Interactive-adaptive geometrically nonlinear analysis of shell structures

This paper presents an investigation of interactive-adaptive techniques for nonlinear finite element structural analysis. In particular, effective methods leading to reliable automated, finite element solutions of nonlinear shell problems are of primary interest here. This includes automated adaptive nonlinear solution procedures based on error estimation and adaptive step length control, reliable finite elements that account for finite deformations and finite rotations, three-dimensional finite element modeling, and an easy-to-use, easy-to-learn graphical user interface with three-dimensional graphics. A computational environment, which interactively couples a comprehensive geometric modeler, an automatic three-dimensional mesh generator and an advanced nonlinear finite element analysis program with real-time computer graphics and animation tools, is presented. Three examples illustrate the merit and potential of the approaches adopted here and confirm the feasibility of developing fully automated computer aided engineering environments.     

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。     

Quasi-automatic 3D finite element model generation for individual single-rooted teeth and periodontal ligament

The paper demonstrates how to generate an individual 3D volume model of a human single-rooted tooth using an automatic workflow. It can be implemented into finite element simulation. In several computational steps, computed tomography data of patients are used to obtain the global coordinates of the tooth's surface. First, the large number of geometric data is processed with several self-developed algorithms for a significant reduction. The most important task is to keep geometrical information of the real tooth. The second main part includes the creation of the volume model for tooth and periodontal ligament (PDL). This is realized with a continuous free form surface of the tooth based on the remaining points. Generating such irregular objects for numerical use in biomechanical research normally requires enormous manual effort and time. The finite element mesh of the tooth, consisting of hexahedral elements, is composed of different materials: dentin, PDL and surrounding alveolar bone. It is capable of simulating tooth movement in a finite element analysis and may give valuable information for a clinical approach without the restrictions of tetrahedral elements. The mesh generator of FE software ANSYS executed the mesh process for hexahedral elements successfully.     

Finite element modeling within an integrated geometric modeling environment: Part II—Attribute specification,domain differences,and indirect element types

This is the second of a two part paper that addresses the integration of finite element modeling and geometric modeling. Instead of considering the integration of currently available systems, this paper addresses both modeling techniques in general terms and identifies the functions that are needed to integrate them, taking full advantage of the capabilities of both. A set of geometric communication operators are identified and defined for use in carrying out this integration process. Part I [1] considered the integration of geometric modeling and finite element mesh generation. This part considers the remaining areas of the specification of finite element analysis attribute information, accounting for domain differences between the geometric and finite element models and the generation of finite element models using element types that are of a lesser dimension than the geometric entity they represent.     

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．     

A method for shape and topology optimization of truss-like structure

We present a method for the shape and topology optimization of truss-like structure. First, an initial design of a truss-like structure is constructed by a mesh generator of the finite element method because a truss-like structure can be described by a finite element mesh. Then, the shape and topology of the initial structure is optimized. In order to ensure a truss-like structure can be easily manufactured via intended techniques, we assume the beams have the same size of cross-section, and a method based on the concept of the SIMP method is used for the topology optimization. In addition, in order to prevent intersection of beams and zero-length beams, a geometric constraint based on the signed area of triangle is introduced to the shape optimization. The optimization method is verified by several 2D examples. Influence on compliance of the representative length of beams is investigated.     

Hexahedral mesh smoothing via local element regularization and global mesh optimization

The quality of finite element meshes is one of the key factors that affect the accuracy and reliability of finite element analysis results. In order to improve the quality of hexahedral meshes, we present a novel hexahedral mesh smoothing algorithm which combines a local regularization for each hexahedral mesh, using dual element based geometric transformation, with a global optimization operator for all hexahedral meshes. The global optimization operator is composed of three main terms, including the volumetric Laplacian operator of hexahedral meshes and the geometric constraints of surface meshes which keep the volumetric details and the surface details, and another is the transformed node displacements condition which maintains the regularity of all elements. The global optimization operator is formulated as a quadratic optimization problem, which is easily solved by solving a sparse linear system. Several experimental results are presented to demonstrate that our method obtains higher quality results than other state-of-the-art approaches.     

Geometric surface mesh optimization

This paper presents a surface mesh optimization method suitable to obtain a geometric finite element mesh, given an initial arbitrary surface triangulation. The first step consists of constructing a geometric support, continuous, associated with the initial surface triangulation, which represents an adequate approximation of the underlying surface geometry. The initial triangulation is then optimized with respect to this geometry as well as to the element shape quality. A specific application of this technique to the geometric mesh simplification is then outlined, which aims at reducing the number of mesh entities while preserving the geometric approximation of the surface. Several examples of surface meshes intended for different application areas emphasize the efficiency of the proposed approach. Received: 11 September 1997 / Accepted: 19 February 1998     

Finite element modeling within an integrated geometric modeling environment: part I—Mesh generation

This is the first of a two part paper that addresses the integration of finite element modeling and geometric modeling. Instead of considering the integration of currently available systems, this paper addresses both modeling techniques in general terms and identifies the functions that are needed to integrate them, taking full advantage of the capabilities of both. A set of geometric communication operators are identified and defined for use in carrying out this integration process. This first part considers the integration of geometric modeling and mesh generation, whereas the second part considers the specification of analysis attributes, accounting for domain differences between the geometric and finite element models and generating finite element models using element types that are of a lesser dimension than the geometry they represent.     

Eulerian shape design sensitivity analysis and optimization with a fixed grid

Conventional shape optimization based on the finite element method uses Lagrangian representation in which the finite element mesh moves according to shape change, while modern topology optimization uses Eulerian representation. In this paper, an approach to shape optimization using Eulerian representation such that the mesh distortion problem in the conventional approach can be resolved is proposed. A continuum geometric model is defined on the fixed grid of finite elements. An active set of finite elements that defines the discrete domain is determined using a procedure similar to topology optimization, in which each element has a unique shape density. The shape design parameter that is defined on the geometric model is transformed into the corresponding shape density variation of the boundary elements. Using this transformation, it has been shown that the shape design problem can be treated as a parameter design problem, which is a much easier method than the former. A detailed derivation of how the shape design velocity field can be converted into the shape density variation is presented along with sensitivity calculation. Very efficient sensitivity coefficients are calculated by integrating only those elements that belong to the structural boundary. The accuracy of the sensitivity information is compared with that derived by the finite difference method with excellent agreement. Two design optimization problems are presented to show the feasibility of the proposed design approach.     

A new scheme for mesh generation and mesh refinement using graph theory

There are an extensive number of algorithms available from graph theory, some of which, for problems with geometric content, make graphs an attractive framework in which to model an object from its geometry to its discretization into a finite element mesh. This paper presents a new scheme for finite element mesh generation and mesh refinement using concepts from graph theory. This new technique, which is suitable for an interactive graphical environment, can also be used efficiently for fully automatic remeshing in association with self-adaptive schemes. Problems of mesh refinement around holes and local mesh refinement are treated. The suitability of the algorithms presented in this paper is demonstrated by some examples.     

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.     

A finite element model of high speed metal cutting with adiabatic shearing

A finite element model of a two-dimensional orthogonal cutting process is developed. The simulation uses standard finite element software together with a special mesh generator that is able to mesh the chip completely with regular quadrilateral elements and a strong mesh refinement in the shear zone for continuous and segmented chips. The techniques of remeshing and to ensure convergence of the implicit calculation is described. Results for the formation of segmented chips are presented and the segmentation process is studied. Of special interest is the occurrence of split shear bands. The influence of the elastic properties and of the cutting speed is also discussed.     

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。     

Layered tetrahedral meshing of thin-walled solids for plastic injection molding FEM

This paper describes a method for creating a well-shaped, layered tetrahedral mesh of a thin-walled solid by adapting the surface triangle sizes to the estimated wall thickness. The primary target application of the method is the finite element analysis of plastic injection molding, in which a layered mesh improves the accuracy of the solution. The edge lengths of the surface triangles must be proportional to the thickness of the domain to create well-shaped tetrahedrons; when the edge lengths are too short or too long, the shape of the tetrahedron tends to become thin or flat. The proposed method creates such a layered tetrahedral mesh in three steps: (1) create a preliminary tetrahedral mesh of the target geometric domain and estimate thickness distribution over the domain; (2) create a non-uniform surface triangular mesh with edge length adapted to the estimated thickness, then create a single-layer tetrahedral mesh using the surface triangular mesh; and (3) subdivide tetrahedrons of the single-layer mesh into multiple layers by applying a subdivision template. The effectiveness of the layered tetrahedral mesh is verified by running some experimental finite element analyses of plastic injection molding.     

Geometry as a basis for finite element automation

This paper discusses the role of geometry in achieving automation of the overall finite element analysis process. Emphasis is placed on the geometry requirements for two of the key technologies within this process: fully automatic mesh generation and adaptive analysis. A geometric framework that permits the implementation of automated finite element procedures is presented. This includes high-level geometry-based problem specification and control, powerful data structures, and the geometric functionality that is necessary to support automation. An open architecture system, called TAGUS, which incorporates these notions and permits manipulation of geometry, topology, and attribute data from within an applications program, is also presented. In addition, the paper contrasts the geometry requirements of problems with static domains versus the special considerations that must be given for dynamically changing domains. Finally, a view of an integrated system architecture for analysis automation is presented.     

Automatic finite element mesh generation for maxillary second premolar.

Developing three dimensional finite element mesh models for irregular geometric objects requires a large amount of manual efforts, hence limiting the three dimensional approach for dental structure analyses. An automatic procedure which can be used to generate a three dimensional finite element mesh for the maxillary second premolar was developed in this study. Firstly, a embedded second premolar was sliced and scanned parallel to the occlusal surface. A self-developed image processing system was employed to detect the boundaries of different materials within each section. An automatic mesh generation program was used on these boundaries to create tetrahedral elements based on moving nodes of uniform cube approach. Six mesh models of the second premolar with different element sizes using linear and quadratic elements were analyzed. Strain energy and von Mises stresses were reviewed for convergence in the crown regions.     

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．     

Numerical comparison between two cost functions in contact shape optimization

A finite element approach to shape optimization in a 2D frictionless contact problem for two different cost functions is presented in this work. The goal is to find an appropriate shape for the contact boundary, performing an almost constant contact-stress distribution. The whole formulation, including the mathematical model for the unilateral problem, sensitivity analysis and geometry definition is treated in a continuous form, independently of the discretization in finite elements. Shape optimization is performed by a direct modification of the geometry throughB-spline curves and an automatic mesh generator is used at each new configuration to provide the finite element input data. Augmented-Lagrangian techniques (to solve the contact problem) and an interior-point mathematical-programming algorithm (for shape optimization) are used to obtain numerical results.