栅格法三维六面体网格局部加密算法

有限元数值分析的精度和效率与网格单元的划分质量以及疏密程度密切相关,针对三维六面体网格单元之间疏密过渡必须平缓和协调的要求,提出了一套基于8分法的六面体网格加密模板,并给出了相应的数据结构和模板应用方式.为使所有加密单元都有相对应的加密模板,建立了加密信息场调整规则;对需要进行加密的区域首先补充加密单元,按照节点加密属性调整加密信息场,然后根据单元加密属性对加密单元进行分类,按照全加密单元、面加密单元、边加密单元以及过渡加密单元的顺序依次采用相应的模板进行加密,从而实现三维六面体网格的局部协调加密.实例结果表明,采用该套加密模板的六面体网格局部加密算法能够保障密集网格向稀疏网格的平缓和协调过渡,所生成的网格可满足有限元数值计算的要求.     

平面任意区域四边形网格自动生成的一种方法

在改进节点连接法的基础上，提出了一种平面任意区域的有限元网格全自动剖分方法，既能快速生成四边形单元网格，也能生成三角形单元网格；     

平面区域三角形网格自动生成

基于协调三角形剖分算法，分子表数据结构和Ｚｉｅｎｋｉｅｗｉｃｚ－Ｚｈｕ误差估计方法，本文研制适用于自适应重网格有限元法的网格生成器。该网格生成器可对任意曲线组成的区域进行自适应加密。当荷载作用边界随时间变化及在动力荷载作用下，网格生成器可随应力集中区域变化而动态退化与再加密网格。     

有限元网格全自动生成的九分法

本文论述了有限元网格全自动生成的九分法．这种方法将等边三角形单元划分为九个小等边三角形单元；允许有限元网格局部加密，加密交接处引入五点元．该法可做为前处理器与有限元分析程序系统的联结．     

用户控制的纹理合成

提出一种基于用户控制的纹理合成算法．该算法适用于任意二维平面和任意拓扑的三维网格．可方便地控制纹理合成时方向和尺度的连续变化．对于任意平面区域需剖分成较均匀的三角网格，以剖分得到的二角形作为基本的合成单元来进行合成．根据用户在此三角网格上指定表示纹理方向和大小的矢量来插值生成矢量场，用以控制合成纹理的变化．该算法可以自然扩展到三维三角网格，以三角面片作为合成单元，合成后直接输出每个顶点的纹理坐标．该算法对二维和三维纹理合成给出了统一实现的框架．实验结果表明，该算法可以在任意目标区域根据用户的交互生成令人满意的纹理合成效果．     

三维实体仿真建模的网格自动生成方法

有限元网格模型的生成与几何拓扑特征和力学特性有直接关系。建立网格模型时，为了更真实地反映原几何形体的特征，在小特征尺寸或曲率较大等局部区域网格应加密剖分；为提高有限元分析精度和效率，在待分析的开口、裂纹、几何突变、外载、约束等具有应力集中力学特性的局部区域，网格应加密剖分。为此，该文提出了基于几何特征和物理特性相结合的网格自动生成方法。该方法既能有效地描述几何形体，又能实现应力集中区域的网格局部加密及粗细网格的均匀过渡。实例表明本方法实用性强、效果良好。     

基于特征识别的多尺度构件网格自动生成算法

随着结构力学领域待解决问题复杂程度不断提高,多尺度构件的高质量网格生成对于其数值模拟的计算精度起着至关重要的作用。本文提出一种基于特征识别的网格自动生成技术方法,该方法将多尺度构件的不同量级尺度几何特征识别出来,根据其不同尺度尺寸设置相关区域的网格尺寸值,利用Delaunay三角化算法和前沿推进法生成能够反映不同尺度几何特征的网格单元,再对小尺度区域周围进行加密处理,最后通过几何指数控制函数将不同尺度网格过渡连接起来,形成多尺度构件的整体网格划分模型。通过2个几何模型的测试表明该方法生成的整体网格质量好,不同尺度区域网格过渡合理,自动化程度较高。     

基于GIS 的高架道路交通噪声环评可视化

针对基于地理信息系统(GIS)的评价区域交通噪声环评可视化问题,引入了基于切 割单元法的评价区域网格生成算法,分别提出了基于道路中心线段集的评价区域边界生成方法 和基于声照区的网格自适应加密与稀疏算法,实现了复杂评价区域内非结构化网格的生成。在 此基础上提出了适应于区域计算的等效声级计算模型,实现了环评计算结果的可视化显示。通 过一个高架高速公路的实例,验证了该方法的准确性与有效性。     

二维自适应前沿推进网格生成

针对二维平面问题,通过曲率计算和基于中轴理论的邻近特征计算控制区域边界曲线的离散;修改经典的前沿推进算法,利用边界驱动的单元尺寸控制方式在区域内部布置疏密过渡合理的三角网格;结合几何和拓扑策略提升网格质量。实验表明,上述算法可生成单元质量高、尺寸过渡合理的计算网格。     

平面有限元网格自动剖分及绘图程序

(一)功能本程序能把复连通区域或边界不规则区域剖分成三角形单元,给出结点坐标和三角形单元信息,并在绘图仪上绘制出剖分图形。(二)方法概要和程序框图见本刊上期《平面有限元网格自动剖分及绘图》一文。(三)使用说明1、把平面区域划分成若干个四边形块。在上机操作时,要把分块数目置于I     

Generation of 3D mixed element meshes using a flexible refinement approach

This paper describes and discusses the main characteristics and implementation issues of a 3D mixed element mesh generator based on a generalization of the modified octree approach. This mesh generator uses primitive elements of different type as internal nodes, a flexible refinement approach as refinement strategy (primitive elements are not always bisected), and bricks, pyramids, prisms and tetrahedra as final elements. The mesh generation process is divided in several steps: the generation of the initial mesh composed of primitive elements, the refinement of primitive elements until the point density requirements are fulfilled, the generation of a graded mesh between dense and coarse regions, and finally, the recognition of the final elements. The main algorithms and data structures are described in detail for each step of the mesh generation process. As result, examples of meshes that satisfy the Delaunay condition and that can be used with the control volume method are shown.     

A finite-element mesh generator based on growing neural networks

A mesh generator for the production of high-quality finite-element meshes is being proposed. The mesh generator uses an artificial neural network, which grows during the training process in order to adapt itself to a prespecified probability distribution. The initial mesh is a constrained Delaunay triangulation of the domain to be triangulated. Two new algorithms to accelerate the location of the best matching unit are introduced. The mesh generator has been found able to produce meshes of high quality in a number of classic cases examined and is highly suited for problems where the mesh density vector can be calculated in advance.     

Using sequential NETGEN as a component for a parallel mesh generator

A parallel tetrahedral mesh generator is developed using the existing sequential NETGEN mesh generator. Mesh generation algorithms developed decompose the geometry into multiple sub-geometries sequentially on a master node and then mesh each sub-geometry in parallel on multiple processors. Two methods are implemented. The first decomposes the geometry and produces conforming surface sub-meshes from which volume meshes can be generated in parallel. A second refinement based method also makes use of the CAD geometry information. A scalable mesh migration algorithm that utilizes “owner updates” rule is implemented. Results show that using the refinement based method, a mesh with a billion elements can be generated in about a minute.     

A two-dimensional paving mesh generator for triangles with controllable aspect ratio and quadrilaterals with high quality

Certain classes of problems result in solution fields of which the characteristic length scales vary with the orientation. Often the orientation of these length scales is related to the orientation of the boundaries. Such solution fields can be captured by the finite element method, using a mesh that is refined in the direction of the short length scales and coarse in the other directions. These meshes contain elements with high aspect ratios in a predefined pattern.The mesh generator presented here can render triangles with high aspect ratios through a paving algorithm. The paving algorithm that is employed applies both triangles and quadrilaterals, combining the advantages of both to render a qualitatively good, oriented triangular mesh, with a concentration of elements in the direction where the internal length scales of the solution field are the shortest.The mesh generator produces triangles with one (almost) orthogonal corner. When low aspect ratio triangles are generated, these are well suited for conversion to quadrilateral elements. Test results indicate that quadrilateral meshes converted from the mesh generator introduced here have a considerably better quality than those converted from several other triangular mesh generators.     

Finite element mesh generation

The capabilities of a geometric modeller are extended towards finite element analysis by a mesh generator which extracts all its geometric and topological information from the model. A coarse mesh is created and subsequently refined to a suitable finite element mesh, which accomodates material properties, loadcase and analysis requirements. The mesh may be optimized by adaptive refinement, ie according to estimates of the discretization errors.A survey of research and development in geometric modelling and finite element analysis is presented, then an implementation of a mesh generator for 3D curvilinear and solid objects is described in detail.     

Techniques to avoid duplicate nodes and relax restrictions on the superelement numbering in a mesh generator

This paper presents techniques to avoid duplicate nodes which may occur in a mesh generator appeared previously in this journal. General strategies for avoiding the duplicate nodes and relaxing restrictions on the super element numbering are embedded in subroutines which can be adapted to mesh generators using the super element input.     

Intelligent finite element mesh generation

A knowledge-based and automatic finite element mesh generator (INTELMESH) for two-dimensional linear elasticity problems is presented. Unlike other approaches, the proposed technique incorporates the information about the object geometry as well as the boundary and loading conditions to generate an a priori finite element mesh which is more refined around the critical regions of the problem domain. INTELMESH uses a blackboard architecture expert system and the new concept of substracting to locate the critical regions in the domain and to assign priority and mesh size to them. This involves the decomposition of the original structure into substructures (or primitives) for which an initial and approximate analysis can be performed by using analytical solutions and heuristics. It then uses the concept of wave propagation to generate graded nodes in the whole domain with proper density distribution. INTELMESH is fully automatic and allows the user to define the problem domain with minimum amount of input such as object geometry and boundary and loading conditions. Once nodes have been generated for the entire domain, they are automatically connected to form well-shaped triangular elements ensuring the Delaunay property. Several examples are presented and discussed. When incorporated into and compared with the traditional approach to the adaptive finite element analysis, it is expected that the proposed approach, which starts the process with near optimal initial meshes, will be more accurate and efficient.     

Mesh optimization: How to obtain good unstructured 3D finite element meshes with not-so-good mesh generators

We propose a new idea, based upon an optimization procedure, for improving three-dimensional finite element meshes. Our method can effectively be coupled with any automatic mesh generator in order to obtain a triangulation without badly distorted elements. In this way, we are able to weaken the requirements on the generator, allowing it to produce singular elements, and post-process the result to obtain a valid mesh. We report some experiments showing how this combination makes the meshing of arbitrary domains much more reliable, as compared to the usual approach of precluding distorted elements during the initial generation stage.     

Adaptive remeshing process with quadrangular finite elements

Since the quality of FEM analysis directly depends on the quality of meshes, various mesh adaptation schemes have been researched. There are two stages on adaptive finite element analysis; to derive error measure and to control meshes based on error measure. The former has been well researched among applied mathematicians. However, the importance of the latter aspect wasn't considered enough. Even if the error measures were well estimated, the total performance of mesh adaptation might be poor with a poor mesh control. This paper proposes an effective mesh control scheme for h-adaptation, or adaptive remeshing scheme with the explicit relation between interpolation theory based on error measure and desirable mesh size. Total mesh adaptation is controlled by introducing Quality Index, or the ratio between the total error norm and the total energy norm which represents the quality of the total meshes; specifying the desirable value of Quality Index, then the adaptive remeshing process can handle it and Quality Index is almost converged to the given value. Since the full automatic feature of the mesh generator is a prerequisite for adaptive remeshing, the author also discusses the algorithm of the quadrangular mesh generator for arbitrary domains. After evaluation on a linear problem, it's confirmed that the proposed mesh control scheme and the proposed error measure-mesh size relations are acceptable. The incompatible case for mesh adaptation is also discussed in this paper.