Hexahedral Mesh Generation Research Articles

A consistent octree hanging node elimination algorithm for hexahedral mesh generation

A new algorithm for hanging node elimination in octree structures is developed. The proposed algorithm utilizes hanging node elimination by refinement templates and a new mesh conditioning technique based on decoupling templates. Refinement templates insert transition elements to eliminate hanging nodes. Decoupling templates insert circular loops in the dual mesh without introducing or removing hanging nodes. Decoupling templates are introduced to avoid full refinement in the cases that do not match any of the available refinement templates. The proposed algorithm eliminates hanging nodes for concavely refined regions without excessive refinement. Another advantage of the proposed algorithm lies in eliminating narrow gaps of coarse meshes between refined regions. This step has a positive effect on the mesh quality as it avoids introducing non-regular templates with a limited penalty of uniform refinement. The presented algorithm produces good quality meshes and provides a consistent and complete method for producing conformally refined octree structures.

Quadrilateral Meshing for Hexahedral Mesh Generation Based on Facet Normal Matching

Because performance testing using actual products is costly, manufacturers use lower-cost Computer-Aided Design (CAD) simulations. In this paper, we focus on hexahedral meshes, which are more accurate than tetrahedral meshes, for finite element analysis. Our final objective is automatic hexahedral mesh generation with sharp features to precisely represent the corresponding features of a target shape. Our hexahedral mesh is generated using a voxel-based algorithm. In our previous works, we fitted the surface of the voxels to the target surface using Laplacian energy minimization and used normal vectors in the fitting to preserve sharp features. However, we were unable to precisely represent sharp concave features using the method. In this proposal, we improve the previously used Laplacian energy minimization by adding a term that depends on facet normalmatching for multi-normal vectors, instead of using normal vector matching.

ℓ 1 -Based Construction of Polycube Maps from Complex Shapes

Polycube maps of triangle meshes have proved useful in a wide range of applications, including texture mapping and hexahedral mesh generation. However, constructing either fully automatically or with limited user control a low-distortion polycube from a detailed surface remains challenging in practice. We propose a variational method for deforming an input triangle mesh into a polycube shape through minimization of the ℓ 1 -norm of the mesh normals, regularized via an as-rigid-as-possible volumetric distortion energy. Unlike previous work, our approach makes no assumption on the orientation, or on the presence of features in the input model. User-guided control over the resulting polycube map is also offered to increase design flexibility. We demonstrate the robustness, efficiency, and controllability of our method on a variety of examples, and explore applications in hexahedral remeshing and quadrangulation.

Quadrilateral mesh fitting that preserves sharp features based on multi-normals for Laplacian energy

Abstract Because the cost of performance testing using actual products is expensive, manufacturers use lower-cost computer-aided design simulations for this function. In this paper, we propose using hexahedral meshes, which are more accurate than tetrahedral meshes, for finite element analysis. We propose automatic hexahedral mesh generation with sharp features to precisely represent the corresponding features of a target shape. Our hexahedral mesh is generated using a voxel-based algorithm. In our previous works, we fit the surface of the voxels to the target surface using Laplacian energy minimization. We used normal vectors in the fitting to preserve sharp features. However, this method could not represent concave sharp features precisely. In this proposal, we improve our previous Laplacian energy minimization by adding a term that depends on multi-normal vectors instead of using normal vectors. Furthermore, we accentuate a convex/concave surface subset to represent concave sharp features.

Computational geometrical and mechanical modeling of woven ceramic composites at the mesoscale

Woven composite materials are receiving particular attention in a wide range of specialized aeronautical applications. Reliable numerical prediction tools based on computational modeling are required to quantitatively characterize the role of the microstructure and damage mechanisms at the mesoscale. In this paper, such a computational strategy is illustrated on a generic SiC/SiC plain weave composite with chemical vapor infiltrated matrix. Matrix and tows damage mechanisms are respectively introduced through the use of an anisotropic damage model, and an homogenized model based on a micromechanical model on the fiber scale. The latter is presented in this paper for the first time. Particular attention is paid to the generation of accurate hexahedral meshes, compatible at the tow–tow and tow–matrix interfaces. The mesh quality is analyzed using an error estimator variable based on the strain energy density. Damage predictions obtained using tetrahedral and hexahedral meshes are compared for basic loading cases, illustrating the need for using high quality meshes in the growing community of woven composites computational modeling.

Hexahedral Mesh Generation Method for Complex Mechanical Structure

An all hexahedral finite element mesh(FEM) generation method is proposed for complex mechanical structure, with the purpose to guarantee finite element simulation efficiency and precision in complex mechanical structure. The error characteristics and its cause in focus local mesh are analyzed by the finite element mesh error estimation. Based on the geometrical features and physical properties of the complex mechanical structure, the recognition criteria of critical region are established. Hexahedral mesh generation algorithm and implementation steps are presented based on the virtual planning model of structure calculation domain and the mesh quality evaluation criterion is also build. Numerical examples show that this method has the ability to generate all hexahedral finite element mesh for complex mechanical structure and critical regions are expressed accurately, and global mesh is distribution with rationality and high quality.

The Finite Element Numerical Modelling of 3D Magnetotelluric

The ideal numerical simulation of 3D magnetotelluric was restricted by the methodology complexity and the time-consuming calculation. Boundary values, the variation of weighted residual equation, and the hexahedral mesh generation method of finite element are three major causes. A finite element method for 3D magnetotelluric numerical modeling is presented in this paper as a solution for the problem mentioned above. In this algorithm, a hexahedral element coefficient matrix for magnetoelluric finite method is developed, which solves large-scale equations using preconditioned conjugate gradient of the first-type boundary conditions. This algorithm is verified using the homogeneous model, and the positive landform model, as well as the low resistance anomaly model.

A digraph-based hexahedral meshing method for coupled quasi-polycubes

Sub-mapping is recognized as the most commonly used method for generating structured hexahedral mesh which has become a prior choice for mechanical simulation. However, volume decomposition process of sub-mapping, due to the diversity of entity structures, still lacks support from stable algorithm. Moreover, as a preprocessing step of sub-mapping, morphing process sometimes leads to unsatisfactory mesh quality. In order to improve stability and meshing quality of sub-mapping, a digraph-based structured hexahedral meshing method for coupled quasi-polycubes is proposed in this paper. The method avoids the processes of volume decomposition and morphing. At first, an initial manual decomposition is carried out. The input model is decomposed into a number of sub-entities with respect to which initial digraphs are built. Secondly, virtual edges and vertices are constructed by means of mean value interpolation and then added into its corresponding digraph, so as to build connections between subgraphs within one digraph. Thirdly, face sheets are obtained by intersecting sub-entities with one another. Vertices and edges of the face sheets are added into their corresponding sub-entities’ digraphs to establish connections between digraphs of sub-entities. Finally, a linear system is constructed according to the solution of which the whole model is meshed. Experiments revealed in this paper demonstrate that the proposed method is applicable for all-structured hexahedral mesh generation of coupled quasi-polycubes.

Optimizing polycube domain construction for hexahedral remeshing

Polycube mapping can provide regular and global parametric representations for general solid models. Automatically constructing effective polycube domains, however, is challenging. We present an algorithm for polycube construction and volumetric parameterization. The algorithm has three steps: pre-deformation, polycube construction and optimization, and mapping computation. Compared with existing polycube mapping methods, our algorithm can robustly generate desirable polycube domain shape and low-distortion volumetric parameterization. It can be used for automatic high-quality hexahedral mesh generation.

Preserving isotropic element size functions in adaptivity, quadrilateral and hexahedral mesh generation

It is well known that the variations of the element size have to be controlled in order to generate a high-quality mesh. However, it is not enough to limit the gradient of the size function to generate a mesh that correctly preserves the prescribed element size. To address this issue, in this work we define a criterion to assess when an element reproduces a size field. Then, using this criterion, we develop a novel technique to modify the initial size function by solving a non-linear equation. The new size function ensures that the elements will preserve the original size function. Moreover, an approximated method is developed to improve the computational cost of solving the non-linear equation. We use these techniques in two applications. First, we show that we can reduce the number of iterations to converge an adaptive process. Second, we show that quadrilateral and hexahedral meshing algorithms benefit from the new size function since it is not needed to perform a refining process to capture the initial size function.

As-rigid-as-possible mesh deformation and its application in hexahedral mesh generation

This paper presents an efficient and stable as-rigid-as-possible mesh deformation algorithm for planar shape deformation and hexahedral mesh generation. The deformation algorithm aims to preserve two local geometric properties: scale-invariant intrinsic variables and elastic deformation energy, which are together represented in a quadric energy function. To preserve these properties, the position of each vertex is further adjusted by iteratively minimizing this quadric energy function to meet the position constraint of the controlling points. Experimental results show that the deformation algorithm is efficient, and can obtain physically plausible results, which have the same topology structure with the original mesh. Such a mesh deformation method is useful to project the source surface mesh onto the target surfaces in hexahedral mesh generation based on sweep method, and application results show that the proposed method is feasible to mesh projection not only between similar surface contours but also dissimilar surface contours.

Incorporating improved refinement techniques for a grid-based geometrically-adaptive hexahedral mesh generation algorithm

This paper presents a density control based adaptive hexahedral mesh generation algorithm for three dimensional models. To improve the mesh quality of hexahedral elements, a set of improved 27-refinement templates is proposed and the refinement modes of these templates are given. A set of effective refinement templates for 8-refinement based mesh generation algorithm is employed. The corresponding date structure and the procedures for realization of the algorithm are also presented. A buffer layer is inserted on the concave domains to resolve the propagation problems. Finally, the effectiveness and robustness of the algorithm are demonstrated by using several examples.

Метод построения неструктурированных шестигранных сеток из объемных данных

Разработан метод преобразования поверхностного представления расчетной области в формат воксельных данных. Предложен алгоритм генерации расчетной шестигранной сетки на основе объемного формата данных.

3101 精密な角を保存するフィッティングにおける最適なパラメータ推定

Nowadays, manufacturers use computer-aided design for simulations. The reason is that the cost of performance test using actual products is expensive, so the cost of performance simulation using CAD models is lower than it. In this paper, we think about hexahedral meshes for finite element analysis, because simulations with hexahedral mesh are more accurate than those with tetrahedral meshes. In the structural analysis between two objects, the stress peaks around the contact regions. This is often at a "sharp feature". Thus, to obtain accurate simulation results, the surface mesh must represent sharp features. Our purpose is automatic hexahedral mesh generation with sharp features to precisely represent the corresponding features of a target shape. To represent sharp feature of target shape, we use normal vector in our fitting of hexahedral mesh In our research, we search appropriate values of parameters that are used in our fitting being considered multi-normal vector through experiments.

Grid-based hexahedral element meshing algorithms for solid models with concave curved boundary lines

This paper presented a grid-based hexahedral element mesh generation algorithm for solid models with concave curved boundary lines. A deep study was focused on the boundary matching and quality improvement techniques. Firstly, a method for computing the curvature values of the triangle facets and sub-surfaces was proposed. In order to improve the surface mesh quality, a layer of new elements was inserted on the surface of the jagged core mesh. Then, a relative position relationship method was used to match C-edges of the solid model. Eight different types of free quadrilateral facet configurations were established. In order to handle the concave curve-matching problem, this paper proposed a method to modify the matching properties of the degenerate quadrilateral facets fitted on the same concave curved boundary line by unifying their orientations to point to the same sub-surface. In addition, six mixed templates were newly proposed to improve the geometrical topology of the degenerate elements associated with concave curves and sharp features. The positions of the nodes were smoothed by the modified Laplacian method and objective function. Finally, the effectiveness and reliability of the algorithms proposed in this paper were demonstrated by a practical example.

TUM.GeoFrame: automated high-order hexahedral mesh generation for shell-like structures

This paper presents a fully automated high-order hexahedral mesh generation algorithm for shell-like structures based on enhanced sweeping methods. Traditional sweeping techniques create all-hexahedral element meshes for solid structures by projecting an initial single surface mesh along a specified trajectory to a specified target surface. The work reported here enhances the traditional method for thin solids by creating conforming high-order all-hexahedral finite element meshes on an enhanced surface model with surfaces intersecting in parallel, perpendicular and skew-angled directions. The new algorithm is based on cheap projection rules separating the original surface model into a set of disjoint single surfaces and a so-called interface skeleton. The core of this process is reshaping the boundary representations of the initial surfaces, generating new sweeping templates along the intersection curves and joining the single swept hex meshes in an independently generated interface mesh.

All-hexahedral mesh generation via inside-out advancing front based on harmonic fields

The generation of hexahedral meshes is an open problem that has undergone significant research. This paper deals with a novel inside-out advancing front method to generate unstructured all-hexahedral meshes for given volumes. Two orthogonal harmonic fields, principal and radial harmonic fields, are generated to guide the inside-out advancing front process based on a few user interactions. Starting from an initial hexahedral mesh inside the given volume, we advance the boundary quadrilateral mesh along the streamlines of radial field and construct layers of hexahedral elements. To ensure high quality and uniform size of the hexahedral mesh, quadrilateral elements are decomposed in such a way that no non-hexahedral element is produced. For complex volume with branch structures, we segment the complex volume into simple sub-volumes that are suitable for our method. Experimental results show that our method generates high quality all-hexahedral meshes for the given volumes.

Improving the quality of hexahedral mesh generated by automatic mesh generators

Automatic hexahedral mesh generation is a very deserving solution for better performance of finite element analysis of complex large structures. At present plastering, whisker weaving and whisker weaving based plastering algorithm are available to perform such tasks. As these hexahedral mesh generation processes are fully automatic, it is possible to form some elements, which don’t have high enough qualities for finite element analysis. For this reason, a reliable post-processing method is presented in this paper which can modify the shapes of the already generated hexahedrons. Four different structural models are tested and the results show that the proposed method can effectively modify the quality of the inverted hexahedrons and eliminate the invalid ones.Keywords: Doublet; triplet; quadruplet; Whisker weaving based plastering algorithm; hexahedral meshDOI: http://dx.doi.org/10.3329/jname.v8i2.5646Journal of Naval Architecture and Marine Engineering 8(2011) 121-128

Comparison of hexahedral and tetrahedral elements in finite element analysis of the foot and footwear

Finite element analysis has been widely used in the field of foot and footwear biomechanics to determine plantar pressures as well as stresses and strains within soft tissue and footwear materials. When dealing with anatomical structures such as the foot, hexahedral mesh generation accounts for most of the model development time due to geometric complexities imposed by branching and embedded structures. Tetrahedral meshing, which can be more easily automated, has been the approach of choice to date in foot and footwear biomechanics. Here we use the nonlinear finite element program Abaqus (Simulia, Providence, RI) to examine the advantages and disadvantages of tetrahedral and hexahedral elements under compression and shear loading, material incompressibility, and frictional contact conditions, which are commonly seen in foot and footwear biomechanics. This study demonstrated that for a range of simulation conditions, hybrid hexahedral elements (Abaqus C3D8H) consistently performed well while hybrid linear tetrahedral elements (Abaqus C3D4H) performed poorly. On the other hand, enhanced quadratic tetrahedral elements with improved stress visualization (Abaqus C3D10I) performed as well as the hybrid hexahedral elements in terms of contact pressure and contact shear stress predictions. Although the enhanced quadratic tetrahedral element simulations were computationally expensive compared to hexahedral element simulations in both barefoot and footwear conditions, the enhanced quadratic tetrahedral element formulation seems to be very promising for foot and footwear applications as a result of decreased labor and expedited model development, all related to facilitated mesh generation.

The receding front method applied to hexahedral mesh generation of exterior domains

Two of the most successful methods to generate unstructured hexahedral meshes are the grid-based methods and the advancing front methods. On the one hand, the grid-based methods generate high-quality hexahedra in the inner part of the domain using an inside–outside approach. On the other hand, advancing front methods generate high-quality hexahedra near the boundary using an outside–inside approach. To combine the advantages of both methodologies, we extend the receding front method: an inside–outside mesh generation approach by means of a reversed advancing front. We apply this approach to generate unstructured hexahedral meshes of exterior domains. To reproduce the shape of the boundaries, we first pre-compute the mesh fronts by combining two solutions of the Eikonal equation on a tetrahedral reference mesh. Then, to generate high-quality elements, we expand the quadrilateral surface mesh of the inner body towards the unmeshed external boundary using the pre-computed fronts as a guide.