Efficient ALE mesh management for 3D quasi‐Eulerian problems

In computational solid mechanics, the ALE formalism can be very useful to reduce the size of finite element models of continuous forming operations such as roll forming. The mesh of these ALE models is said to be quasi‐Eulerian because the nodes remain almost fixed—or almost Eulerian—in the main process direction, although they are required to move in the orthogonal plane in order to follow the lateral displacements of the solid. This paper extensively presents a complete node relocation procedure dedicated to such ALE models. The discussion focusses on quadrangular and hexahedral meshes with local refinements. The main concern of this work is the preservation of the geometrical features and the shape of the free boundaries of the mesh. With this aim in view, each type of nodes (corner, edge, surface and volume) is treated sequentially with dedicated algorithms. A special care is given to highly curved 3D surfaces for which a CPU‐efficient smoothing technique is proposed. This new method relies on a spline surface reconstruction, on a very fast weighted Laplacian smoother with original weights and on a robust reprojection algorithm. The overall consistency of this mesh management procedure is finally demonstrated in two numerical applications. The first one is a 2D ALE simulation of a drawbead, which provides similar results to an equivalent Lagrangian model yet is much faster. The second application is a 3D industrial ALE model of a 16‐stand roll forming line. In this case, all attempts to perform the same simulation by using the Lagrangian formalism have been unsuccessful. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

An extended advancing front technique for closed surfaces mesh generation

An extended advancing front technique (AFT) with shift operations and Riemann metric named as shifting‐AFT is presented for finite element mesh generation on 3D surfaces, especially 3D closed surfaces. Riemann metric is used to govern the size and shape of the triangles in the parametric space. The shift operators are employed to insert a floating space between real space and parametric space during the 2D parametric space mesh generation. In the previous work of closed surface mesh generation, the virtual boundaries are adopted when mapping the closed surfaces into 2D open parametric domains. However, it may cause the mesh quality‐worsening problem. In order to overcome this problem, the AFT kernel is combined with the shift operator in this paper. The shifting‐AFT can generate high‐quality meshes and guarantee convergence in both open and closed surfaces. For the shifting‐AFT, it is not necessary to introduce virtual boundaries while meshing a closed surface; hence, the boundary discretization procedure is largely simplified, and moreover, better‐shaped triangles will be generated because there are no additional interior constraints yielded by virtual boundaries. Comparing with direct methods, the shifting‐AFT avoids costly and unstable 3D geometrical computations in the real space. Some examples presented in this paper have demonstrated the advantages of shift‐AFT in 3D surface mesh generation, especially for the closed surfaces. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

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.     

A generalized automatic mesh generation scheme for finite element method

This paper presents a generalized method which generates linear, triangular, quadrilateral and pentahedral elements for the finite element method. Depending on geometrical and material variations, the region to be discretized is manually divided into blocks such as lines, triangles, quadrilaterals, pentahedrons and hexahedrons in several appropriate co-ordinate systems. However, no connectivity information of the adjacent blocks is required by the user as input. The continuity of the generated nodal co-ordinates and element configurations at the block interface are automatically maintained to describe the geometry of structures, no matter how these five types of blocks are connected. Furthermore, a mesh grading algorithm which generates reliable mesh grade distributions in the interior of the triangular and quadrilateral blocks is established corresponding to the arbitrarily defined subdivision numbers for each edge line of blocks. This algorithm is extended to the mesh grading in the interior of the hexahedral and pentahedral blocks. Element numbers are also renumbered in this scheme, in addition to node numbers, in order to increase the computational efficiency of the global matrix assembly. Additional facilities, i.e. loading data generation, boundary condition data generation and so on, are also discussed. An illustrative and a practical example are given to demonstrate the capabilities of this scheme.     

Adaptive mesh refinement and coarsening for cohesive zone modeling of dynamic fracture

Adaptive mesh refinement and coarsening schemes are proposed for efficient computational simulation of dynamic cohesive fracture. The adaptive mesh refinement consists of a sequence of edge‐split operators, whereas the adaptive mesh coarsening is based on a sequence of vertex‐removal (or edge‐collapse) operators. Nodal perturbation and edge‐swap operators are also employed around the crack tip region to improve crack geometry representation, and cohesive surface elements are adaptively inserted whenever and wherever they are needed by means of an extrinsic cohesive zone model approach. Such adaptive mesh modification events are maintained in conjunction with a topological data structure (TopS). The so‐called PPR potential‐based cohesive model (J. Mech. Phys. Solids 2009; 57 :891–908) is utilized for the constitutive relationship of the cohesive zone model. The examples investigated include mode I fracture, mixed‐mode fracture and crack branching problems. The computational results using mesh adaptivity (refinement and coarsening) are consistent with the results using uniform mesh refinement. The present approach significantly reduces computational cost while exhibiting a multiscale effect that captures both global macro‐crack and local micro‐cracks. Copyright © 2012 John Wiley & Sons, Ltd.     

Octree‐based reasonable‐quality hexahedral mesh generation using a new set of refinement templates

An octree‐based mesh generation method is proposed to create reasonable‐quality, geometry‐adapted unstructured hexahedral meshes automatically from triangulated surface models without any sharp geometrical features. A new, easy‐to‐implement, easy‐to‐understand set of refinement templates is developed to perform local mesh refinement efficiently even for concave refinement domains without creating hanging nodes. A buffer layer is inserted on an octree core mesh to improve the mesh quality significantly. Laplacian‐like smoothing, angle‐based smoothing and local optimization‐based untangling methods are used with certain restrictions to further improve the mesh quality. Several examples are shown to demonstrate the capability of our hexahedral mesh generation method for complex geometries. Copyright © 2008 John Wiley & Sons, Ltd.     

Repairing unstructured triangular mesh intersections

Computational analysis and design has become a fundamental part of product research, development, and manufacturing in aerospace, automotive, and other industries. In general, the success of the specific application depends heavily on the accuracy and consistency of the computational model used. The aim of this work is to reduce the time needed to prepare geometry for volume grid generation. This will be accomplished by developing tools that semi‐automatically repair discrete data. Providing another level of automation to the process of repairing large, complex problems in discrete data will significantly accelerate the grid generation process. The developed algorithms are meant to offer a semi‐automated solution to a complicated geometrical problem — specifically discrete mesh intersection. The intersection‐repair strategy presented here focuses on repairing the intersection in‐place as opposed to rediscretizing the intersecting geometries. Combining robust, efficient methods of detecting intersections and then repairing intersecting geometries in‐place produces a significant improvement over techniques used in current literature. The result of this intersection process is a nonintersecting geometry that is free of duplicate and degenerate geometry. Results are presented showing the accuracy and consistency of the intersection repair tool. Copyright © 2012 John Wiley & Sons, Ltd.     

LayTracks: a new approach to automated geometry adaptive quadrilateral mesh generation using medial axis transform

A new mesh generation algorithm called ‘LayTracks’, to automatically generate an all quad mesh that is adapted to the variation of geometric feature size in the domain is described. LayTracks combines the merits of two popular direct techniques for quadrilateral mesh generation—quad meshing by decomposition and advancing front quad meshing. While the MAT has been used for the domain decomposition before, this is the first attempt to use the MAT, for the robust subdivision of a complex domain into a well defined sub‐domain called ‘Tracks’, for terminating the advancing front of the mesh elements without complex interference checks and to use radius function for providing sizing function for adaptive meshing. The process of subdivision of a domain is analogous to, formation of railway tracks by laying rails on the ground. Each rail starts from a node on the boundary and propagates towards the medial axis (MA) and then from the MA towards the boundary. Quadrilateral elements are then obtained by placing nodes on these rails and connecting them inside each track, formed by adjacent rails. The algorithm has been implemented and tested on some typical geometries and the quality of the output mesh obtained are presented. Extension of this technique to all hexahedral meshing is discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

Model and mesh generation of cracked tubular Y-joints

In this study, the methods for constructing accurate and consistent geometrical and finite element (FE) models for general cracked tubular Y-joints are described. Firstly, geometrical analysis of welded tubular joint is given and it is then extended to the modelling of general cracked Y-joints. The concept of crack surface and a simple mapping approach are suggested to model either through-thickness or surface cracks which can be of any length and located at any position along the brace-chord intersection. Secondly, the geometrical model developed will be used in the generation of consistent FE meshes. The basic concepts used for the design and generation of three-dimensional FE meshes will be described. This will include the meshing procedures for discretization of tubular joints with through-thickness and surface cracks which are frequently regarded as one of the most difficult steps in the construction of tubular joint models. Finally, some mesh generation examples for uncracked and cracked Y-joints will be presented to demonstrate the use of the purposed geometrical model and mesh generation scheme developed.     

‘Ultimate’ robustness in meshing an arbitrary polyhedron

Given a boundary surface mesh (a set of triangular facets) of a polyhedron, the problem of deciding whether or not a triangulation exists is reported to be NP‐hard. In this paper, an algorithm to triangulate a general polyhedron is presented which makes use of a classical Delaunay triangulation algorithm, a phase for recovering the missing boundary facets by means of facet partitioning, and a final phase that makes it possible to remove the additional points defined in the previous step. Following this phase, the resulting mesh conforms to the given boundary surface mesh. The proposed method results in a discussion of theoretical interest about existence and complexity issues. In practice, however, the method should provide what we call ‘ultimate’ robustness in mesh generation methods. Copyright © 2003 John Wiley & Sons, Ltd.     

Simultaneous surface and tetrahedron mesh adaptation using mesh‐free techniques

We present a method to adapt a tetrahedron mesh together with a surface mesh with respect to a size criterion. The originality of our work lies in the fact that both surface and tetrahedron mesh adaptation are carried out simultaneously and that no CAD is required to adapt the surface mesh. The adaptation procedure consists of splitting or removing interior and surface edges which violate a given size criterion. The enrichment process is based on a bisection technique. In order to guarantee mesh conformity during the refinement process, all possible remeshing configurations of tetrahedra have been examined. Once the tetrahedron mesh has been adapted, surface nodes are projected on a geometrical model. The building of a surface model from discrete data has already been presented in this journal. The method is based on a mesh‐free technique called Hermite Diffuse Interpolation. Surface and volume mesh optimization procedures are carried out during the adaptation and at the end of the process to enhance the mesh. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

Quality improvements in extruded meshes using topologically adaptive generalized elements

This paper describes a method to extrude near‐body volume meshes that exploits topologically adaptive generalized elements to improve local mesh quality. Specifically, an advancing layer algorithm for extruding volume meshes from surface meshes of arbitrary topology, appropriate for viscous fluid flows, is discussed. First, a two‐layer reference mesh is generated from the layer initial surface mesh by extruding along the local surface normals. The reference mesh is then smoothed using a Poisson equation. Local quality improvement operations such as edge collapse, face refinement, and local reconnection are performed in each layer to drive the mesh toward isotropy and improve the transition from the extruded mesh to a void‐filling tetrahedral mesh. A few example meshes along with quality plots are presented to demonstrate the efficacy of this approach. Copyright © 2004 John Wiley & Sons, Ltd.     

Meshing curved wire‐frame models through energy minimization and packing of ellipses

In the initial phase of structural part design, wire‐frame models are sometimes used to represent the shapes of curved surfaces. Finite Element Analysis (FEA) of a curved surface requires a well shaped, graded mesh that smoothly interpolates the wire frame. This paper describes an algorithm that generates such a triangular mesh from a wire‐frame model in the following two steps: (1) construct a triangulated surface by minimizing the strain energy of the thin‐plate‐bending model, and (2) generate a mesh by the bubble meshing method on the projected plane and project it back onto the triangulated surface. Since the mesh elements are distorted by the projection, the algorithm generates an anisotropic mesh on the projected plane so that an isotropic mesh results from the final projection back onto the surface. Extensions of the technique to anisotropic meshing and quadrilateral meshing are also discussed. The algorithm can generate a well‐shaped, well‐graded mesh on a smooth curved surface. Copyright © 1999 John Wiley & Sons, Ltd.