Generation and optimization of tetrahedral meshes by advancing front technique

An algorithm for tetrahedron mesh generation and optimization with respect to a shape and a size criterion is presented. A well distributed set of nodes is first generated by an octree method, and the set is then triangulated. The advancing front technique is used to mesh the whole volume. Emphasis has been placed on management of the front. The method involves priority construction of enhanced quality tetrahedra. Each face is assigned to a front corresponding to the quality of the best tetrahedron which can be constructed. Elements are destroyed in the case of non-convergence. Optimization procedures make local use of the algorithm used to mesh the complete model. Industrial examples of relatively complex volumes are given, demonstrating that a high quality and optimized mesh can be obtained by the proposed method. © 1998 John Wiley & Sons, Ltd.     

A new approach to free-form surface mesh control in a CAD environment

An adaptive process controlling the position of nodes on a surface mesh is presented. The control can depend on one (or more) criterion(ria) about element quality. The mesh is attached, through the concept of classification, to a geometric model issued by a computer aided design software. Thus, the surface domain is described by entities currently available in such systems, i.e. any free-form patches like Non-Uniform Rational B-Spline or Bézier patches can be used, even if they are restricted. Multi-connected surface domains can be treated using the same geometrical definition. The method described allows nodes to slide on a patch or jump from a patch onto another one. Such movements greatly improve the mesh quality with regard to a chosen criterion. Problems occurring with patch-by-patch meshing techniques when surfaces patches exhibit significant size differences are then overcome. The adaptation technique can be made independent of CAD data structures and meshing techniques, hence it constitutes the basis of a mesh management module.     

Towards automatic structured multiblock mesh generation using improved transfinite interpolation

The quality of any numerical flowfield solution is inextricably linked to the quality of the mesh used. It is normally accepted that structured meshes are of higher quality than unstructured meshes, but are much more difficult to generate and, furthermore, for complex topologies a multiblock approach is required. This is the most resource‐intensive approach to mesh generation, since block structures, mesh point distributions, etc., need to be defined before the generation process, and so is seldom used in an industrial design loop, particularly where a novice user may be involved. This paper considers and presents two significant advances in multiblock mesh generation: the development of a fast, robust, and improved quality interpolation‐based generation scheme and a fully automatic multiblock optimization and generation method. A volume generation technique is presented based on a form of transfinite interpolation, but modified to include improved orthogonality and spacing control and, more significantly, an aspect ratio‐based smoothing algorithm that removes grid crossover and results in smooth meshes even for discontinuous boundary distributions. A fully automatic multiblock generation scheme is also presented, which only requires surface patch(es) and a target number of mesh cells. Hence, all user input is removed from the process, and a novice user is able to obtain a high‐quality mesh in a few minutes. It also means the code can be run in batch mode, or called as an external function, and so is ideal for incorporation into a design or optimization loop. To demonstrate the power and efficiency of the code, multiblock meshes of up to 256 million cells are presented for wings and rotors in hover and forward flight. Copyright © 2007 John Wiley & Sons, Ltd.     

Inserting a surface into an existing unstructured mesh

In this work, a new method for inserting a surface as an internal boundary into an existing unstructured tetrahedral mesh is developed. The surface is discretized by initially placing vertices on its bounding curves, defining a length scale at every location on each boundary curve based on the local underlying mesh, and equidistributing length scale along these curves between vertices. The surface is then sampled based on this boundary discretization, resulting in a surface mesh spaced in a way that is consistent with the initial mesh. The new points are then inserted into the mesh, and local refinement is performed, resulting in a final mesh containing a representation of the surface while preserving mesh quality. The advantage of this algorithm over generating a new mesh from scratch is in allowing for the majority of existing simulation data to be preserved and not have to be interpolated onto the new mesh. This algorithm is demonstrated in two and three dimensions on problems with and without intersections with existing internal boundaries. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive generation of hexahedral element meshes for finite element analysis of metal plastic forming process

A method for the adaptive generation of hexahedral element mesh based on the geometric features of solid model is proposed. The first step is to construct the refinement information fields of source points and the corresponding ones of elements according to the surface curvature of the analyzed solid model. A thickness refinement criterion is then used to construct the thickness-based refinement information field of elements from digital topology. The second step is to generate a core mesh through removing all the undesired elements using even and odd parity rules. Then the core mesh is magnified in an inside–out manner method through a surface node projection process using the closest position approach. Finally, in order to match the mesh to the characteristic boundary of the solid model, a threading method is proposed and applied. The present method was applied in the mesh construction of different engineering problems. The resulting meshes are well-shaped and capture all the geometric features of the original solid models.     

等值面的生成原理与算法

本文从工程实际中引出,由四变量离散数据图示等值曲面的问题,提出了构造等值曲面的四维画法几何生成方法,在用计算机实现此生成方法的过程中,从理论上证明了1982年Nguyen-Van-Phai提出的四面体网格化算法,这种算法的性质,即四面体球面过剩为最大的情况下是最佳的,可以有效地应用于计算机绘图和有限元分析的网格自动生成等方面。本文用此算法求出四变量离散数据的等值点,从而实现等值曲面的拟合。     

Coupling of non‐conforming meshes in a component mode synthesis method

A common mesh refinement‐based coupling technique is embedded into a component mode synthesis method, Craig–Bampton. More specifically, a common mesh is generated between the non‐conforming interfaces of the coupled structures, and the compatibility constraints are enforced on that mesh via L2‐minimization. This new integrated method is suitable for structural dynamic analysis problems where the substructures may have non‐conforming curvilinear and/or surface interface meshes. That is, coupled substructures may have different element types such as shell, solid, and/or beam elements. The proposed method is implemented into a commercial finite element software, B2000++, and its demonstration is carried out using an academic and industry oriented test problems. Copyright © 2013 John Wiley & Sons, Ltd.     

复合材料细观结构三维有限元网格模型的建立

提出了针对颗粒夹杂为椭球形状并呈随机分布的多相复合材料的三维有限元网格的建立方法,为复合材料细观结构研究提供了一种全自动的建模工具。引入了以体积为标度的任意两椭球骨料侵入的判别准则,实现了一种三维随机骨料的投放算法;在基于映射法的颗粒表面有限元网格生成算法中通过扫描线布点和局部连接技术较好地解决了网格极化现象;采用改进的三维AFT方法生成基体的四面体网格,并利用AFT特性一次生成所有颗粒夹杂的四面体网格;为进一步的复合材料细观结构与宏观力学性能的多尺度计算打下了基础。最后用几个算例验证了算法的有效性。     

An L∞–Lp mesh‐adaptive method for computing unsteady bi‐fluid flows

This paper discusses the contribution of mesh adaptation to high‐order convergence of unsteady multi‐fluid flow simulations on complex geometries. The mesh adaptation relies on a metric‐based method controlling the L ^p‐norm of the interpolation error and on a mesh generation algorithm based on an anisotropic Delaunay kernel. The mesh‐adaptive time advancing is achieved, thanks to a transient fixed‐point algorithm to predict the solution evolution coupled with a metric intersection in the time procedure. In the time direction, we enforce the equidistribution of the error, i.e. the error minimization in L ^∞ norm. This adaptive approach is applied to an incompressible Navier–Stokes model combined with a level set formulation discretized on triangular and tetrahedral meshes. Applications to interface flows under gravity are performed to evaluate the performance of this method for this class of discontinuous flows. Copyright © 2010 John Wiley & Sons, Ltd.     

A gradient‐based adaptation procedure and its implementation in the element‐free Galerkin method

A gradient‐based adaptation procedure is proposed in this paper. The relative error in the total strain energy from two adjacent adaptation stages is used as a stop‐criterion. The refinement–coarsening process is guided by the gradient of strain energy density, based on the assumption: a larger gradient needs a richer mesh and vice versa. The procedure is then implemented in the element‐free Galerkin method for linear elasto‐static problems. Numerical examples are presented to show the performance of the proposed procedure. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

Automatic metric 3D surface mesh generation using subdivision surface geometrical model. Part 2: Mesh generation algorithm and examples

In this paper, a new metric advancing front surface mesh generation scheme is suggested. This new surface mesh generator is based on a new geometrical model employing the interpolating subdivision surface concept. The target surfaces to be meshed are represented implicitly by interpolating subdivision surfaces which allow the presence of various sharp and discontinuous features in the underlying geometrical model. While the main generation steps of the new generator are based on a robust metric surface triangulation kernel developed previously, a number of specially designed algorithms are developed in order to combine the existing metric advancing front algorithm with the new geometrical model. As a result, the application areas of the new mesh generator are largely extended and can be used to handle problems involving extensive changes in domain geometry. Numerical experience indicates that, by using the proposed mesh generation scheme, high quality surface meshes with rapid varying element size and anisotropic characteristics can be generated in a short time by using a low‐end PC. Finally, by using the pseudo‐curvature element‐size controlling metric to impose the curvature element‐size requirement in an implicit manner, the new mesh generation procedure can also generate finite element meshes with high fidelity to approximate the target surfaces accurately. Copyright © 2003 John Wiley & Sons, Ltd.     

Simultaneous untangling and smoothing of moving grids

In this work, a technique for simultaneous untangling and smoothing of meshes is presented. It is based on an extension of an earlier mesh smoothing strategy developed to solve the computational mesh dynamics stage in fluid–structure interaction problems. In moving grid problems, mesh untangling is necessary when element inversion happens as a result of a moving domain boundary. The smoothing strategy, formerly published by the authors, is defined in terms of the minimization of a functional associated with the mesh distortion by using a geometric indicator of the element quality. This functional becomes discontinuous when an element has null volume, making it impossible to obtain a valid mesh from an invalid one. To circumvent this drawback, the functional proposed is transformed in order to guarantee its continuity for the whole space of nodal coordinates, thus achieving the untangling technique. This regularization depends on one parameter, making the recovery of the original functional possible as this parameter tends to 0. This feature is very important: consequently, it is necessary to regularize the functional in order to make the mesh valid; then, it is advisable to use the original functional to make the smoothing optimal. Finally, the simultaneous untangling and smoothing technique is applied to several test cases, including 2D and 3D meshes with simplicial elements. As an additional example, the application of this technique to a mesh generation case is presented. Copyright © 2008 John Wiley & Sons, Ltd.     

A surface remeshing approach

A method is presented to remesh three‐dimensional discrete data surfaces. The originality of the method resides in mimicking heavily the classical adva10ncing front method for quality while always relying on a valid mesh for robustness. Therefore, local operations are applied in a first step to obtain a mesh of appropriate length scale compared to the specified size, and an original procedure has been developed for refinement that automatically degenerates to a surface mesh optimization if the size map has been respected. A valid mesh is then always available during the remeshing procedure. A new background grid is proposed that relies on a Cartesian mesh for the size distribution. Interpolation is performed very quickly and the size distribution is smoothed out to provide a slowly varying mesh size distribution. Various numerical results are presented to illustrate the efficiency but mainly the quality and robustness of the method. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamic simulation of spur gear with tooth root crack propagating along tooth width and crack depth

Gear tooth crack will cause changes in vibration characteristics of gear system, based on which, operating condition of the gear system is always monitored to prevent a presence of serious damage. However, it is also a unsolved puzzle to establish the relationship between tooth crack propagation and vibration features during gear operating process. In this study, an analytical model is proposed to investigate the effect of gear tooth crack on the gear mesh stiffness. Both the tooth crack propagations along tooth width and crack depth are incorporated in this model to simulate gear tooth root crack, especially when it is at very early stage. With this analytical formulation, the mesh stiffness of a spur gear pair with different crack length and depth can be obtained. Afterwards, the effects of gear tooth root crack size on the gear dynamics are simulated and the corresponding changes in statistical indicators – RMS and kurtosis are investigated. The results show that both RMS and kurtosis increase with the growth of tooth crack size for propagation whatever along tooth width and crack length. Frequency spectrum analysis is also carried out to examine the effects of tooth crack. The results show that sidebands caused by the tooth crack are more sensitive than the mesh frequency and its harmonics. The developed analytical model can predict the change of gear mesh stiffness with presence of a gear tooth crack and the corresponding dynamic responses could supply some guidance to the gear condition monitoring and fault diagnosis, especially for the gear tooth crack at early stage.     

On advancing front mesh generation in three dimensions

This paper deals with some aspects of unstructured mesh generation in three dimensions by the advancing front technique. In particular, the parameters used in the algorithm are characterized, and strategies that may be used to improve robustness are suggested. We also describe a method whereby structured tetrahedral meshes with exceptionally stretched elements adjacent to boundary surfaces may be produced. The suggested method can be combined with the advancing front concept in a natural way.     

A new automatic adaptive 3D solid mesh generation scheme for thin‐walled structures

A new algorithm to generate three‐dimensional (3D) mesh for thin‐walled structures is proposed. In the proposed algorithm, the mesh generation procedure is divided into two distinct phases. In the first phase, a surface mesh generator is employed to generate a surface mesh for the mid‐surface of the thin‐walled structure. The surface mesh generator used will control the element size properties of the final mesh along the surface direction. In the second phase, specially designed algorithms are used to convert the surface mesh to a 3D solid mesh by extrusion in the surface normal direction of the surface. The extrusion procedure will control the refinement levels of the final mesh along the surface normal direction. If the input surface mesh is a pure quadrilateral mesh and refinement level in the surface normal direction is uniform along the whole surface, all hex‐meshes will be produced. Otherwise, the final 3D meshes generated will eventually consist of four types of solid elements, namely, tetrahedron, prism, pyramid and hexahedron. The presented algorithm is highly flexible in the sense that, in the first phase, any existing surface mesh generator can be employed while in the second phase, the extrusion procedure can accept either a triangular or a quadrilateral or even a mixed mesh as input and there is virtually no constraint on the grading of the input mesh. In addition, the extrusion procedure development is able to handle structural joints formed by the intersections of different surfaces. Numerical experiments indicate that the present algorithm is applicable to most practical situations and well‐shaped elements are generated. Copyright © 2004 John Wiley & Sons, Ltd.     

Verification of three‐dimensional anisotropic adaptive processes

A verification methodology for adaptive processes is devised. The mathematical claims made during the process are identified and measures are presented in order to verify that the mathematical equations are solved correctly. The analysis is based on a formal definition of the optimality of the adaptive process in the case of the control of the L^∞‐norm of the interpolation error. The process requires a reconstruction that is verified using a proper norm. The process also depends on mesh adaptation toolkits in order to generate adapted meshes. In this case, the non‐conformity measure is used to evaluate how well the adapted meshes conform to the size specification map at each iteration. Finally, the adaptive process should converge toward an optimal mesh. The optimality of the mesh is measured using the standard deviation of the element‐wise value of the L^∞‐norm of the interpolation error. The results compare the optimality of an anisotropic process to an isotropic process and to uniform refinement on highly anisotropic 2D and 3D test cases. Copyright © 2011 John Wiley & Sons, Ltd.     

Automated computer simulation of two-dimensional elastostatic problems by the finite element method

A software system for the automated computer simulation of two-dimensional elastostatic problems by the finite element method is described. This system consists of two parts, automated mesh generation and automated stress analysis. The mesh generation is based on a method in which equilateral triangles are generated successively in the unmeshed region. Automated mesh refinement is carried out in the latter part of the simulation process. The stress analysis is based on the assumed stress hybrid method and the successive over relaxation method. The computer program developed for this paper can generate a succession of increasingly refined triangular meshes until a certain mesh convergence criterion is achieved. The mesh convergence criterion is based on a comparison of nodal stresses in successive analyses until all the stress differences are within a specified tolerance.