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.     

Automatic mesh generation for finite element analysis

The finite element analysis in engineering applications comprises three phases: domain discretization, equation solving and error analysis. The domain discretization or mesh generation is the pre-processing phase which plays an important role in the achievement of accurate solutions. In this paper, the improvement of one particularly promising technique for generating two-dimensional meshes is presented. Our technique shows advantages and efficiency over some currently available mesh generators.     

扫掠法有限元网格生成方法

为了提高有限元网格的生成质量,扫掠法生成六面体网格过程中内部节点定位成为关键一步,在研究复杂扫掠体六面体有限元网格生成算法过程中,提出了一种基于扫掠法的六面体网格生成算法,算法利用源曲面已经划分好的网格和连接曲面的结构化网格,用仿射映射逐层投影,生成目标曲面,提出基于Roca算法的内部节点定位的新算法,运用由外向内推进的波前法思想,生成全部的六面体网格。通过实例表明,该算法快速,稳定,可靠,可处理大量复杂2.5维实体六面体网格生成问题。     

Accurate recovery-based upper error bounds for the extended finite element framework

This paper introduces a recovery-type error estimator yielding upper bounds of the error in energy norm for linear elastic fracture mechanics problems solved using the extended finite element method (XFEM). The paper can be considered as an extension and enhancement of a previous work in which the upper bounds of the error were developed in a FEM framework. The upper bound property requires the recovered solution to be equilibrated and continuous. The proposed technique consists of using a recovery technique, especially adapted to the XFEM framework that yields equilibrium at a local level (patch by patch). Then a postprocess based on the partition of unity concept is used to obtain continuity. The result is a very accurate but only nearly-statically admissible recovered stress field, with small equilibrium defaults introduced by the postprocess. Sharp upper bounds are obtained using a new methodology accounting for the equilibrium defaults, as demonstrated by the numerical tests.     

Semiautomated finite element mesh generation methods for a long bone

The objective of this work was to develop and test a semi-automated finite element mesh generation method using computed tomography (CT) image data of a canine radius. The present study employs a direct conversion from CT Hounsfield units to elastic moduli. Our method attempts to minimize user interaction and eliminate the need for mesh smoothing to produce a model suitable for finite element analysis. Validation of the computational model was conducted by loading the CT-imaged canine radius in four-point bending and using strain gages to record resultant strains that were then compared to strains calculated with the computational model. Geometry-based and uniform modulus voxel-based models were also constructed from the same imaging data set and compared. The nonuniform voxel-based model most accurately predicted the axial strain response of the sample bone (R(2)=0.9764).     

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.     

Feature-based design and finite element mesh generation for functional surfaces

This paper describes an approach to feature-based design and feature-based mesh generation for multi-featured functional surfaces. Unlike standard free-form parametric surface representation where the parametric surface patch plays the key role in both surface design and finite element mesh generation, we propose an approach to these two tasks which proceeds from the level of a complete feature (for example, a pocket or channel). The result is a more direct method for modeling functional surface characteristics and a more efficient feature-based implementation of Delaunay surface triangulation.     

Three-dimensional mesh generation using principles of finite element method

The present work deals with the development of a three-dimensional mesh generation algorithm using the principles of FEM with special emphasis on the computational efficiency and the memory requirement. The algorithm makes use of a basic mesh that defines the total number of elements and nodes. Wavefront technique is used to renumber the nodes in order to reduce the bandwidth. By elastic distortion of the basic mesh, it is redefined to map onto actual geometry to be discretized. Later a finer distribution of mesh is done in the zones of interest to suit the nature of the problem. The same Finite Element code meant for stress analysis is adopted with necessary modifications. The algorithm has been extended to three-dimensional geometries. The current methodology is used to discretize a straight bevel gear and an hourglass worm to study their stress patterns.     

Tetrahedral finite element mesh generation from NURBS solid models

In this paper, the development and the implementation of a tetrahedral meshing algorithm for generation of finite element meshes from NURBS solid models is presented. The meshing algorithm is based on a Delaunay technique, and makes use of some spatial data structures. The algorithm is capable of generating both uniform and varying size four-node and ten-node tetrahedral meshes. The algorithm has been implemented in a building block approach as part of a software library. It has been used as a practical tool in engineering design processes. Several representative test cases illustrate the effectiveness of the automatic solid mesh generator.     

面向有限元网格生成的单元尺寸场光滑化算法

针对单元尺寸场的合适与否会直接影响到后续有限元网格质量的问题,提出一种尺寸修正算法来优化单元尺寸场。在Borouchaki等提出的H变化量（BOROUCHAKI H, HECHT F, FREY P J. Mesh gradation control. International Journal for Numerical Methods in Engineering, 1998,43(6):1143-1165）的基础上,引入尺寸梯度概念,进行一系列公式推导,得到二维的单元尺寸场的合理过渡要求,从而以定义在非结构背景网格的单元尺寸场为例,改进Borouchaki修正算法,提出了一种最少量地重置尺寸场中节点单元尺寸值,最大化地全局光滑单元尺寸场的新算法。最后给出若干实例的网格生成效果图,证明算法能帮助工程应用的模型生成更高质量的网格,跟其他修正算法相比,网格尺寸过渡明显更均匀。     

Realistic computable error bounds for three dimensional finite element analyses in linear elasticity

We obtain a computable estimator for the energy norm of the error in piecewise affine and piecewise quadratic finite element approximations of linear elasticity in three dimensions. We show that the estimator provides guaranteed upper bounds on the energy norm of the error as well as (up to a constant and data oscillation terms) local lower bounds.     

2D finite element mesh generation by medial axis subdivision

An algorithm for the automatic generation of two-dimensional finite element meshes using quadrilateral elements has been demonstrated. The technique uses information derived from the medial axis of a 2D region, the locus of the centre of an inscribed disc of maximal diameter as it rolls around the region interior. Using this information, an arbitrarily complex object can be subdivided into a series of meshable subregions. Within these subregions relatively conventional meshing patterns are then generated. The resulting meshes are well structured and flow smoothly round the object boundary with minimum mesh irregularity.     

An algorithm for automatic 2D finite element mesh generation with line constraints

In this study, an algorithm is designed specifically for automatic finite element (FE) mesh generation on the transverse structure of hulls reinforced by stiffeners. Stiffeners attached to the transverse structure are considered as line constraints in the geometry boundary. For the FE mesh generation used in this study, the line constraints are treated as boundaries and by that means the geometry domain attached to the line constraints is decomposed into sub-domains, constrained only by the closed boundaries. Then, the mesh can be generated directly on those sub-domains by the traditional approach. The performance of the proposed algorithm is evaluated and the quality of the generated mesh meets expectations.     

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.     

Computer graphics aided geometric modeling and mesh generation schemes for preprocessing and finite element analysis

The paper describes automated generation and editing schemes together with the development of computer-aided geometric models for general applications. For the construction of general finite element models of complex shapes, conventional approaches typical of wireframe, surface, or solid modeling cannot be effectively utilized for generating continuum solid models as well as discrete models simultaneously. In view of these facts, features to generate and model two-dimensional as well as threedimensional continuum and discrete models by isoparametric mapping/solid geometrical modeling techniques via a common interactive processor are described. The proposed scheme is demonstrated for modeling structural, thermal, or flow networks that are commonly encountered in engineering applications. In a research environment, the techniques addressed in this paper should prove to be very useful in providing flexibility and thereby significantly reducing the work load of frequent CAD users.     

A posteriori error estimation and adaptive mesh refinement for combined thermal-stress finite element analysis

Local and global error estimators and an associated h-based adaptive mesh refinement schemes are proposed for coupled thermal-stress problems. The error estimators are based on the “flux smoothing” technique of Zienkiewicz and Zhu with important modifications to improve convergence performance and computational efficiency. Adaptive mesh refinement is based on the concept of adaptive accuracy criteria, previously presented by the authors for stress-based problems and extended here for coupled thermal-stress problems. Three methods of mesh refinement are presented and numerical results indicate that the proposed method is the most efficient in terms of number of adaptive mesh refinements required for convergence in both the thermal and stress solutions. Also, the proposed method required a smaller number of active degrees of freedom to obtain an accurate solution.     

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.     

Adaptive error control for multigrid finite element

We consider the problem of adaptive error control in the finite element method including the error resulting from, inexact solution of the discrete equations. We prove a posteriori error estimates for a prototype elliptic model problem discretized by the finite element with a canomical multigrid algorithm. The proofs are based on a combination of so-called strong stability and, the orthogonality inherent in both the finite element method can the multigrid algorithm.