基于弹簧质点模型的自由曲面四边形网格平面化研究  

Architectural Planar Quadrilateral Grid Generation for Free-form Surfaces Based on Spring-mass Model

作　　者：高博青[1] 李峥 吴慧 GAO Boqing;LI Zheng;WU Hui(College of Civil Engineering and Architecture,Zhejiang University,Hangzhou 310058,Zhejiang,China;Public Administration College,Zhejiang University of Finance & Economics,Hangzhou 310018,Zhejiang,China)

机构地区：[1]浙江大学建筑工程学院,浙江杭州310058 [2]浙江财经大学公共管理学院,浙江杭州310018

出　　处：《华南理工大学学报（自然科学版）》2019年第7期32-39,共8页Journal of South China University of Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(51678521,51778558)~~

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kij、边界约束刚度kc、对网格点的吸附刚度km、平面化控制系数pc,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.

关 键 词：自由曲面 网格平面化 力学模拟 优化算法 动力松弛法 迭代 评价指标 

分 类 号：TU393.3[建筑科学—结构工程]