有限元网格划分技术

本文试图提供有限元网格划分领域的一个清晰的概貌。本文对已发表的有限元网格划分方法进行了综述，并对其进行了分类和优缺点分析。此外，本文还讨论了有限元网格划分的研究前沿。     

基于AutoCAD的有限元网格划分系统

本文利用ＡｕｔｏＣＡＤ强大的造型和显示功能,结合快速、可靠的网格划分技术,采用接口技术形成了以ＡＬｌｔＯＣＡＤ为平台的有限元网格划分前置处理系统。     

基于三角形连接的有限元网格划分

文中创新地提出了三角形连接的有限元网格划分的算法,但是三角形并不是有限元计算的基本单元,而是根据已经生成的三角形生成较为规整的四边形。在实际的项目过程中,创新地提出了三种有效的算法,并利用C＋＋面向对象的MFC程序设计和编写。本程序可以从模型文件读取边界以及点约束和线约束特征数据,程序自动计算出一个较为合理的边界间距值,并且根据需要人工或自动选择一种划分算法,从而自动完成高质量的四边形网格划分。三种算法皆可以处理大量数据点和线,并且划分速度较为高效。本程序模块成功应用于有限元计算软件中。     

有限元网络划分技术

本文试图提供有限元网格划分领域的一个清晰的概貌。本文对已发表的有限元网格划分方法进行了综述，并其进行了分类和优缺点分析，此外，本文还讨论了有限元网格划分的研究前沿。     

汽轮机内缸有限元分析与网格划分方案优化

为研究不同网格划分方案对汽轮机内缸应力场计算结果的影响,对某汽轮机中压内缸进行建模,选择热固耦合的有限元法采用4种不同的网格划分方案进行计算,得到额定负荷工况下典型应力集中部位的等效应力。根据计算结果,分析网格整体控制和局部细化过程的不同设置参数对整个求解过程的影响。综合考虑求解成本和计算精度,最终确定一种理想的四面体网格划分方案,该方案可在结果准确合理的前提下提高计算效率。     

有限元网格划分及发展趋势

总结近十年有限元网格划分技术发展状况。首先,研究和分析有限元网格划分的基本原则;其次,对当前典型网格划分方法进行科学地分类,结合实例,系统地分析各种网格划分方法的机理、特点及其适用范围,如映射法、基于栅格法、节点连元法、拓扑分解法、几何分解法和扫描法等;再次,阐述当前网格划分的研究热点,综述六面体网格和曲面网格划分技术;最后,展望有限元网格划分的发展趋势。     

一种面向对象的集成技术在有限元网格自动划分系统中的实现

有限元方法作为一种便利和高铲的数值分析方法做方法的应用于工程分析领域。为了准确快速地将离散域划分为规则的有限元网格单元。本文提出了一种四边形各生成方法Ｌｏｏｐｉｎｇ算法,并且给出了实现该算法的数据结构,最后运用面向对象的技术实现了该系统的集成。     

有限元网格自动生成典型方法及发展方向

在分析大量的有限元网格自动生成算法的基础上，阐述了有限元网格的一般描述和通用方法，总结了各类主要的网格生成方法的优缺点及数据特性，最后指出了自动网格生成的几个主要发展方向。     

结构有限元分析中的网格划分技术及其应用实例

一、前言 有限元网格划分是进行有限元数值模拟分析至关重要的一步,它直接影响着后续数值计算分析结果的精确性.网格划分涉及单元的形状及其拓扑类型、单元类型、网格生成器的选择、网格的密度、单元的编号以及几何体素.从几何表达上讲,梁和杆是相同的,从物理和数值求解上讲则是有区别的.     

NURBS曲面的有限元网格三角划分

主要介绍一种ＮＵＲＢＳ曲面的有限元网格三角剖分算法，首先讨论ＮＵＲＢＳ曲面的离散算法，接着在此基础上，提出了利用网格前沿技术剖分ＮＵＲＢＳ曲面的算法，并且网格单元和结点同时生成。     

曲面的有限元网格顶点法矢算法

分析计算有限元三角形网格顶点法矢的各种算法原理,比较各种算法的结果精度,指出Max方法考虑了三角形网格的形状,且本质上是一种通过对四面体进行外接球面拟合的计算方法,结果精度很高.在此基础上,针对曲面在有限元网格划分后可能同时存在三角形网格和四边形网格,提出适应于单独的三角形网格和四边形网格与两者并存的混合网格的顶点法矢求取算法,计算结果表明了算法的适应性和有效性.     

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.     

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.     

Anisotropic mesh adaptation for finite element solution of Anisotropic Porous Medium Equation

Anisotropic Porous Medium Equation (APME) is developed as an extension of the Porous Medium Equation (PME) for anisotropic porous media. A special analytical solution is derived for APME for time-independent diffusion. Anisotropic mesh adaptation for linear finite element solution of APME is discussed and numerical results for two dimensional examples are presented. The solution errors using anisotropic adaptive meshes show second order convergence.     

Higher degree immersed finite element spaces constructed according to the actual interface

We discuss the construction of higher degree immersed finite element (IFE) spaces that can be used to solve two dimensional second order elliptic interface problems having general interfaces without requiring the mesh to be aligned with the material interfaces. The optimal approximation capability of the proposed piecewise $p$th degree IFE spaces are demonstrated by numerical experiments with interpolations. Numerical solutions to interface problems generated from a partially penalized method based on the proposed higher order IFE spaces also suggest optimal convergence in both the $L^2$ and $H^1$ norms under mesh refinement.     

Galerkin's finite element formulation of the second-order boundary-value problems

A Galerkin's finite element approach based on weighted-residual formulation is presented to find approximate solutions to obstacle, unilateral and contact second-order boundary-value problems. The approach utilizes a piece-wise linear approximations utilizing linear Langrange polynomials. Numerical studies have shown the superior accuracy and lesser computational cost of this scheme in comparison to collocation, finite-difference and spline methods.     

一种新的六面体有限元网格算法

在有限元网格产生过程中,吸取弦须编织法中的STC概念,将六面体以节点剖分为基础的思想转变为以单元点为基础,建立了以单元生长为核心的剖分算法,以期解决节点拓扑结构在三维情况下的控制问题,对进一步实现稳定、全自动的六面体剖分具有很大的帮助。     

A hybrid ant colony optimization approach for finite element mesh decomposition

This paper examines the application of the ant colony optimization algorithm to the partitioning of unstructured adaptive meshes for parallel explicit time-stepping finite element analysis. The concept of the ant colony optimization technique for finding approximate solutions to combinatorial optimization problems is described.The application of ant colony optimization for partitioning finite element meshes based on triangular elements is described.A recursive greedy algorithm optimization method is also presented as a local optimization technique to improve the quality of the solutions given by the ant colony optimization algorithm. The partitioning is based on the recursive bisection approach.The mesh decomposition is carried out using normal and predictive modes for which the predictive mode uses a trained multilayered feed-forward neural network which estimates the number of triangular elements that will be generated after finite elements mesh generation is carried out.The performance of the proposed hybrid approach for the recursive bisection of finite element meshes is examined by decomposing two mesh examples.     

Skeleton-based computational method for the generation of a 3D finite element mesh sizing function

This paper focuses on the generation of a three-dimensional (3D) mesh sizing function for geometry-adaptive finite element (FE) meshing. The mesh size at a point in the domain of a solid depends on the geometric complexity of the solid. This paper proposes a set of tools that are sufficient to measure the geometric complexity of a solid. Discrete skeletons of the input solid and its surfaces are generated, which are used as tools to measure the proximity between geometric entities and feature size. The discrete skeleton and other tools, which are used to measure the geometric complexity, generate source points that determine the size and local sizing function at certain points in the domain of the solid. An octree lattice is used to store the sizing function as it reduces the meshing time. The size at every lattice-node is calculated by interpolating the size of the source points. The algorithm has been tested on many industrial models, and it can be extended to consider other non-geometric factors that influence the mesh size, such as physics, boundary conditions, etc.Sandia National Laboratory is a multiprogram laboratory operated by the Sandia Corporation, a Lockheed Martin Company, for the US Department of Energy under contract DE-AC04-94AL85000.     

The geometric element transformation method for mixed mesh smoothing

The geometric element transformation method (GETMe) is a geometry-based smoothing method for mixed and non-mixed meshes. It is based on a simple geometric transformation applicable to elements bounded by polygons with an arbitrary number of nodes. The transformation, if applied iteratively, leads to a regularization of the polygons. Global mesh smoothing is accomplished by averaging the new node positions obtained by local element transformations. Thereby, the choice of transformation parameters as well as averaging weights can be based on the element quality which leads to high quality results. In this paper, a concept of an enhanced transformation approach is presented and a proof for the regularizing effect of the transformation based on eigenpolygons is given. Numerical examples confirm that the GETMe approach leads to superior mesh quality if compared to other geometry-based methods. In terms of quality it can even compete with optimization-based techniques, despite being conceptually significantly simpler.