A scheme for the automatic generation of triangular finite elements (original) (raw)
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A New Triangular Mesh Generation Technique
International Journal of Machine Learning and Computing
Objective of this paper is to propose a new semi-automatic, adaptive and optimized triangular mesh generation technique for any domain (including free formed curves). This new technique is found by merging the generalised equations which were proposed in previous works with Delaunay triangulation method. The new technique is demonstrated for several domains with various boundaries. Initial meshes are generated for these domains, which are later optimized manually by addition, removal or replacement of sampling points. Finalized meshes consist of triangular elements with aspect ratio of less than 2 and minimum skewness of more than 45 degrees.
Terrestrial, Atmospheric and Oceanic Sciences, 2016
This research developed an automatic two-dimensional finite element meshing system to resolve practical engineering problems in the fields of geology, hydrology, and water resources. This system first used the Delaunay triangulation method to create reasonable-density triangular mesh and then converted it into quadrilateral mesh by combining proper pairs of adjacent triangles. A series of combination patterns aiming at three cases were established. The effect of the number of boundary edges on the subsequent meshing procedures were studied and summarized. For the geometry with multiple domains an adjustment method is proposed to completely eliminate the residual triangles during quadrilateral meshing through adjusting the number of boundary edges in each loop to be even. A special boundary loop identification method is proposed for priority treatment. Corresponding treatment methods aimed at three different situations are established for common boundary loops. For a certain boundary loop with an odd number of boundary edges, the appropriate edge for new point insertion is determined by the position properties and relative density errors. Practical applications confirm that the method proposed in this paper could successfully implement the full conversion from the triangular mesh to the quadrilateral mesh.
AGTHOM—automatic generation of triangular and higher order meshes
International Journal for Numerical Methods in Engineering, 1983
The development and implementation of a comprehensive interactive computer package for the generation of finite element meshes for two-dimensional problems is described. The package, AGTHOM, minimizes the user defined input and attempts to maximize the flexibility for the user with regard to modifying the mesh. An important feature of AGTHOM is its independence of expensive graphics hardware by using approximate terminal plots. Versions are available in both extended BASIC and FORTRAN.
Automatic triangular mesh generation of trimmed parametric surfaces for finite element analysis
Computer Aided Geometric Design, 1998
This paper describes a new computational method for fully automated triangulation of the trimmed parametric surfaces used in finite element analysis. The method takes as input the domain geometry and a node-spacing function, and then generates a mesh, or a set of connected triangles, that satisfies basic requirements such as (1) precise control over node spacing or triangle size, (2) node placement that is compatible with domain boundaries, (3) generation of well-shaped triangles, and (4) continuous remeshing and local remeshing capabilities. The approach consists of two stages: placing initial nodes using recursive spatial subdivision, and relaxing the mesh by assuming the presence of proximity-based, repulsive/attractive internode forces and then performing dynamic simulation for a force-balancing configuration of nodes. In both stages, algorithms are developed in accordance with the observation that a pattern of tightly packed spheres mimics Voronoi polygons, from which well-shaped Delaunay triangles can be created by connecting the centers of the spheres.
2014
This paper describes a scheme for finite element mesh generation of a convex, non-convex polygon and multiply connected linear polygon. We first decompose the arbitrary linear polygon into simple sub regions in the shape of polygons.These subregions may be simple convex polygons or cracked polygons.We can divide a nonconvex polygon into convex polygons and cracked polygons We then decompose these polygons into simple sub regions in the shape of triangles. These simple regions are then triangulated to generate a fine mesh of triangular elements. We propose then an automatic triangular to quadrilateral conversion scheme. Each isolated triangle is split into three quadrilaterals according to the usual scheme, adding three vertices in the middle of the edges and a vertex at the barrycentre of the element. To preserve the mesh conformity a similar procedure is also applied to every triangle o f the domain to fully discretize the given convex polygonal domain into all quadrilaterals, thus...
PolyFront: an algorithm for fast generation of high quality triangular mesh
Engineering with Computers, 2011
In this article the authors present PolyFront, a new triangulation algorithm for two dimensional domains with holes. PolyFront is based on a normal offsetting technique, where a domain is triangulated starting from a discretization of its boundary and constructing the mesh layer by layer going toward the interior of the domain. The authors propose some numerical experiments to compare this algorithm with other four mesh generators. This comparison shows that the algorithm gives good quality meshes with reduced computational time.
A New Technique for Constructing Adaptive 3-D Triangulations
In this paper we present new ideas and applications of an innovative tetrahedral mesh generator which was introduced in [1, 2]. This automatic mesh generation strategy uses no Delaunay triangulation, nor advancing front technique, and it simplifies the geometrical discretization problem in particular cases. The main idea of the new mesh generator is to combine a local refinement/derefinement algorithm for 3-D nested triangulations [3] and a simultaneous untangling and smoothing procedure . 3-D complex domains, which surfaces can be mapped from a meccano face to object boundary, are discretized by the mesh generator. Resulting adaptive meshes have an appropriate quality for finite element applications. Finally, an example is showed.
International Journal Of Engineering And Computer Science, 2016
A new method is presented for subdividing a large class of solid objects into topologically simple subregions suitable for automatic finite element meshing with pentagonal elements. It is known that one can improve the accuracy of the finite element solution by uniformly refining a triangulation or uniformly refining a quadrangulation. Recently a refinement scheme of pentagonal partition was introduced in [31,32,33]. It is demonstrated that the numerical solution based on the pentagonal refinement scheme outperforms the solutions based on the traditional triangulation refinement scheme as well as quadrangulation refinement scheme. It is natural to ask if one can create a hexagonal refinement or general polygonal refinement schemes with a hope to offer even further improvement. It is shown in literature that one cannot refine a hexagon using hexagons of smaller size. In general, one can only refine an n-gon by n-gons of smaller size if n ≤ 5. Furthermore, we introduce a refinement scheme of a general polygon based on the pentagon scheme. This paper first presents a pentagonalization (or pentagonal conversion) scheme that can create a pentagonal mesh from any arbitrary mesh structure. We also introduce a pentagonal preservation scheme that can create a pentagonal mesh from any pentagonal mesh. This paper then presents a new numerical integration technique proposed earlier by the first author and co-workers, known as boundary integration method [34-40] is now applied to arbitrary polygonal domains using pentagonal finite element mesh. Numerical results presented for a few benchmark problems in the context of pentagonal domains with composite numerical integration scheme over triangular finite elements show that the proposed method yields accurate results even for low order Gauss Legendre Quadrature rules. Our numerical results suggest that the refinement scheme for pentagons and polygons may lead to higher accuracy than the uniform refinement of triangulations and quadrangulations.
Triangulation of arbitrary polyhedra to support automatic mesh generators
International Journal for Numerical Methods in Engineering, 2000
An algorithm is presented for the triangulation of arbitrary non-convex polyhedral regions starting with a prescribed boundary triangulation matching existing mesh entities in the remainder of the domain. The algorithm is designed to circumvent the termination problems of volume meshing algorithms which manifest themselves in the inability to successfully create tetrahedra within small subdomains to be referred to herein as cavities. To address this need, a robust Delaunay algorithm with an e cient and termination guaranteed face recovery method is the most appropriate approach. The algorithm begins with Delaunay vertex insertion followed by a face recovery method that conserves the boundary of the cavity by utilizing local mesh modi cation operations such as edge split, collapse and swap and a new set of tools which we call complex splits. The local mesh modi cations are performed in such a manner that each original surface triangulation is represented either as was, or as a concatenation of triangles. When done in this manner, it is always possible to split the matching mesh entities, ensuring that a compatible mesh is created. The algorithm is robust and has been tested against complex manifold and non-manifold cavities resulting in a valid mesh of the entire domain.