几何自适应参数曲面网格生成

为满足有限元分析的需要,针对参数曲面提出一种几何自适应的网格生成方法.通过黎曼度量控制下的曲面约束Delaunay三角化获得曲面中轴,将其用于自动识别曲面邻近特征,并通过曲率计算自动识别曲率特征;根据邻近特征和曲率特征,融合传统网格尺寸控制技术控制边界曲线离散,并创建密度场;结合映射法和前沿推进技术对组合参数曲面生成几何自适应的网格.实验结果表明,该方法能够处理复杂的几何外形,生成的网格具有很好的自适应效果和质量.     

Poisson-Boltzmann方程的并行有限元求解及网格自适应生成

说明如何利用并行自适应有限元软件平台PHG 求解生物分子溶液体系的非线性Poisson-Boltzmann方程,并介绍一种解决这类问题的方法,它将网格生成与自适应计算过程结合在一起,可自动产生合适的网格,避免复杂的曲面网格生成步骤.之前的网格生成工作有：（1） TMSmesh生成高斯曲面的三角网格; （2） TransforMesh删除自相交的三角网格; （3） ISO2Mesh提高表面网格质量3个步骤.而基于PHG的自适应加密模块可以在逐次调整网格的同时保持动态负载平衡,高效地得到计算网格用于近似求解非线性Poisson-Boltzmann方程.计算了小球模型和AChE系统,分别从误差指示子下降阶和溶剂化能收敛的角度验证了方法的有效性,并且还将网格生成算法成功地应用于gA离子通道.     

利用调和映射的复杂网格曲面螺旋刀轨生成算法

针对截平面法规划的复杂网格曲面刀轨的加工效率不高问题,提出一种复杂网格曲面螺旋刀轨生成算法.首先采用调和映射的方法对网格曲面进行参数化,然后根据残留高度确定参数网格中的参数环,在相邻参数环的参数点之间进行“分组匹配”,并依次计算初始和精确的对角参数螺旋线;在此基础上采用“区域划分”的方法快速生成了无干涉的网格曲面螺旋刀轨.对于复杂网格曲面的实验结果表明,文中的螺旋刀轨能够有效地提高截平面法刀轨的加工效率,且能够保证较好的加工质量.     

基于球填充法的STL模型曲面自适应网格生成方法

为满足有限元分析的需要,针对STL模型提出一种基于球填充法的自适应网格生成方法.首先识别STL模型的线曲率、面曲率和区域形状特征;其次采用八叉树做背景网格来建立尺寸场信息;最后,利用球填充算法在STL曲面生成自适应网格.文中方法不需要点面投影、前沿判交等复杂计算,能高效地生成STL曲面自适应网格.数值实验结果表明,该方法比NetGen速度更快,产生的自适应网格质量更优.     

参数化曲面网格生成的气泡堆积法研究

结合微分几何理论知识,提出了一种参数曲面网格生成的气泡堆积算法。将曲面上的节点看作具有相互作用力的气泡,通过基于曲率的控制度量确定的节点间隔函数和弧长偏差因子来有效地控制网格尺寸,并借助三维桶结构建立和更新邻近气泡列表,当各气泡经动态模拟后达到力平衡状态时,连接气泡的中心就构成高质量的曲面网格。算例表明,生成的网格质量高、有很好的渐进性和对复杂曲面的适应性。     

基于波前法的参数曲面有限元网格生成算法

为克服参数曲面有限元网格生成中的单元形状映射畸变问题,提出一种曲面有限元网格自动生成算法.该算法由弹性矢量确定曲面上新节点的生成方向和空间位置,利用相应的参数域网格进行新单元拓扑相容性判断.在生成闭曲面网格时,通过添加参/虚边界棱边对闭曲面边界进行调整,确保闭曲面边界信息相对其参数域的完整性;在给出闭曲面极点初始化方法和适当设置单元边线段相等条件的基础上,该算法适用于各种不同形式闭曲面的网格自动生成.实验算例表明,文中算法可生成质量良好的参数曲面和组合面有限元网格.     

多裁剪自由曲面生成有限元网格的实现

论述了多裁剪自由曲面生成有限元曲面网格的几个关键技术.采用了推进波前法生成曲面网格,给出了核心算法;在曲面算法中运用了介于参数法与直接法之间的新方法.针对求解曲面上最优点的参数域反算问题,引入了切矢逆求方法,可使迭代次数大为降低.测试表明,该算法快速、稳定.对大型的多裁剪自由曲面生成的曲面有限元网格,可直接用于有限元计算.     

边界面法数值结果的云图表征

边界面法继承了传统边界元法的优点,并将几何实体的边界曲面离散为参数空间里的曲面单元,在处理一些特殊问题如移动边界、高梯度、大变形等方面显示出特殊的优越性.但是也使得计算结果的后处理遇到困难.提出了一种基于黎曼度量推进波前法生成三角背景网格的实用边界面法计算结果后处理方法.该法对求解域剖分成三角背景网格然后将计算结果映射...     

边界优先的Delaunay-层推进曲面四边形网格生成

为了提高复杂组合曲面四边形网格生成的鲁棒性和边界单元质量,提出一种边界优先的Delaunay-层推进网格生成方法.首先在剖分域内粗的约束Delaunay背景网格的辅助下,以物理域的位置偏差为引导,在参数域中迭代计算边界点的法矢量;然后结合层推进策略,在几何特征附近生成各向异性或各向同性正交网格;最后使用Coring技术加速内部网格的生成并进行单元合并,得到四边形为主的网格.若干复杂平面区域和组合曲面模型的剖分结果表明,所提方法可生成等角扭曲度和纵横比优于主流商业软件的网格;在12个线程的PC平台上,使用OpenMP并行剖分包含21 772张曲面的引擎模型只用了38.68 s.     

扫掠法有限元网格生成方法

为了提高有限元网格的生成质量,扫掠法生成六面体网格过程中内部节点定位成为关键一步,在研究复杂扫掠体六面体有限元网格生成算法过程中,提出了一种基于扫掠法的六面体网格生成算法,算法利用源曲面已经划分好的网格和连接曲面的结构化网格,用仿射映射逐层投影,生成目标曲面,提出基于Roca算法的内部节点定位的新算法,运用由外向内推进的波前法思想,生成全部的六面体网格。通过实例表明,该算法快速,稳定,可靠,可处理大量复杂2.5维实体六面体网格生成问题。     

Generation of anisotropic mesh by ellipse packing over an unbounded domain

With the advance of the finite element method, general fluid dynamic and traffic flow problems with arbitrary boundary definition over an unbounded domain are tackled. This paper describes an algorithm for the generation of anisotropic mesh of variable element size over an unbounded 2D domain by using the advancing front ellipse packing technique. Unlike the conventional frontal method, the procedure does not start from the object boundary but starts from a convenient point within an open domain. The sequence of construction of the packing ellipses is determined by the shortest distance from the fictitious centre in such a way that the generation front is more or less a circular loop with occasional minor concave parts due to element size variation. As soon as an ellipse is added to the generation front, finite elements are directly generated by properly connecting frontal segments with the centre of the new ellipse. Ellipses are packed closely and in contact with the existing ellipses by an iterative procedure according to the specified anisotropic metric tensor. The anisotropic meshes generated by ellipse packing can also be used through a mapping process to produce parametric surface meshes of various characteristics. The size and the orientation of the ellipses in the pack are controlled by the metric tensor as derived from the principal surface curvatures. In contrast to other mesh generation schemes, the domain boundary is not considered in the process of ellipse packing, this reduces a lot of geometrical checks for intersection between frontal segments. Five examples are given to show the effectiveness and robustness of anisotropic mesh generation and the application of ellipse packing to mesh generation over various curved surfaces.     

参数曲面网格生成的改进波前法

采用从曲面两条边界向曲面中心推进的方法．避免了常规波前法中由于曲面角点的不良形态导致网格规划的失败和生成低质量网格．提出了一种新的节点生成方法，直接在三维空间中生成节点，然后映射到参数平面，使得在平面上进行节点及单元的合法性检查成为可能．针对从两侧推进的波前法，给出一种新的判断网格收敛的疗法．算例表明．文中方法易于实施、稳定性好，生成的网格质量高．     

Generation of triangular mesh with specified size by circle packing

This paper describes an algorithm for the generation of a finite element mesh with a specified element size over an unbound 2D domain using the advancing front circle packing technique. Unlike the conventional frontal method, the procedure does not start from the object boundary but starts from a convenient point within the open domain. As soon as a circle is added to the generation front, triangular elements are directly generated by properly connecting frontal segments with the centre of the new circle. Circles are packed closely and in contact with the existing circles by an iterative procedure according to the specified size control function. In contrast to other mesh generation schemes, the domain boundary is not considered in the process of circle packing, this reduces a lot of geometrical checks for intersection between frontal segments. If the mesh generation of a physical object is required, the object boundary can be introduced. The boundary recovery procedure is fast and robust by tracing neighbours of triangular elements. The finite element mesh generated by circle packing can also be used through a mapping process to produce parametric surface meshes of the required characteristics. The sizes of circles in the pack are controlled by the principal surface curvatures. Five examples are given to show the effectiveness and robustness of mesh generation and the application of circle packing to mesh generation over curved surfaces.     

Mesh generation and mesh refinement procedures for the analysis of concrete shells

In this paper, a mesh generation and mesh refinement procedure for adaptive finite element (FE) analyses of real-life surface structures are proposed. For mesh generation, the advancing front method is employed. FE meshes of curved structures are generated in the respective 2D parametric space of the structure. Thereafter, the 2D mesh is mapped onto the middle surface of the structure. For mesh refinement, two different modes, namely uniform and adaptive mesh refinement, are considered. Remeshing in the context of adaptive mesh refinement is controlled by the spatial distribution of the estimated error of the FE results. Depending on this distribution, remeshing may result in a partial increase and decrease, respectively, of the element size. In contrast to adaptive mesh refinement, uniform mesh refinement is characterized by a reduction of the element size in the entire domain. The different refinement strategies are applied to ultimate load analysis of a retrofitted cooling tower. The influence of the underlying FE discretization on the numerical results is investigated.     

基于STEP的三维表面有限元网格生成技术的研究*

研究了三维表面有限元网格自动生成的技术,利用映射法实现了模型表面的三角网格剖分。基于STEP文件格式的模型的导入和重建,将模型的每个表面映射至参数空间,利用推进波前法生成参数面网格,然后映射回三维表面。研制了一套网格剖分策略,运用该策略对多种类型表面进行了分析求解。     

Adaptive mesh refinement for shells with modified Ahmad elements

This paper presents a simple scheme for the generation of a quadrilateral element mesh for shells with arbitrary three-dimensional geometry. The present mesh generation scheme incorporates a normal mesh generator for generating a mesh in the two-dimensional plane and a specific mapping technique which maps the two-dimensional mesh onto the three-dimensional curved surface. As the mapping is a one-to-one mapping between the mesh in the plane and that on the curved surface, the resulting surface discretization is compatible with the local mesh parameters in two dimensions. This scheme is further combined, both with a sophisticated error estimate determined by using the best guess values of bending moments and membrane and transverse shear forces obtained from a previous solution, and an effective mesh refinement strategy established at an element level in order to complete an adaptive analysis for shell structures. Numerical examples are shown to illustrate the principles and procedure of the present adaptive analysis.     

Triangulation of <Emphasis Type="Italic">p</Emphasis>-Order Parametric Surfaces

The generation of triangulations on p-order parametric surfaces is a fundamental first step to numerical solutions for multidomain problems involving complex geometries such as those encountered in biological fluid dynamics and other applications. In this study we develop a novel, computationally efficient method for generating triangulations in computational space, which, under parametric mapping, are of high geometric quality. Computational efficiency is maintained over parametric orders (p) through approximating the parametric surface by a grid of simplified vector functions. Unlike other length metric approximations, a maximum bound on the error introduced to the calculation of lengths by this approximation is defined to ensure the fidelity of the transformation. This technique is applied to three parametric functions which demonstrate its robustness in handling high mesh distortions, singularities, and high order surfaces. Further, three complex high-order biological finite element meshes are triangulated. High mesh quality and a linear relationship between triangle generation and CPU time is observed for each of these meshes.