三维实体网格自适应划分算法

高质量的网格划分是三维建模研究的关键。根据对三维形体的几何特征和物理特征进行分析,给出三维网格划分的加密规则。通过研究网格加密区域和网格节点算法,设计基于Delaunay剖分的动态节点单元一体化三维网格自适应生成算法。在对对象的加密区域、区域布点等前期处理后,对选取的节点集进行Delaunay三角剖分,选取最优节点,并对特征集中区域进行局部加密,从而完成对三维体的网格划分,与传统划分方法相比较更具精确性和高效性。通过对机械零件进行网格划分,根据加密规则实现网格的疏密分布,划分结果能够准确描述出三维体的几何形体特征和物理特征分布,与传统划分方法的网格图形进行对比验证该方法的有效性,为更深入地研究形体提供基本保证。     

接触问题的自适应无网格伽辽金方法

针对接触问题提出了基于应变能梯度的自适应无网格伽辽金方法。通过对自适应无网格伽辽金方法的原理讨论,给出了基于背景网格的误差估计方法,并对自适应求解流程进行了阐述。研究了无网格节点加密技术和自适应搜索半径等关键技术。编程求解了圆柱体接触问题,并与理论解和均匀密化数值解进行比较,给出了接触计算中合理的参数范围,对真实粗糙表面接触问题进行了计算,计算结果表明,在相当计算精度下,自适应加密计算耗时仅为同等整体加密计算的18.6%。     

梯度引导电学成像自适应网格生成方法

电学层析成像是一种观测场域内电导率分布的无损检测技术。有限元法是求解电学层析成像问题的常用方法。其作为线性化的近似方法,剖分单元的大小会影响有限元法求解的精度。更密的尺寸可以提高重建图像的空间分辨率,但会增加计算成本,同时未知量个数的增加会加剧逆问题的欠定性。针对上述问题,提出一种基于图像梯度的自适应网格生成方法。根据初始重建图像的梯度,自适应地提高内含物区域的网格密度,降低其他区域的网格密度,并对场域边界进行精确拟合来优化被测场域的网格剖分。通过仿真与实验研究对比分析了所提方法与常用网格剖分方法。结果表明,所提方法的重建结果图像误差平均降低15%,相关系数平均提高7%,因此所提方法在不显著增加或减少网格数的情况下,可以有效提高内含物的重建精度和图像重建质量。     

基于散乱点的全自动四边形网格剖分方法

提出一种基于散乱点的全自动三维非结构化四边形网格剖分方法。对散乱点进行自适应预处理，包括冗余点的自动删除和模型边界提取。使用改进节点计算和铺路面相交搜索处理的铺路算法，自动生成全四边形网格。该方法可有效地控制生成网格单元的尺寸和质量，网格模型满足有限元分析的要求。与常规的基于CAD几何信息的网格生成方法相比，该方法避免了繁琐的模型修补问题，可快速生成高质量的全四边形网格模型。算例证明了该方法的有效性和实用性。     

有限元网格剖分与网格质量判定指标

讨论了网格剖分中的一些常见问题,阐述了网格剖分中应遵循的要求,介绍了近十多年来网格剖分方法的研究进展,回顾了网格剖分的各种算法,并比较了各种算法的优缺点。基于工程计算需求,提出了网格质量要求及判定指标,探讨了网格质量优化问题。同时,介绍了当前广泛使用的网格剖分前处理商业软件及其应用状况,并结合工作实际,给出了复杂模型网格剖分的具体实例。最后展望了网格剖分的发展趋势。     

基于实体局部表面曲率和厚度的变密度三维六面体网格自动生成算法

提出一种基于传统栅格法的变密度三维全六面体网格自动生成算法,建立基于实体局部表面曲率的加密源点信息场的生成技术和基于几何实体局部厚度特征的网格加密技术,并给出自动生成全六面体协调网格的加密原则与加密模板。实现了在厚度较小的特征区域和曲率较大区域局部协调加密及平缓变密度的网格自动剖分,可获得局部协调加密及平缓变密度的全六面体网格。实例表明,所提出的算法实用性强,效果良好。     

散乱模型的四边形网格剖分方法

针对基于CAD几何信息的网格剖分方法无法避免繁琐模型修补,导致网格剖分效率低下的现状,提出一种基于散乱模型的全四边形网格剖分方法.使用散乱点或者STL格式文件作为网格剖分的输入模型,使用改进的基于散乱模型进行网格剖分的铺路算法,在很大程度上减少甚至避免了模型修补问题.提出以散乱模型作为背景网格,作为控制网格单元尺寸调整的依据:使用网格细分和网格粗化的手段实现网格疏密变化的光滑过渡;自动识别几何模型中的特征并在网格模型中保留.提出了一种高效的铺路面相交搜索方法,综合考虑影响相交处理的多种因素,有效地处理了铺路面相交问题.多个复杂的汽车覆盖件网格剖分的算例结果表明,运用所提出方法完成的网格模型质量很高,算法具有较强的工程实用性.     

CSDF:一种基于STL的无锯齿差分网格剖分算法

针对基于差分的铸造CAE系统生成体网格时图像显示呈锯齿状这一问题,提出了一种基于STL面片模型的无锯齿网格剖分算法。算法采用一种新的组件式有符号距离场(CSDF)模型来对多个STL实体进行剖分。该模型采用了一种稳健的容错方法,能够对不封闭、缺点、少面的STL实体进行正确的剖分;使用BSP树来加速计算每个网格中心点距离铸件、砂芯、铸型以及浇注系统等STL几何实体的最小距离,并规定位于内部的中心点的距离为负,外部为正,表面为零,使得每一个网格点有一个表示材质的数据,同时还有几个不同的距离值;材质数据用来表示物理属性,而距离值用来进行STL实体的布尔运算,以实现组件式的网格剖分和几何模型的重建,获得光滑的后处理图像。实例表明:算法可行,可实现组件式的几何实体无锯齿网格剖分,且剖分结果能进行数值计算。     

斜齿轮有限元网格自适应加密技术研究

为了实现有限元法分析过程中计算精度和计算时耗的平衡,对斜齿轮自适应加密进行了研究。完成了斜齿轮模型建立和网格划分,并对其进行有限元分析,得到了齿根中点拉应力的值,以及齿根中点拉应力、单元密度、齿宽三者之间的关系。利用Matlab软件对齿根中点拉应力的值进行曲线拟合,将齿根中点拉应力作为实现斜齿轮自适应加密的关键参数,引入齿模比的概念,根据齿模比值的范围实现斜齿轮有限元网格的自适应加密,使得斜齿轮的有限元分析过程中在耗时较短的同时保证了有限元分析结果的准确。     

斜齿轮有限元网格自适应加密技术研究

为了实现有限元法分析过程中计算精度和计算时耗的平衡,对斜齿轮自适应加密进行了研究。完成了斜齿轮模型建立和网格划分,并对其进行有限元分析,得到了齿根中点拉应力的值,以及齿根中点拉应力、单元密度、齿宽三者之间的关系。利用Matlab软件对齿根中点拉应力的值进行曲线拟合,将齿根中点拉应力作为实现斜齿轮自适应加密的关键参数,引入齿模比的概念,根据齿模比值的范围实现斜齿轮有限元网格的自适应加密,使得斜齿轮的有限元分析过程中在耗时较短的同时保证了有限元分析结果的准确。     

基于STL文件的变密度三维全六面体网格自动生成方法

针对STL文件在传递复杂几何实体模型信息方面具有精度较高的特点，提出了一种基于STL文件变密度三维全六面体网格自动生成方法，给出了STL文件的数据格式及其内容约定，详细阐述了基于STL文件空间CAE模型表面特征自动识别、拓扑关系的生成和变密度栅格法加密信息场的建立等关键技术。实现了在实体模型表面曲率较大和厚度较小的局部区域进行协调加密，可以获得与实体模型边界吻合良好的全六面体协调网格，适合于工程问题的有限元分析计算。若干复杂实体模型算例表明，该算法实用性强，效果良好。     

一种基于子域分解的表面混合网格生成方法

提出了一种新的基于子域分解的混合网格生成方法。该方法首先用映射法生成结构化背景网格,并确定实体表面上包含的小孔、键槽等小特征在背景网格中的位置,然后删除这些小特征覆盖的背景网格,并在这些区域内生成三角形网格,最后将剩余的背景网格和生成的三角形网格合并,得到整个目标域的网格。该算法综合了映射法效率高、网格质量好、四边形网格计算精度高,以及三角形网格几何适应能力强的优势。数值实验表明,针对复杂的实体表面,新方法能够全自动地生成质量较好的混合网格,生成的网格质量及算法效率均优于传统的推进波前法和铺砖法。     

METHOD FOR ADAPTIVE MESH GENERATION BASED ON GEOMETRICAL FEATURES OF 3D SOLID

In order to provide a guidance to specify the element size dynamically during adaptive finite element mesh generation, adaptive criteria are firstly defined according to the relationships between the geometrical features and the elements of 3D solid. Various modes based on different datum geometrical elements, such as vertex, curve, surface, and so on, are then designed for generating local refined mesh. With the guidance of the defined criteria, different modes are automatically selected to apply on the appropriate datum objects to program the element size in the local special areas. As a result, the control information of element size is successfully programmed covering the entire domain based on the geometrical features of 3D solid. A new algorithm based on Delaunay triangulation is then developed for generating 3D adaptive finite element mesh, in which the element size is dynamically specified to catch the geometrical features and suitable tetrahedron facets are selected to locate interior nodes continuously. As a result, adaptive mesh with good-quality elements is generated. Examples show that the proposed method can be successfully applied to adaptive finite element mesh automatic generation based on the geometrical features of 3D solid.     

基于STEP中性文件的有限元自动建模

直接利用CAD系统的几何造型 ,以STEP中性文件为CAD造型系统与有限元单元剖分系统间的几何和拓朴信息传递媒介 ,实现有限元单元的自动剖分。按STEP/AP2 0 3的语义模型提取STEP中性文件中三维形体的表面信息 ,将该形体的每个表面映射到二维参数平面 ;利用参数平面的边界数据和二维单元自动剖分模块 ,用推进波前法实现表面网络的自动生成 ;然后由表及里实现三维实体单元的生成 ,系统基于STEP中性数据文件 ,可以与多个流行的CAD系统实行连接。     

Development of a 2-D flow solver on unstructured and adaptive Cartesian meshes

A two-dimensional flow solver using mixed grids has been developed for accurate and efficient simulation of steady and unsteady flow fields. The flow solver was cast to accommodate two different topologies of computational meshes: unstructured triangular meshes in the near-body region such that complex geometric configurations can be easily modeled, while unstructured adaptive Cartesian meshes are utilized in the off-body region to resolve the flow more accurately with less numerical dissipation by adopting a spatially high-order accurate scheme and solution-adaptive mesh refinement technique. The unstructured adaptive Cartesian meshes can be generated automatically and allow to handle data efficiently via quad-tree data structures. A chimera mesh approach has been employed to link the two flow regimes adopting each mesh topology. A second-order accurate vertex-centered scheme and a 3^rd- or 5^th-order accurate cellcentered WENO scheme has been utilized in the near-body region and in the off-body region, respectively. Validations were made for the unsteady inviscid vortex convection and the steady and unsteady turbulent flows over an NACA0012 airfoil, and the results were compared with other computational and experimental results.     

A simple nodal force distribution method in refined finite element meshes

In finite element analyses, mesh refinement is frequently performed to obtain accurate stress or strain values or to accurately define the geometry. After mesh refinement, equivalent nodal forces should be calculated at the nodes in the refined mesh. If field variables and material properties are available at the integration points in each element, then the accurate equivalent nodal forces can be calculated using an adequate numerical integration. However, in certain circumstances, equivalent nodal forces cannot be calculated because field variable data are not available. In this study, a very simple nodal force distribution method was proposed. Nodal forces of the original finite element mesh are distributed to the nodes of refined meshes to satisfy the equilibrium conditions. The effect of element size should also be considered in determining the magnitude of the distributing nodal forces. A program was developed based on the proposed method, and several example problems were solved to verify the accuracy and effectiveness of the proposed method. From the results, accurate stress field can be recognized to be obtained from refined meshes using the proposed nodal force distribution method. In example problems, the difference between the obtained maximum stress and target stress value was less than 6 % in models with 8-node hexahedral elements and less than 1 % in models with 20-node hexahedral elements or 10-node tetrahedral elements.     

An adaptive procedure based on combining finite elements with meshless methods

This paper presents a new method for combining finite elements with meshless methods, which increases the accuracy of computational solutions in a coarse mesh by adding nodes in the domain of interest. The present method shares the features of the finite element and meshless methods such as (a) the meshless interpolation of the MLS type is employed; (b) integration domains are consistent with support domains; and (c) essential boundary conditions can be applied directly. In the present method, a ground mesh with triangular or quadrilateral elements is constructed to define polygonal support domains, and then additional nodes are placed arbitrarily in a domain without the reconstruction of a mesh. The method is very useful in an adaptive calculation, because nodes can be easily added or removed without any remeshing process. This paper was recommended for publication in revised form by Associate Editor Maenghyo Cho Hyun-Gyu Kim received his B.S. degree from Seoul National University in 1990. He then received M.S. and Ph.D. degrees from KAIST in 1993 and 1998, respectively. Dr. Kim is currently a Professor at the Department of Mechanical Engineering in Seoul National University of Technology, Korea. His research interests include multi-physics coupling analysis, interfacing non-matching meshes, development of special elements, and inverse problems.     

Adaptive multiscale method for two-dimensional nanoscale adhesive contacts

There are two separate traditional approaches to model contact problems: continuum and atomistic theory. Continuum theory is successfully used in many domains, but when the scale of the model comes to nanometer, continuum approximation meets challenges. Atomistic theory can catch the detailed behaviors of an individual atom by using molecular dynamics (MD) or quantum mechanics, although accurately, it is usually time-consuming. A multiscale method coupled MD and finite element (FE) is presented. To mesh the FE region automatically, an adaptive method based on the strain energy gradient is introduced to the multiscale method to constitute an adaptive multiscale method. Utilizing the proposed method, adhesive contacts between a rigid cylinder and an elastic substrate are studied, and the results are compared with full MD simulations. The process of FE meshes refinement shows that adaptive multiscale method can make FE mesh generation more flexible. Comparison of the displacements of boundary atoms in the overlap region with the results from full MD simulations indicates that adaptive multiscale method can transfer displacements effectively. Displacements of atoms and FE nodes on the center line of the multiscale model agree well with that of atoms in full MD simulations, which shows the continuity in the overlap region. Furthermore, the Von Mises stress contours and contact force distributions in the contact region are almost same as full MD simulations. The method presented combines multiscale method and adaptive technique, and can provide a more effective way to multiscale method and to the investigation on nanoscale contact problems.