Automatic three-dimensional mesh generation by the modified-octree technique

An approach for the fully automatic generation of three-dimensional finite element meshes is presented. The method is specifically designed for use with solid modelling systems which provide a complete and unique definition of the geometry of a part. The method follows from the basic concepts of the octree encoding technique with specific modifications made to produce valid, user controllable finite element meshes. Example problems are included to demonstrate the technique.     

Automatic three-dimensional finite element mesh generation via modified ray casting

Three-dimensional (3-D) finite element mesh generation has been the target of automation due to the complexities associated with generating and visualizing the mesh. A fully automatic 3-D mesh generation method is developed. The method is capable of meshing CSG solid models. It is based on modifying the classical ray-casting technique to meet the requirements of mesh generation. The modifications include the utilization of the element size in the casting process, the utilization of 3-D space box enclosures, and the casting of ray segments (rays with finite length). The method begins by casting ray segments into the solid. Based on the intersections between the segments and the solid boundary, the solid is discretized into cells arranged in a structure. The cell structure stores neighbourhood relations between its cells. Each cell is meshed with valid finite elements. Mesh continuity between cells is achieved via the neighbourhood relations. The last step is to process the boundary elements to represent closely the boundary. The method has been tested and applied to a number of solid models. Sample examples are presented.     

Periodic three-dimensional mesh generation for crystalline aggregates based on Voronoi tessellations

In this paper a method for the generation of three-dimensional periodic meshes for the numerical simulation of polycrystalline aggregates is presented. The mesh construction is based on Voronoi and Hardcore Voronoi tessellations of random point seeds. Special emphasis is paid on the periodicity of the mesh topologies which leads to favorable numerical properties for the determination of effective properties using unit cells. The mesh generation algorithm is able to produce high quality meshes at low computational costs. Based on unit cell simulations with different but statistically equivalent microstructures, the effective linear elastic properties of polycrystals consisting of grains with a cubic symmetry are determined. The numerical results are compared with first-, third- and fifth-order bounds and experimental data. Numerical simulations show the efficiency of the proposed homogenization technique.     

Automatic and efficient hybrid viscous mesh generation based on clipped Voronoi diagrams

The commonly used advancing layers method to generate hybrid meshes suffers from many drawbacks. The generation of isotropic meshes for far-field domains with irregular and complex boundary subdivisions after boundary layers advancing is time consuming and, in some cases, is not robust in 3D. To address these difficulties, this paper presents a novel method to generate hybrid polygonal meshes in 2D and polyhedral meshes in 3D for viscous flow simulations. In the proposed method, first, we generate a full Voronoi diagram for the appropriate distribution of generators that avoids the extra mesh generation required for the remaining holes in the advancing layers method. To recover the inner solid boundaries, we implement a robust boundary cell cutting process. Because the generators are located layer by layer near the boundaries, there is no requirement to consider all of the Voronoi cells. Only the first layer Voronoi cells must be cut, making the calculation very efficient. We have generated hybrid meshes using the present method for many viscous flow cases. The results show close agreement between the computations and the experimental results, thus indicating the reliability and effectiveness of the hybrid mesh generated by our method.     

Automatic mesh generation from solid models based on recursive spatial decompositions

This paper introduces a two-stage algorithm for the automatic conversion of solid models into finite element meshes. In Stage 1 the solid is approximated by a collection of variably sized cells generated by recursive spatial decomposition and stored in a logical tree. In Stage 2 the approximating cell structure, which includes cells that are wholly inside the solid (IN) as well as cells that are neither inside nor outside (NIO), is transformed into a finite element model. IN cells are directly mapped into finite elements while NIO cells are decomposed according to their topologically complexity through either template mapping or recursive element extraction. Although specifically designed for adaptive remeshing, the algorithm is of general use and can be implemented in any Solid Modelling System that supports Boolean operations on solids and maintains a complete boundary representation. Core algorithms for Stages i and 2 are rigorously developed to insure their applicability within a genuinely automatic procedure. Specific issues related to boundary evaluation and decomposition procedures are identified and discussed. The implementation of the algorithm into an experimental system based on the PADL-2 solid modeller is described. The paper concludes with a comparative study of existing meshing algorithms based on recursive spatial decompositions.     

模糊控制与图像处理技术实现的聚焦方法

为提高图像测量系统的精度,提出了一种由模糊控制与图像处理技术实现的自动聚焦方法。通过线性拟合与同态滤波滤除噪声后,用改进的梯度平方函数作为聚焦评价函数,提高了聚焦灵敏度;运用模糊控制技术改换搜索方式,实现了实时自适应变步长搜索,保证系统快速准确聚焦。实验结果表明,该聚焦方法具有单峰性,响应快,鲁棒性强,在±100μm范围内自动搜索,定位时间小于2″,聚焦不确定度达±1μm。     

Automatic mesh generation over intersecting surfaces

A fully automatic general scheme is proposed to determine and analyse the intersections between two groups of surfaces composed of triangular facets. By carefully maintaining the spatial position of the lines of intersection in regenerating mesh locally around surface intersections, pieces of surfaces can be arbitrarily combined and merged. A great variety of objects can be easily created by selectively putting together different surface parts derived from surface intersections. The new algorithm is best applied in conjunction with an existing surface mesh generator to enhance its general capability in dealing with objects built from intersecting surfaces. In fact, it is a powerful surface mesh manipulator, and through the repeated use of the process, complex structures can be rapidly and accurately constructed.     

Automatic mesh generation with tetrahedron elements

To reduce the manual work involved in the application of the FEM in practice, preprocessors can be applied for the construction of network structures, which are complicated in generation strategy and do not form any optimum discrete structure. The time necessary for generation can be minimized even more by the application of only one element type within the whole network structure. A technique for the automatic generation of 3D-network structures with tetrahedron elements is presented in this paper. In this proposed technique, the nodal points of the network structure must be defined manually before the generation procedure, since a random positioning of points is usually undesirable for FEM calculation. The nodal points are connected by a program to a network structure consisting of tetrahedron elements which have optimum form for the numerical computation of the element matrices. After the generation, the element sides forming any part of the boundary surface of the network structure can be automatically identified. If necessary, the network structure can be automatically refined.     

Resonance fluorescence based two- and three-dimensional atom localization

Two- and three-dimensional atom localization in a two-level atom–field system via resonance fluorescence is suggested. For the two-dimensional localization, the atom interacts with two orthogonal standing-wave fields, whereas for the three-dimensional atom localization, the atom interacts with three orthogonal standing-wave fields. The effect of the detuning and phase shifts associated with the corresponding standing-wave fields is investigated. A precision enhancement in position measurement of the single atom can be noticed via the control of the detuning and phase shifts.     

Automatic mesh generation and adaptation by using contours

A general and efficient remeshing algorithm is presented for the discretization of arbitrary planar domains into triangular elements in consistency with the given node spacing function. The contour lines of the node spacing function at suitable calculated levels provide the natural lines of division of the problem domain into subregions, where finite element meshes of different element sizes are generated using the available general-purpose mesh generators.^{1, 2} Examples of remeshing for various node spacing functions are given to illustrate that high-quality gradation meshes can be generated automatically without any user's intervention by this simple contour line method.     

Automatic sizing functions for unstructured surface mesh generation

Accurate sizing functions are crucial for efficient generation of high‐quality meshes, but to define the sizing function is often the bottleneck in complicated mesh generation tasks because of the tedious user interaction involved. We present a novel algorithm to automatically create high‐quality sizing functions for surface mesh generation. First, the tessellation of a Computer Aided Design (CAD) model is taken as the background mesh, in which an initial sizing function is defined by considering geometrical factors and user‐specified parameters. Then, a convex nonlinear programming problem is formulated and solved efficiently to obtain a smoothed sizing function that corresponds to a mesh satisfying necessary gradient constraint conditions and containing a significantly reduced element number. Finally, this sizing function is applied in an advancing front mesher. With the aid of a walk‐through algorithm, an efficient sizing‐value query scheme is developed. Meshing experiments of some very complicated geometry models are presented to demonstrate that the proposed sizing‐function approach enables accurate and fully automatic surface mesh generation. Copyright © 2016 John Wiley & Sons, Ltd.     

An apporach to automatic three-dimensional finite element mesh generation

Recently developed solid modelling systems for the design of complex physical solids using interactive computer graphics offer the exciting possibility of an integrated design/analysis system. Called geometric modellers, these systems build complex solids from primitive solids (cubes, cylinders, spheres, solid patches, etc.) and macro solids (combination of primitives)^{3, 4, 8, 16, 18, 25, 38}. To provide an effective structural analysis capability for these systems, methods must be devised to ease the burden of discretizing the solid geometry into a user controlled (usually locally graded) finite element mesh. The purpose of this paper is to describe an interactive solid mesh generation system capable of generating valid meshes of well-proportional tetrahedral finite elements for the decomposition of multiply connected solid structures. The system uses a semi-automatic node insertion procedure to locate element node points within and on the surface of a structure. An independent automatic three-dimensional triangulator then accepts these nodes as input and connects them to form a valid finite element mesh oftetrahedral elements. Although this report makes use of a modeller based on a constructive solid geometry representation (a so-called CSG modeller), the mesh generation strategy elaborated herein is completely general and makes no particular use of the CSG representation.     

Strain-energy based homogenisation of two- and three-dimensional hyperelastic solid foams

A possible classification of cellular solids can be made based on the dimension into honeycombs and foams. In numerical simulations 2D models that are employed primarily to study honeycombs can also be used to model open-cell foams. Thereby, a loss of information regarding the 3D connectivity of the microstructure is involved. To answer the question how the missing third dimension in 2D models affects the overall properties, spatially periodic 2D and 3D model foams are adopted. From the point of homogenisation, a strain-energy based scheme is used for adequately determining the effective mechanical properties at large strains. The key idea behind this method is to use directly the equivalence condition between the meso-strain energy and the macro-strain energy. In a first step a representative volume element with the given microstructure and a corresponding volume element containing the effective medium are subjected to equivalent states of deformation. Subsequently, the macroscopic stress-strain relationships are determined by volume-averaging of the stored strain energy. The results of some fundamental loading cases indicate that both model foams represent the deformation characteristics of hyperelastic solid foams like localized bending and elastic buckling. In addition, the development of anisotropy due to microstructural changes at large strains can be traced with both model foams. Nevertheless, the different cell morphology affects the stress-strain curves in a quantitative manner.     

Tetrahedral mesh generation based on space indicator functions

An algorithm for the generation of tetrahedral volume meshes is developed for highly irregular objects specified by volumetric representations such as domain indicator functions and tomography data. It is based on red–green refinement of an initial mesh derived from a body‐centered cubic lattice. A quantitative comparison of alternative types of initial meshes is presented. The minimum set of best‐quality green refinement schemes is identified. Boundary conformity is established by deforming or splitting surface‐crossing elements. Numerical derivatives of input data are strictly avoided. Furthermore, the algorithm features surface‐adaptive mesh density based on local surface roughness, which is an integral property of finite surface portions. Examples of applications are presented for computer tomography of porous media. Copyright © 2012 John Wiley & Sons, Ltd.     

Delaunay versus max-min solid angle triangulations for three-dimensional mesh generation

The Delaunay triangulation has been used in several methods for generating finite element tetrahedral meshes in three-dimensional polyhedral regions. Other types of three-dimensional triangulations are possible, such as a triangulation satisfying a local max-min solid angle criterion. In this paper, we present experimental results to show that max-min solid angle triangulations are better than Delaunay triangulations for finite element tetrahedral meshes, since the former type of triangulations contains tetrahedra of better shape than the latter type. We also describe how mesh points are generated and triangulated in our tetrahedral mesh generation method.     

Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations

The centroidal Voronoi tessellation based Delaunay triangulation (CVDT) provides an optimal distribution of generating points with respect to a given density function and accordingly generates a high‐quality mesh. In this paper, we discuss algorithms for the construction of the constrained CVDT from an initial Delaunay tetrahedral mesh of a three‐dimensional domain. By establishing an appropriate relationship between the density function and the specified sizing field and applying the Lloyd's iteration, the constrained CVDT mesh is obtained as a natural global optimization of the initial mesh. Simple local operations such as edges/faces flippings are also used to further improve the CVDT mesh. Several complex meshing examples and their element quality statistics are presented to demonstrate the effectiveness and efficiency of the proposed mesh generation and optimization method. Copyright © 2003 John Wiley & Sons, Ltd.     

Automatic quadrilateral/triangular free-form mesh generation for planar regions

Automation of finite element mesh generation holds great benefits for mechanical product development and analysis. In addition to freeing engineers from mundane tasks, automation of mesh generation reduces product cycle design and eliminates human-related errors. Most of the existing mesh generation methods are either semi-automatic or require specific topological information. A fully automatic free-form mesh generation method is described in this paper to alleviate some of these problems. The method is capable of meshing singly or multiply connected convex/concave planar regions. These regions can be viewed as crosssectional areas of 2 1/2 D objects analysed as plane stress, plane strain or axisymmetric stress problems. In addition to being fully automatic, the method produces quadrilateral or triangular elements with aspect rations near one. Moreover, it does not require any topological constraints on the regions to be meshed; i.e. it provides free-form mesh generation. The input to the method includes the region's boundary curves, the element size and the mesh grading information. The method begins by decomposing the planar region to be meshed into convex subregions. Each subregion is meshed by first generating nodes on its boundaries using the input element size. The boundary nodes are then offset to mesh the subregion. The resulting meshes are merged together to form the final mesh. The paper describes the method in detail, algorithms developed to implement it and sample numerical examples. Results on parametric studies of the method performance are also discussed.     

基于模糊聚类的模态参数自动识别

多参考点最小二乘复频域法（p-LSCF）是最近几年来提出的宽频带模态参数识别算法,该算法在抗干扰能力、识别密集模态、以及处理大阻尼复杂结构方面具有非常好的特性。区分真实极点与计算极点是该算法中非常重要的一步,这项工作通常是借助于稳定图由人工完成。对于复杂结构,这个过程尤其繁琐并且耗时。模糊聚类肥西已经在多个领域得到了成功的应用,通过将模糊聚类作为自动分析稳定图的工具引入到模态分析中,实现了模态参数的自动识别。     

Control of vortex shedding on two- and three-dimensional aerofoils

We review and expand on the control of separated flows over flat plates and aerofoils at low Reynolds numbers associated with micro air vehicles. Experimental observations of the steady-state and transient lift response to actuation, and its dependence on the actuator, aerofoil geometry and flow conditions, are discussed and an attempt is made to unify them in terms of their excitation of periodic and transient vortex shedding. We also examine strategies for closed-loop flow and flight control using actuation of leading-edge vortices.