空间网格结构几何形态研究与实现
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摘要
空间网格结构几何外形与网格划分模式日趋丰富多彩,给设计建模与修改调整工作带来难度。本文针对此问题提出了空间网格结构几何形态的概念,将创建与优化问题作为研究对象,着重探讨几何形态的实现过程。论文完善了空间网格结构几何形态的基础理论;提出了三类几何造型技术:生成设计、基于力学原理的造型方法以及逆向建模方法;研究了网格划分模式的扩展与网格体系的优化方法。
本文首先分析了空间网格结构曲面形式和网格划分的多样性,归纳出几何形态研究的若干关键问题。介绍了曲面造型与网格划分技术的发展和现状,并阐述了空间网格结构领域围绕几何形态研究所遇到的一些问题。
空间网格结构曲面形态一般可分为函数曲面与自由曲面。论文中,对于函数曲面采用解析方式进行描述。对于自由曲面表达则引入表现力较强的B样条曲面以及准均匀B样条曲面,并根据曲线曲面边界趋势,结合数值方法,形成边界预测切矢技术使曲面表达更为精确。提炼出几何基本参数及曲面曲率性质。提出基于二次插值的网格映射划分方法以解决曲面曲率不均造成的网格畸变问题。
几何造型的生成设计实现了空间网格结构几何形态程序化操作。针对函数曲面与仿生类自由曲面形态特征,由参数设定构建呈矩形拓扑关系的型值点阵,通过B样条曲面插值算法分别进行曲面重构与曲面造型设计。特别地,在构建仿生类自由曲面时,分别讨论了仿梅花形体与仿花瓣形体两类自然形态的参数设置原理。通过数值模拟与对比分析验证了生成设计能够满足曲面重构精度要求并有效地提高了几何形态生成效率。
基于力学原理的曲面造型方法将几何形态与力学原理相结合,简化了依靠几何参数调整的繁复操作。其一为能量法造型技术:由薄板弹性变形推导了变形曲面的完备能量模型,明确了各项设计参数的物理意义,统一了曲面构造设计与曲面修改调整的控制方程,并引入双三次准均匀B样条曲面单元,简化了曲面边界处简支及固支约束条件的处理。另一类是基于薄膜平衡的曲面造型技术:引入差分预测切矢技术及双三次准均匀B样条曲面描述初始曲面,根据曲率性质推导了结点虚拟刚度,将拉普拉斯方程与动力松弛法相结合,由薄膜平衡的自然性质构造与优化曲面形态。数值模拟表明此技术在寻找极小曲面,类比相似曲面形态以及获取加密网格方面有比较便利的应用。
逆向建模方法借鉴逆向工程的操作原理。首先利用自组激光三维扫描系统进行实物样件的点云数据采集,然后将点云经逆向软件预处理,由改良后的蒙皮法进行曲面造型以及网格初步划分,得到网格结构数字模型,再经曲面条带化旋转展开,由纸板加工放样,实现实体模型的加工制作。上述工作表明了逆向建模方法的可行性与实用性。
论文给出网格质量评价标准,扩展了网格划分模式。运用改进后的能量法进行网格体系光顺,并得到了光顺罚因子与各项网格质量评价指标的变化规律。提出考虑曲面特征、网格质量、杆件单元长度偏差等因素的网格体系优化目标函数,并考虑权重影响,统一目标函数,经一维搜索技术,得到最优网格体系。
根据上述理论与方法编制了几何形态设计程序系统GCCAD。该程序系统具有图形化的用户界面、几何形态设计和结果处理功能。为实际工程应用提供了操作平台,提高了几何形态设计的工作效率。
通过理论推导、数值模拟以及程序系统的编制表明,本文总结与提出的空间网格结构几何形态造型的实现方法是可行且有效的,解决了复杂几何形态空间网格结构建模的相关问题。同时论文还提出了今后有待解决的若干问题。
Various types of shapes and grid modes of space grid structures bring on lots of difficulties in structural modeling and design. Thus, based on the proposed concept of geometric configuration of space grid structures, this dissertation researches on the modeling and optimization technique, and focuses on the realization process of structures. In this work, three primary modeling techniques are investigated, i.e. generation design, mechanics-based modeling technique and reverse modeling method. Moreover, the extension of grid meshing modes and the optimization of grid system are also discussed.
The types of surface shapes and grid modes are firstly analyzed. A number of key technical issues on geometric configuration are then concluded. A state-of-the-art review on modeling and meshing techniques of space grid structures is given and some involved problems are also expounded.
The surfaces of space grid structures generally include regular and free-form surfaces, which are respectively expressed by analytic function and B-splines as well as quasi-uniform B-splines. With the combination of numerical method, the prediction technology of clamping boundary is discussed according to the trend. Basic geometric parameters and surface curvature are described. The re-interpolation reflection meshing method is proposed to avoid the uneven grids caused by the distortion curvature.
Generation design technique realizes the computer aided design of geometric configuration. Firstly, the characteristic parameters of surfaces used as data points which distribute in rectangular topological relationship can be generated. Then B-splines interpolation is implemented to reconstruct or reshape surface. Especially, how to generate parameters of clubs-shaped and petal-shaped pattern is discussed. Numerical examples prove that the generation design can satisfy the accuracy and improve the efficiency.
Mechanics-based modeling techniques are comprised of the theory of geometric and mechanics. One modeling technique is energy modeling method. A complete energy model and physical meanings of parameters are presented. The uniform control equation is given, and with the introduction of quasi-uniform B-spline elements, the simply and clamped supported constraints problems are simplified. Another modeling technique is based on self-equilibrium membrane. The prediction technology of clamping boundary and quasi-uniform B-splines are introduced to express surface, and suppositional stiffness of point is deduced. With the combination of Laplace-Young's equation and dynamic relaxation method, the optimal surface inherited is shaped according to the change of average curvature. Numerical examples present that it is convenient to get minimal surface, seek for similar surfaces and mesh more grids by using above techniques.
Reverse modeling method is derived from the principle of reverse engineering. Firstly, it scans the physical model to get cloud data by 3-dimensional laser scanning system. Secondly, the cloud data are handled by reverse software to get scan-lines data. Thirdly, the scan-lines data are shaped by improved skinning surface technique and meshed to CAD model. Finally, the CAD model can be fabricated by paper through the board-lofting technique. Several examples and experiments prove that the reverse modeling method is feasible.
In dissertation, some grid quality criteria are given. Several practical grid modes are extended. The improved energy method is applied to smooth grid system, and disciplinarian with punished factor and grid quality criteria is concluded. One optimization algorithm of grid system is proposed, where the grid system characteristics, grid quality and tolerance of elements length, etc. are weighted to perform objective function.
According to the theory and algorithm aforementioned, a computer aided design program named geometric configuration, GCCAD for short, is developed. GCCAD has friendly pre- and post- processing functions, and graphical interfaces. It provides operating platform and improve the efficiency and convenience of design work.
The conclusions and problems that should be studied further are summarized at the end of dissertation.
本文首先分析了空间网格结构曲面形式和网格划分的多样性,归纳出几何形态研究的若干关键问题。介绍了曲面造型与网格划分技术的发展和现状,并阐述了空间网格结构领域围绕几何形态研究所遇到的一些问题。
空间网格结构曲面形态一般可分为函数曲面与自由曲面。论文中,对于函数曲面采用解析方式进行描述。对于自由曲面表达则引入表现力较强的B样条曲面以及准均匀B样条曲面,并根据曲线曲面边界趋势,结合数值方法,形成边界预测切矢技术使曲面表达更为精确。提炼出几何基本参数及曲面曲率性质。提出基于二次插值的网格映射划分方法以解决曲面曲率不均造成的网格畸变问题。
几何造型的生成设计实现了空间网格结构几何形态程序化操作。针对函数曲面与仿生类自由曲面形态特征,由参数设定构建呈矩形拓扑关系的型值点阵,通过B样条曲面插值算法分别进行曲面重构与曲面造型设计。特别地,在构建仿生类自由曲面时,分别讨论了仿梅花形体与仿花瓣形体两类自然形态的参数设置原理。通过数值模拟与对比分析验证了生成设计能够满足曲面重构精度要求并有效地提高了几何形态生成效率。
基于力学原理的曲面造型方法将几何形态与力学原理相结合,简化了依靠几何参数调整的繁复操作。其一为能量法造型技术:由薄板弹性变形推导了变形曲面的完备能量模型,明确了各项设计参数的物理意义,统一了曲面构造设计与曲面修改调整的控制方程,并引入双三次准均匀B样条曲面单元,简化了曲面边界处简支及固支约束条件的处理。另一类是基于薄膜平衡的曲面造型技术:引入差分预测切矢技术及双三次准均匀B样条曲面描述初始曲面,根据曲率性质推导了结点虚拟刚度,将拉普拉斯方程与动力松弛法相结合,由薄膜平衡的自然性质构造与优化曲面形态。数值模拟表明此技术在寻找极小曲面,类比相似曲面形态以及获取加密网格方面有比较便利的应用。
逆向建模方法借鉴逆向工程的操作原理。首先利用自组激光三维扫描系统进行实物样件的点云数据采集,然后将点云经逆向软件预处理,由改良后的蒙皮法进行曲面造型以及网格初步划分,得到网格结构数字模型,再经曲面条带化旋转展开,由纸板加工放样,实现实体模型的加工制作。上述工作表明了逆向建模方法的可行性与实用性。
论文给出网格质量评价标准,扩展了网格划分模式。运用改进后的能量法进行网格体系光顺,并得到了光顺罚因子与各项网格质量评价指标的变化规律。提出考虑曲面特征、网格质量、杆件单元长度偏差等因素的网格体系优化目标函数,并考虑权重影响,统一目标函数,经一维搜索技术,得到最优网格体系。
根据上述理论与方法编制了几何形态设计程序系统GCCAD。该程序系统具有图形化的用户界面、几何形态设计和结果处理功能。为实际工程应用提供了操作平台,提高了几何形态设计的工作效率。
通过理论推导、数值模拟以及程序系统的编制表明,本文总结与提出的空间网格结构几何形态造型的实现方法是可行且有效的,解决了复杂几何形态空间网格结构建模的相关问题。同时论文还提出了今后有待解决的若干问题。
Various types of shapes and grid modes of space grid structures bring on lots of difficulties in structural modeling and design. Thus, based on the proposed concept of geometric configuration of space grid structures, this dissertation researches on the modeling and optimization technique, and focuses on the realization process of structures. In this work, three primary modeling techniques are investigated, i.e. generation design, mechanics-based modeling technique and reverse modeling method. Moreover, the extension of grid meshing modes and the optimization of grid system are also discussed.
The types of surface shapes and grid modes are firstly analyzed. A number of key technical issues on geometric configuration are then concluded. A state-of-the-art review on modeling and meshing techniques of space grid structures is given and some involved problems are also expounded.
The surfaces of space grid structures generally include regular and free-form surfaces, which are respectively expressed by analytic function and B-splines as well as quasi-uniform B-splines. With the combination of numerical method, the prediction technology of clamping boundary is discussed according to the trend. Basic geometric parameters and surface curvature are described. The re-interpolation reflection meshing method is proposed to avoid the uneven grids caused by the distortion curvature.
Generation design technique realizes the computer aided design of geometric configuration. Firstly, the characteristic parameters of surfaces used as data points which distribute in rectangular topological relationship can be generated. Then B-splines interpolation is implemented to reconstruct or reshape surface. Especially, how to generate parameters of clubs-shaped and petal-shaped pattern is discussed. Numerical examples prove that the generation design can satisfy the accuracy and improve the efficiency.
Mechanics-based modeling techniques are comprised of the theory of geometric and mechanics. One modeling technique is energy modeling method. A complete energy model and physical meanings of parameters are presented. The uniform control equation is given, and with the introduction of quasi-uniform B-spline elements, the simply and clamped supported constraints problems are simplified. Another modeling technique is based on self-equilibrium membrane. The prediction technology of clamping boundary and quasi-uniform B-splines are introduced to express surface, and suppositional stiffness of point is deduced. With the combination of Laplace-Young's equation and dynamic relaxation method, the optimal surface inherited is shaped according to the change of average curvature. Numerical examples present that it is convenient to get minimal surface, seek for similar surfaces and mesh more grids by using above techniques.
Reverse modeling method is derived from the principle of reverse engineering. Firstly, it scans the physical model to get cloud data by 3-dimensional laser scanning system. Secondly, the cloud data are handled by reverse software to get scan-lines data. Thirdly, the scan-lines data are shaped by improved skinning surface technique and meshed to CAD model. Finally, the CAD model can be fabricated by paper through the board-lofting technique. Several examples and experiments prove that the reverse modeling method is feasible.
In dissertation, some grid quality criteria are given. Several practical grid modes are extended. The improved energy method is applied to smooth grid system, and disciplinarian with punished factor and grid quality criteria is concluded. One optimization algorithm of grid system is proposed, where the grid system characteristics, grid quality and tolerance of elements length, etc. are weighted to perform objective function.
According to the theory and algorithm aforementioned, a computer aided design program named geometric configuration, GCCAD for short, is developed. GCCAD has friendly pre- and post- processing functions, and graphical interfaces. It provides operating platform and improve the efficiency and convenience of design work.
The conclusions and problems that should be studied further are summarized at the end of dissertation.
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