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。     

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AutoCAD的有限元前处理系统设计

以AutoCAD为几何平台,并利用其提供的二次开发技术实现了有限元前处理系统的编程。该方法解决了常规的有限元分析系统中的几何建模系统和前处理系统脱节的问题。集成了造型、单元属性设置、网格划分、显示等多种模块。研究了有限元前处理系统的若干关键技术,包括如何控制网格形态、输出求解数据接口、基于ObjectARX的CAD/CAE集成设计、复杂三维实体的四面体网格全自动生成算法。建立了一个基于AutoCAD的有限元前处理系统。     

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。     

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。     

自动生成空心叶片三维有限元网格

本文对空心叶片的三维有限元网格自动生成了作了初步探讨。介绍了利用空心叶片造型提供的几何信息，求出了实现三维有限多格分割所需的全部立体单元的节点坐标、单元及节点编号的方法。     

二维自适应有限元网格生成

自适应有限元网格生成是基于误差估计，自动进行有限元网格优化的一种策略。本文提出了一种基于单元误差估计的二维自适应有限元网格生成算法，并讨论了其实现过程。     

任意形状平面域的通用三角化算法

基于平面上散乱数据点的Ｄｅｌａｕｎａｙ三角剖分准则，提出了任意形状平面域的通用三角剖分算法。该算法不仅能用于Ｔｒｉｍｍｅｄ曲面的消隐显示及加工，也能用于有限元网格自动生成及其它领域。该算法已经成功应用于ＨＵＳＴＣＡＤＭ曲面造型及加工系统。     

三角形拓扑网格上曲面造型的切割磨光法

本文考虑三角形拓扑网格上的自由曲面造型方法.讨论了三角形拓扑网格上的切割磨光方法,研完了生成曲面——TC曲面的性质,给出了生成TC曲面的两种算法,并对算法进行了分析.结果表明,TC曲面具有凸包性、几何连续性、局部性、插值性等许多良好的性质,适合在曲面造型系统中采用.     

Mesh Quality: A Function of Geometry, Error Estimates or Both?

The issue of mesh quality for unstructured triangular and tetrahedral meshes is considered. The theoretical background to finite element methods is used to understand the basis of present-day geometrical mesh quality indicators. A survey of more recent research in the development of finite element methods describes work on anisotropic meshing algorithms, and on providing good error estimates that reveal the relationship between the error and both the mesh and the solution gradients. The reality of solving complex three-dimensional problems is that such indicators are presently not available for many problems of interest. A simple tetrahedral mesh quality measure using both geometrical and solution information is described. Some of the issues in mesh quality for unstructured tetrahedral meshes are illustrated by means of two simple examples.     

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.     

GeoTran-HC: Geometric transformation of highly coupled variable topology multi-body problems

Manipulating geometry to prepare a CAD design model for mesh generation is an important step in the finite element analysis (FEA) process. However, complex problems such as electronic chip packages often consist of hundreds or even thousands of sub-features with varying materials, complex geometrical shapes and changeable connectivity configurations. We define a subclass of such problems, termed highly coupled variable topology multi-body (HCVTMB) problems, where configuration and relative geometric sizes cause meshing changes in one body to propagate throughout much of the model. Today creating FEA models for HCVTMB problems typically requires manual geometrical manipulation which is labour-intensive and error-prone.In this paper we introduce an automated geometric transformation method-GeoTran-HC-within the context of a knowledge-based modeling method for CAD-FEA integration. Through five steps-geometry extraction, cell decomposition, associativity maintenance, feature recognition and associativity recovery-this transformation method automatically decomposes an HCVTMB analytical model into a meshable model. It also manages mesh quality and attribution of non-geometrical information such as material properties and boundary conditions.A plastic ball grid array chip package thermo-mechanical case study demonstrates the efficacy of GeoTran-HC within the context of our knowledge-based FEA modelling method. This and similar studies show reductions in total FEA modeling time from days/hours (using traditional methods) to hours/minutes (using the presented method), as well as enhanced modularity and reusability.     

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．     

面向有限元分析的实体表面网格模型的优化

针对CAE软件开发的需要,将通用CAD软件输出的以表面三角形网格形式表示的实体模型输入CAE软件,作为有限元分析用几何模型。然后根据特定领域有限元分析的要求对表面网格进行优化处理,优化网格的数量和质量,以便进一步生成适合有限元计算需要的各种单元模型。     

Generation of a finite element MESH from stereolithography (STL) files

The aim of the method proposed here is to show the possibility of generating adaptive surface meshes suitable for the finite element method, directly from an approximated boundary representation of an object created with CAD software. First, we describe the boundary representation, which is composed of a simple triangulation of the surface of the object. Then we will show how to obtain a conforming size-adapted mesh. The size adaptation is made considering geometrical approximation and with respect to an isotropic size map provided by an error estimator. The mesh can be used “as is” for a finite element computation (with shell elements), or can be used as a surface mesh to initiate a volume meshing algorithm (Delaunay or advancing front). The principle used to generate the mesh is based on the Delaunay method, which is associated with refinement algorithms, and smoothing. Finally, we will show that not using the parametric representation of the geometrical model allows us to override some of the limitations of conventional meshing software that is based on an exact representation of the geometry.     

基于非结构网格的Gas-Kinetic方法

为解决带有复杂几何边界条件的高速流体计算问题,提出基于非结构网格的Gas-Kinetic方法.对于二维非结构网格,以三角形网格作为计算单元,形成在该网格控制单元中物理量导数求解的新方法.通过物理量导数得到在控制体积元边界上的通量,然后用每个计算时间步中求出的边界通量和控制体积元中的物理量,求出下一计算时间步所需的新物理量,依次进行计算直到计算结果收敛为止.采用NACA0012翼型进行数值计算验证,结果表明该方法简单高效,适用于低速和高速流体的计算.     

The hp-version of the boundary element method for Helmholtz screen problems

We study the boundary element method for weakly singular and hypersingular integral equations of the first kind on screens resulting from the Dirichlet and Neumann problems for the Helmholtz equation. It is shown that the hp-version with geometrical refined meshes converges exponentially fast in both cases. We underline our theoretical results by numerical experiments for the pure h-, p-versions, the graded mesh and the hp-version with geometrically refined mesh.     

A two-dimensional mesh generator for variable order triangular and rectangular elements

An improved method is presented for generating variable order elements by superelement generation. This method is simple to apply and requires less execution time in comparison with other variable order mesh generators. Depending on geometrical complexity and material variation, the superelements are manually determined to be refined into high or low order elements. Different mesh generation subroutines are employed to generate elements of different orders. The refined elements of different orders are finally patched to form a hybrid mesh. A FORTRAN program is given to generate finite element meshes of linear and quadratic triangular and rectangular elements automatically.     

Optimization of passive microwave devices through geometrical parameterization—Application to the design of a cylindrical dual‐mode cavity filter

A new algorithm, based on geometrical parameterization and finite element method is presented for the optimization of microwave devices. Using geometrical parameterization, the field quantities are expressed as a polynomial in design parameters. Automatic differentiation is used for calculation of higher order derivatives. To ensure continuous gradients, an integrated mesh deformation algorithm is deployed to morph initial finite elements mesh into the perturbed geometry. The resulting parametric model is deployed through quadratic surface reconstruction to find local minimum at each stage. The convergence of the optimization through the reconstructed surfaces is discussed. As an example, a 5‐pole dual‐mode cavity filter is designed and optimized using the presented algorithm. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009.