Hybrid meshing using constrained Delaunay triangulation for viscous flow simulations

In this paper, we present a generalized prismatic hybrid meshing method for viscous flow simulations. One major difficulty in implementing a robust prismatic hybrid meshing tool is to handle boundary layer mesh collisions, and normally an extra data structure (e.g. quadtree in two‐dimensional and octree in three‐dimensional) is required. The proposed method overcomes this difficulty via an heuristic approach, and it only relies on constrained delaunay triangulation/tetrahedralization(CDT). No extra data structures are required. Geometrical reasoning is used to approximate the maximum marching distance of each point by walking through the CDT. This is combined with post‐processing of marching vectors and distance and prohibition of multilevel differences to form an automatic and robust mechanism to remove boundary layer mesh collisions. Benefiting from the matureness of CDT techniques, the proposed method is robust, efficient and simple to implement. Its capability is demonstrated by generating quality prismatic hybrid meshes for industrial models with complex geometries. The proposed method is believed to be able considerably reduce the effort to implement a robust hybrid prismatic mesh generator for viscous flow simulations. © 2016 The Authors. International Journal for Numerical Methods in Engineering. Published by John Wiley & Sons Ltd.     

The Adaptive Delaunay Tessellation: a neighborhood covering meshing technique

In this paper we propose an unstructured hybrid tessellation of a scattered point set that minimally covers the proximal space around each point. The mesh is automatically obtained in a bounded period of time by transforming an initial Delaunay tessellation. Novel types of polygonal interpolants are used for interpolation applications and the geometric qualities of the elements make them also useful for discretization schemes. The approach proves to be superior to classical Delaunay one in a finite element context.     

Adaptive tetrahedral mesh generation by constrained Delaunay refinement

This paper presents a tetrahedral mesh generation method for numerically solving partial differential equations using finite element or finite volume methods in three‐dimensional space. The main issues are the mesh quality and mesh size, which directly affect the accuracy of the numerical solution and the computational cost. Two basic problems need to be resolved, namely boundary conformity and field points distribution. The proposed method utilizes a special three‐dimensional triangulation, so‐called constrained Delaunay tetrahedralization to conform the domain boundary and create field points simultaneously. Good quality tetrahedra and graded mesh size can be theoretically guaranteed for a large class of mesh domains. In addition, an isotropic size field associated with the numerical solution can be supplied; the field points will then be distributed according to it. Good mesh size conformity can be achieved for smooth sizing informations. The proposed method has been implemented. Various examples are provided to illustrate its theoretical aspects as well as practical performance. Copyright © 2008 John Wiley & Sons, Ltd.     

3D boundary recovery by constrained Delaunay tetrahedralization

Three‐dimensional boundary recovery is a fundamental problem in mesh generation. In this paper, we propose a practical algorithm for solving this problem. Our algorithm is based on the construction of a constrained Delaunay tetrahedralization (CDT) for a set of constraints (segments and facets). The algorithm adds additional points (so‐called Steiner points) on segments only. The Steiner points are chosen in such a way that the resulting subsegments are Delaunay and their lengths are not unnecessarily short. It is theoretically guaranteed that the facets can be recovered without using Steiner points. The complexity of this algorithm is analyzed. The proposed algorithm has been implemented. Its performance is reported through various application examples. Copyright © 2010 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.     

An approach to refining three-dimensional tetrahedral meshes based on Delaunay transformations

A technique for refining three-dimensional tetrahedral meshes is proposed in this paper. The proposed technique is capable of treating arbitrary unstructured tetrahedral meshes, convex or non-convex with multiple regions resulting in high quality constrained Delaunay triangulations. The tetrahedra generated are of high quality (nearly equilateral). Sliver tetrahedra, which present a real problem to many algorithms are not produced with the new method. The key to the generation of high quality tetrahedra is the iterative application of a set of topological transformations based on the Voronoi–Delaunay theory and a reposition of nodes technique. The computational requirements of the proposed technique are in linear relationship with the number of nodes and tetrahedra, making it ideal for direct employment in a fully automatic finite element analysis system for 3-D adaptive mesh refinement. Application to some test problems is presented to show the effectiveness and applicability of the new method.     

Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints

A method is described which constructs three-dimensional unstructured tetrahedral meshes using the Delaunay triangulation criterion. Several automatic point creation techniques will be highlighted and an algorithm will be presented which can ensure that, given an initial surface triangulation which bounds a domain, a valid boundary conforming assembly of tetrahedra will be produced. Statistics of measures of grid quality are presented for several grids. The efficiency of the proposed procedure reduces the computer time for the generation of realistic unstructured tetrahedral grids to the order of minutes on workstations of modest computational capabilities.     

The boundary recovery and sliver elimination algorithms of three‐dimensional constrained Delaunay triangulation

A boundary recovery and sliver elimination algorithm of the three‐dimensional constrained Delaunay triangulation is proposed for finite element mesh generation. The boundary recovery algorithm includes two main procedures: geometrical recovery procedure and topological recovery procedure. Combining the advantages of the edges/faces swappings algorithm and edges/faces splittings algorithm presented respectively by George and Weatherill, the geometrical recovery procedure can recover the missing boundaries and guarantee the geometry conformity by introducing fewer Steiner points. The topological recovery procedure includes two phases: ‘dressing wound’ and smoothing, which will overcome topology inconsistency between 3D domain boundary triangles and the volume mesh. In order to solve the problem of sliver elements in the three‐dimensional Delaunay triangulation, a method named sliver decomposition is proposed. By extending the algorithm proposed by Canvendish, the presented method deals with sliver elements by using local decomposition or mergence operation. In this way, sliver elements could be eliminated thoroughly and the mesh quality could be improved in great deal. Copyright © 2006 John Wiley & Sons, Ltd.     

Generation of oriented three-dimensional Delaunay grids suitable for the control volume integration method

A fully automatic algorithm for three-dimensional mesh generation is presented. The algorithm preserves the robustness and time efficiency of the finite octree technique; replacing octrees by more general 2–4–8- trees, it is capable of generating oriented meshes. In a post-processing step, meshes are transformed in order to satisfy the Delaunay criterion, and so that non-overlapping, closed control volumes can be defined for each mesh point through edge bisectors. The method is shown to be appropriate for modelling semiconductor devices, where the control volume scheme is the method of choice due to the peculiarities of the partial differential equations involved, and where locally refined and oriented meshes are essential to describe the relevant internal physical quantities adequately while keeping the number of mesh points practical.     

Discrete transfinite mappings for the description and meshing of three-dimensional surfaces using interactive computer graphics

A system for describing three-dimensional surfaces in a form suitable for finite element analysis is described. The system makes extensive use of real-time interactive computer graphics techniques for both input and display. Discrete transfinite mappings are used as the mathematical basis for the surface representation. The mathematical basis and the reasons for choosing this form of representation are discussed. Explicit forms of the mappings based on Lagrange polynomial interpolation functions are presented. Finally, the interactive graphics procedures for defining finite element meshes are described.     

面向四面体网格生成的曲面Delaunay三角化算法

提出了一种曲面域Delaunay三角网格的直接构造算法。该算法在曲面网格剖分的边界递归算法和限定Delaunay四面体化算法的基础上,利用曲面采样点集的空间Delaunay四面体网格来辅助曲面三角网格的生成,曲面上的三角网格根据最小空球最小准则由辅助四面体网格中选取,每个三角形都满足三维Delaunay空球准则,网格质量有保证,并且极大的方便了进一步的曲面边界限定下的Delaunay四面体化的进行。     

Automatic multiscale meshing through HRBF networks

A procedure for the real-time construction of three-dimensional (3-D) multiscale meshes from not evenly sampled 3-D points is described and discussed in this paper. The process is based on the connectionist model named hierarchical radial basis functions network (HRBF), which has been proved effective in the reconstruction of smooth surfaces from sparse noisy data points. The network goal is to achieve a uniform reconstruction error, equal to measurement error, by stacking noncomplete grids of Gaussians at decreasing scales. It is shown here how the HRBF properties can be used to develop a configuration algorithm, which produces a continuous surface in real time. In addition, the model is extended to automatically convert the continuous surface into a 3-D mesh according to an adequate error measure.     

动力总成NVH分析齿轮啮合特性研究

研究动力总成中部分齿轮的啮合特性,及其对NVH的影响,介绍了发动机启动电机传动齿轮和变速器齿轮的啮合特性.分析启动电机传动齿轮重合度,通过提高重合度,解决电机传动噪声问题和提高齿轮寿命,噪声试验表明,声品质有所改善;同时,研究了变速器齿轮的啮合动刚度,通过分析单对齿轮刚度和啮合线长度变化,快速得到随时间变化的齿轮啮合变刚度,并形成齿轮啮合动刚度计算标准方法,开发相应计算程序,大幅提高了工作效率,该方法的特点是计算简单、高效以及能得到随啮合转角变化的齿轮啮合刚度.     

Delaunay triangulation of non-convex planar domains

This paper investigates the possibility of integrating the two currently most popular mesh generation techniques, namely the method of advancing front and the Delaunay triangulation algorithm. The merits of the resulting scheme are its simplicity, efficiency and versatility. With the introduction of ‘non-Delaunay’ line segments, the concept of using Delaunay triangulation as a means of mesh generation is clarified. An efficient algorithm is proposed for the construction of Delaunay triangulations over non-convex planar domains. Interior nodes are first generated within the planar domain. These interior nodes and the boundary nodes are then linked up together to produce a valid triangulation. In the mesh generation process, the Delaunay property of each triangle is ensured by selecting a node having the smallest associated circumcircle. In contrast to convex domains, intersection between the proposed triangle and the domain boundary has to be checked; this can be simply done by considering only the ‘non-Delaunay’ segments on the generation front. Through the study of numerous examples of various characteristics, it is found that high-quality triangular element meshes are obtained by the proposed algorithm, and the mesh generation time bears a linear relationship with the number of elements/nodes of the triangulation.     

Automatic finite element meshing of planar Voronoi tessellations

The concept of Voronoi tessellation has recently been extensively used in materials science, especially to model the geometrical features of random microstructures like aggregates of grains in polycrystals, patterns of intergranular cracks and composites. Solution of the underlying field equations usually requires use of numerical methods such as finite elements.The framework for automatic generation of quadrilateral finite element meshing of planar Voronoi tessellation is proposed in the paper, resulting in a powerful set of tools to be used in the rather wide field of micromechanics. As far as feasible, the implementation of features built in commercially available mesh generators was pursued. Additionally, the minimum geometric requirements for a “meshable” tessellation are outlined.Special attention is given to the meshes, which enable explicit modelling of grain boundary processes, such as for example contact (closure of cracks) or friction between grains. This is inline with numerical examples, which are oriented towards the fracture mechanics, in particular to the development of intergranular microcracks and/or their impact on the effective behaviour of the polycrystal.The examples were evaluated using the commercially available general-purpose finite element code abaqus. The usual continuum mechanics based numerical methods and boundary conditions were safely applied to aggregates of randomly oriented polycrystals with anisotropic elastic material behaviour as computational domains.     

Finite element triangular meshing optimization for pure torsion

This paper presents a new approach to the mesh generation for torsional problems in the finite element discretization using quadratic triangular elements. A nonlinear constrained optimization program is used as a tool. As a criterion for the optimum meshing, the minimum error of second-order differential operator is adopted. An example problem is included to demonstrate the applicability of the method. Final results of the mesh distribution show significant improvements in meeting the criterion's objectives.     

采煤机行走机构动态啮合特性分析

为分析渐开线采煤机行走轮与Ⅲ型销轨的动态啮合特性,基于ANSYS/LS_DYNA建立行走机构动态啮合过程数值分析模型,以牵引阻力和行走速度为变量研究行走机构动态啮合特性,得到动态啮合时行走速度波动、节线和齿根受力的变化规律．研究结果表明：牵引阻力对行走机构速度波动和节线及齿根受力规律影响显著,随着牵引阻力增大,啮合点在节线附近时对应齿面应力相对较低,但整个啮合过程中应力波动增大;行走速度变化对速度波动持续时间有较大影响;随着行走速度增大,各项载荷峰值呈现先减小后小幅增大的现象,且到达峰值后衰减加剧．     

行星齿轮箱太阳轮故障动态啮合周期特性

与定轴齿轮箱相比,行星齿轮箱内部齿轮副复杂的相对运动所引发的振动响应更加复杂多样,因而对其关键部件进行故障诊断颇具挑战。当内部轮齿发生故障时,由于故障啮合位置的动态性引起传递路径的时变性,固定在系统箱体上的单个传感器观测到的故障信息强度亦将呈现不规则变化的独特性。若想恰如其分的利用这些故障信息实现简单而有效的诊断,需重点关注故障啮合位置的周期特性,而后基于该周期所观测的信号进行“统筹兼顾”的分析,便可突显出各类故障的差异性。该研究在深入研究行星齿轮系统内部齿轮副的运行规律的基础上,创新性的提出了确定太阳轮故障动态啮合位置周期的方法,并考虑了以下两种情况:行星轮各不相同;行星轮完全相同。基于上述两种情况分别推导出太阳轮和行星架所需的最小旋转圈数的一般性表达式,该表达式可用于计算齿圈固定型的行星齿轮箱中的太阳轮故障啮合位置的运动周期。最后通过实验提出并验证了基于上述周期的故障诊断最小数据长度。     

一种利用Delaunay三角剖分的碰撞检测算法

虚拟现实中物体对象分布及运动情况呈现复杂多样,碰撞检测算法很难达到实时性和准确性的要求.提出了一种基于Delaunay三角剖分的多物体碰撞检测实时算法.该算法运用包围体紧密拟合物体对象,以包围体的中心构建离散数据点集,生成Delaunay三角网格,实施碰撞检测,避免层次包围盒和空间划分的不利因素,物体的更新等操作限定在局部的三角形内.实验表明在多物体的碰撞检测中,即使存在若干移动物体,算法能够满足实时性和准确性的要求.