基于几何特征和力学特性的自适应网格生成算法

为获得适合有限元分析的满意网格划分,提出了平面域的基于几何特征和力学特性相结合的自适应网络生成方法,实现了应力集中区的网格局部加密及平稳变密度的网格自动剖分,通过实例表明本方法实用性强、效果良好。     

二维几何特征自适应有限元网格生成(一)--几何特征识别

发现二维形体边界均匀离散点集Delaunay三角剖分所具有的4个性质．根据这4个性质所描述的Delaunay三角剖分和形体几何特征之间的关系提出几何特征自动识别方法,并建立网格自适应机制,实现三维形体几何特征和部分力学特性自适应有限元网格自动生成．     

二维几何特征自适应有限元网格生成(二)--算法描述

以Delaunay三角剖分为基础,构造几何特征自适应有限元网格单元尺寸信息场,给出动态节点一单元一体化生成算法,实现二维形体几何特征自适应有限元网格的自动生成,并使分析对象力学特性得到一定程度的自适应．     

三维实体有限元自适应网格规划生成

为实现三维实体有限元网格自适应生成,设计了中心点、沿指定曲线和基于实体表面等网格加密生成方式;并根据分析对象几何特征和物理特性经验估计,以规划的方式构造自适应网格单元尺寸信息场．在此基础上,提出基于Delaunay剖分的动态节点单元一体化算法,生成几何特征和物理特性整体自适应的有限元网格．     

基于几何造型的有限元前处理技术

本文在综述了有限元网格生成技术的基础上,着重介绍一个基于几何造型系统的有限元分析的前处理系统。这个系统作为几何造型系统与有限元分析程序之间的接口,主要功能是对几何造型系统的二维任意形体进行有限元网格的划分,并能够进行局部加密,自动节点编号,交互划分定义单元组,定义单元节点信息、载荷信息、边界条件等,最终生成有限元分析程序所需的输入文件。同时,还能够处理平移扫描体和旋转扫描体等二维半形体。本文主要算法可以推广到三维形体的网格生成,实现对更广泛的三维结构的有限元网格生成。     

基于几何造型的有限元网格的自适应生成

介绍一个基于几何造型系统的有限元分析的前处理系统。该系统可对几何造型的二维任意形体进行快速可靠的Ｄｅｌａｕｎａｙ三角剖分，提出网格自动生成的网格密度的控制和基于误差估计的自适应有限元网格生成算法，并给出了应用实例。     

一种基于多边形剖分的有限元网格生成方法

在两步网格化过程中,待分析区域首先被剖分为具有三条或四条边的简单子区域部分.然后将利用传递模板法或映射法对这些子区域进行网格生成.本文结合计算几何和有限元网格自动生成问题,给出了一种基于简单多边形剖分的全四边形有限元网格自动生成方法.该方法分两步实现有限元网格生成首先通过权函数的引导,对待分析的简单多边形区域先进行子域剖分,得到一组三角形和凸四边形子域(大单元)的集合;然后利用中点剖分方法,将三角形和凸四边形子域单元剖分为全四边形有限元网格.实践证明,本文提出的方法实现简单、使用灵活,结果网格的质量良好.     

基于几何造型的有限元网络自适应生成

介绍一个基于几何造型系统的有限元分析的前处理系统。该系统可对几何造型的二维任意形体进行快速可靠的Ｄｅｌａｕｎａｙ三角剖分，提出网络自动生成的网络密度的控制和基于误差估计的自适应有限元网格生成算法，并给出了应用实例。     

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。     

基于B样条有限元机载激光陀螺测量装置系统的建模与仿真

建立了激光惯性导航系统的三维有限元模型,对其力学特性进行了模态分析,建立了整个模型B样条小波有限元模型;研究了一类新的有限元空间,它以B样条小波函数作为有限等参元的形状函数;建立了IMU模型的B样条小波有限元序列,利用B样条小波函数的变尺度特性在不改变网格的剖分下提高分辨率,因此在处理局部应力集中,曲率分布突变边界等应用中具有一定的优势,所以它的结果更接近于实际;最后对系统模型进行了仿真,给出了各个阶次模态值,通过与传统有限元比较发现小波有限元具有收敛性好、求解迅速和网格划分灵活优点,离散的单元数减少了13％,计算时间也是原来的35％,这对于激光惯性导航系统的优化设计具有重要参考价值.     

Feature preserving Delaunay mesh generation from 3D multi-material images

Generating realistic geometric models from 3D segmented images is an important task in many biomedical applications. Segmented 3D images impose particular challenges for meshing algorithms because they contain multi-material junctions forming features such as surface patches, edges and corners. The resulting meshes should preserve these features to ensure the visual quality and the mechanical soundness of the models. We present a feature preserving Delaunay refinement algorithm which can be used to generate high-quality tetrahedral meshes from segmented images. The idea is to explicitly sample corners and edges from the input image and to constrain the Delaunay refinement algorithm to preserve these features in addition to the surface patches. Our experimental results on segmented medical images have shown that, within a few seconds, the algorithm outputs a tetrahedral mesh in which each material is represented as a consistent submesh without gaps and overlaps. The optimization property of the Delaunay triangulation makes these meshes suitable for the purpose of realistic visualization or finite element simulations.     

多边形单元网格自动生成技术

近年来兴起的多边形有限元方法,在有限元计算中采用多边形单元划分网格,不仅可以更好地适应求解区域的几何形状,而且增加了网格划分的灵活性。为了更方便有效地生成多边形单元网格,在Delaunay三角形的基础上,通过将共圆Delaunay三角形合并为一个圆内接多边形,首先提出了Delaunay多边形的概念,进而提出了一种多边形网格自动生成的Delaunay多边形化算法。利用该Delaunay多边形化技术,对工程中常见的几何形状进行网格划分的具体算例表明,Delaunay多边形化方法可以生成性质优良的多边形单元网格。     

Development of an object-oriented finite element program with adaptive mesh refinement for multi-physics applications

In this paper, an object-oriented framework for numerical analysis of multi-physics applications is presented. The framework is divided into several basic sets of classes that enable the code segments to be built according to the type of problem to be solved. Fortran 2003 was used in the development of this finite element program due to its advantages for scientific and engineering programming and its new object-oriented features. The program was developed with h-type adaptive mesh refinement, and it was tested for several classical cases involving heat transfer, fluid mechanics and structural mechanics. The test cases show that the adaptive mesh is refined only in the localization region where the feature gradient is relatively high. The overall mesh refinement and the h-adaptive mesh refinement were justified with respect to the computational accuracy and the CPU time cost. Both methods can improve the computational accuracy with the refinement of mesh. The overall mesh refinement causes the CPU time cost to greatly increase as the mesh is refined. However, the CPU time cost does not increase very much with the increase of the level of h-adaptive mesh refinement. The CPU time cost can be saved by up to 90%, especially for the simulated system with a large number of elements and nodes.     

A modified advancing layers mesh generation for thin three-dimensional objects with variable thickness

A method of generating modified advancing layers mesh is proposed. In this paper the mesh generation process of semi-unstructured prismatic/tetrahedral mesh is presented for relatively thin three-dimensional geometries with variable thickness, as in the case of injection molding analysis. Prismatic meshes are generated by offsetting initial surface triangular meshes. During the mesh generation process, mesh quality is efficiently improved with the use of a new node relocation method. Finally, tetrahedral meshes are automatically generated in the rest of the domain. The mesh generating capability of the proposed algorithm is demonstrated with the several practical test cases.     

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.     

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.     

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.