation.Then,considering the requirements of different performance,the elastic coefficient k_(ij),boundary constraint stiffness k_c,adsorption stiffness k_m,and planarity coefficient p_c were calculated.The mesh spring particle model with coplanar target was established,and the coplanar mesh was obtained by multiple iterations through dynamic relaxation method.Then,combined with the quadrilateral planarization index,the quality of the grid was evaluated comprehensively by fluency index and uniformity index,and the grid deviation index was introduced to control the shape of the grid.Finally,examples were given to verify the results.Examples show that the planarity optimization algorithm can be well adapted to free-form surfaces.By adjusting the parameters,the allowable error limits of planarization can reach a reasonable range with fluent and uniform architectural grids under certain conditions.
引文
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[18] 徐斌,高跃飞,余龙.MATLAB有限元结构动力学分析与工程应用 [M].北京:清华大学出版社,2009.
[2] 李承铭,卢旦.自由曲面单层网格的智能布局设计研究 [J].土木工程学报,2011(3):1- 7.LI Cheng-ming,LU Dan.Study of intelligent layout design of single-layer lattice shell of free form surface [J].China Civil Engineering Journal,2011(3):1- 7.
[3] 江存,高博青.基于自定义单元法的自由曲面网格划分研究 [J].建筑结构,2015(5):44- 48.JIANG Cun,GAO Bo-qing.Research on free-form surface meshing based on self-defined element method [J].Building Structure,2015(5):44- 48.
[4] 危大结,舒赣平.自由曲面网格的划分与优化方法 [J].建筑结构,2013(19):48- 53.WEI Da-jie,SHU Gan-ping.Mesh generation and optimization method for free-form surface grid [J].Building Structure,2013(19):48- 53.
[5] 潘炜,单艳玲,李铁瑞,等.自由曲面网格划分的研究现状 [C]//全国现代结构工程学术研讨会.天津:天津大学,2015.
[6] 沈利刚,龚景海.自由曲面四边形网格等杆长划分算法 [J].空间结构,2016,22(1):11- 15.SHEN Li-gang,GONG Jing-hai.An algorithm for equilateral quadrilateral mesh models of free-form surface [J].Spatial Structures,2016,22(1):11- 15.
[7] 马腾.自由曲面网格结构的网格划分技术研究 [D].杭州:浙江大学,2015.
[8] GLYMPH J,SHELDEN D,CECCATO C,et al.A parametric strategy for free-form glass structures using quadrilate-ral planar facets [J]Automation in Construction,2004,13(2):187- 202.
[9] DOUTHE C,MESNIL R,ORTS H,et al.Isoradial meshes:covering free-form architecture with planar facets [J].Automation in Construction,2017,83:222- 236.
[10] LIU Y,XU W,WANG J,et al.General planar quadrila-teral mesh design using conjugate direction field [J].Acm Transactions on Graphics,2011,30(6):1- 10.
[11] 周磊.复杂建筑形体自由曲面量化处理方法 [D].长沙:湖南大学,2012.
[12] PIEGL L,TILLER W.The NURBS book [M].New York:Springer,1995.
[13] 施法中.计算机辅助几何设计与非均匀有理B样条 [M].北京:高等教育出版社,2013.
[14] 覃先云,张见明.基于改进波前法的曲面网格生成算法 [J].计算机辅助工程,2014,23(4):69- 75.QIN Xian-yun,ZHANG Jian-ming.Surface mesh generation algorithm based on improved advancing front method [J].Computer Aided Engineering,2014,23(4):69- 75.
[15] 吴宝海,王尚锦.参数曲面网格生成的改进波前法 [J].计算机辅助设计与图形学学报,2005,17(8):1686- 1690.WU Bao-hai,WANG Shang-jin.An improved advancing front method for mesh generation over parametric surfaces [J].Journal of Computer-Aided Design & Compu-ter Graphics,2015,17(8):1686- 1690.
[16] 单建,蓝天.动力松驰法在张拉结构静力分析中的应用 [J].东南大学学报(自然科学版),1994(3):94- 98.SHAN Jian,LAN Tian.On dynamic relaxation and its application to static analysis of tension structure [J].Journal of Southeast University(Natural Science Edition),1994(3):94- 98.
[17] 李重阳.动力松弛法在索膜结构分析中的应用研究 [D].广州:华南理工大学,2003.
[18] 徐斌,高跃飞,余龙.MATLAB有限元结构动力学分析与工程应用 [M].北京:清华大学出版社,2009.
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