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．     

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．     

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。     

三维有限元网格尺寸场光滑化的优化模型和算法

针对单元尺寸值过渡剧烈会导致有限元网格包含低质量单元的问题,提出基于优化原理的单元尺寸场光滑化理论及对应的几何自适应四面体网格生成算法.首先输入CAD模型,生成一套覆盖模型内部的非结构背景网格;然后结合用户参数计算背景网格点上的曲率和邻近特征,以获得自适应CAD模型几何特征的初始单元尺寸场;再以最小化初始单元尺寸场的改变为目标,以单元尺寸值过渡受控为约束,通过求解一类凸优化问题光滑初始尺寸场;最后以光滑后的尺寸场为输入,先后在CAD模型表面与内部生成曲面网格和实体网格.实验结果表明,文中算法仅需5个用户参数,即可在给定CAD模型内部全自动生成高质量的四面体网格.     

基于非流形几何与特征树的异质材料实体可视化方法

提出一种异质材料实体可视化的方法．采用边界曲面细分技术减小材料分布的突变视觉效应;在不损失渲染质量的前提下,采用自适应曲面细分和冗余曲面滤除方法解决异质实体可视化效率差、难以实时显示的问题．给出了详细的异质实体边界网格生成算法,以显示异质实体的外部几何信息及其内部材料组分的三维分布．该算法采用基于特征树的曲面网格自适应细分策略,通过对异质实体特征树的拓扑结构分析来判定待渲染曲面的材料分布特性,仅对确实需要细分的曲面进行额外的网格细分,有效地减小了实体渲染中所需的计算量;利用非流形异质实体的表征方法,采用冗余曲面滤除方法直接滤除非相关的边界曲面,以满足实时可视化的要求．该方法已用于异质实体建模软件CAD4D中,实验结果表明,其可有效地实现异质实体的实时可视化显示．     

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。     

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.     

基于NURBS表示的实体三维有限元网格生成

有限元网格生成是零件几何定义和有限元分析之间必不可少的步骤。为实现有限元网格生成的自动化,人们编制了许多程序,但大多数难以应用于复杂的三维物体。本文借助于参数映射法的支持,对基于NURBS表示的实体进行有限元网格划分,并给出了一带网格的长方体和弯曲变形后的网格形状实例。     

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。     

Adaptive generation of hexahedral element mesh using an improved grid-based method

An improved grid-based algorithm for the adaptive generation of hexahedral finite element mesh is presented in this paper. It is named as the inside-out grid-based method and involves the following four steps. The first step is the generation of an initial grid structure which envelopes the analyzed solid model completely. And the elements size and density maps are constructed based on the surface curvature and local thickness of the solid model. Secondly, the core mesh is generated through removing all the undesired elements using even and odd parity rules. The third step is to magnify the core mesh in an inside-out manner through a surface node projection process using the closest position approach. To match the mesh to the characteristic boundary of the solid model, a minimal Scaled Jacobian criterion is employed. Finally, in order to handle the degenerated elements and improve the quality of the resulting mesh, two comprehensive techniques are employed: the insertion technique and collapsing technique. The present method was applied in the mesh construction of different engineering problems. Scaled Jacobian and Skew metrics are used to evaluate the hexahedral element mesh quality. The application results show that all-hexahedral element meshes which are well-shaped and capture all the geometric features of the original solid models can be generated using the inside-out grid-based method presented in this paper.     

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.     

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.     

Adaptive hexahedral mesh generation and quality optimization for solid models with thin features using a grid-based method

This paper presented an automatic inside-out grid-based hexahedral element mesh generation algorithm for various types of solid models. For the thin features with small thickness of the geometric model, corresponding treatment methods were given for successfully implementing each meshing step, containing the techniques for adaptive refinement, boundary match, topological optimization and local refinement. In order to realize the reasonable identification of refinement regions and resolve the expansion problem of refinement information fields, a thin-feature criterion and a supplementary criterion were proposed aiming at thin features of the geometry. To implement accurate boundary match for thin features, ten basic types and five complementary types of facet configurations were established, and a priority-node identification method was proposed additionally. Three topological optimization modes were newly proposed to improve the topological connections of the boundary mesh in thin features. Local refinement techniques were also built to refine the thin features of solid models. Finally, several examples were provided to demonstrate the effectiveness and reliability of the proposed algorithms.     

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.     

Construction of near optimal meshes for 3D curved domains with thin sections and singularities for p-version method

The adaptive variable p- and hp-version finite element method can achieve exponential convergence rate when a near optimal finite element mesh is provided. For general 3D domains, near optimal p-version meshes require large curved elements over the smooth portions of the domain, geometrically graded curved elements to the singular edges and vertices, and a controlled layer of curved prismatic elements in the thin sections. This paper presents a procedure that accepts a CAD solid model as input and creates a curved mesh with the desired characteristics. One key component of the procedure is the automatic identification of thin sections of the model through a set of discrete medial surface points computed from an Octree-based tracing algorithm and the generation of prismatic elements in the thin directions in those sections. The second key component is the identification of geometric singular edges and the generation of geometrically graded meshes in the appropriate directions from the edges. Curved local mesh modification operations are applied to ensure the mesh can be curved to the geometry to the required level of geometric approximation.     

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.