Topological improvement procedures for quadrilateral finite element meshes

Canann, Scott A.; Muthukrishnan, S. N.; Phillips, Robert K.

doi:10.1007/bf01213591

Cited by 39 publications

(28 citation statements)

References 7 publications

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“…The first two-recursively splitting the domain through heuristic algorithms and marching out from boundaries-are unsuited to the current problem because of the line constraints imposed by the structural members intersecting the skin. Two additional ideas that have been successful are topology clean-up [24,25,26] and smoothing [27].…”

Section: D8mentioning

confidence: 99%

Geometry and Structural Modeling for High-Fidelity Aircraft Conceptual Design Optimization

Hwang

Kenway

Martins

2014

15th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

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High-fidelity computational design tools have advanced considerably in the last few decades, but there are still bottlenecks that suppress their impact in conceptual design. This paper aims to address some of these bottlenecks through a parametric geometry modeler for unconventional configurations with an efficient derivative computation and a parametric structural modeler that automatically generates full finite element meshes. As a demonstration, lift-constrained drag minimization of a truss-braced wing design is performed with respect to 532 design variables and 951 constraints with the Euler equations solved on a 1.42 million cell mesh.

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Section: D8mentioning

confidence: 99%

Geometry and Structural Modeling for High-Fidelity Aircraft Conceptual Design Optimization

Hwang

Kenway

Martins

2014

15th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

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“…For example, the well-known Delaunay algorithm for generating tetrahedral meshes, when applied in three dimensions, leaves sliver or flat elements, which are typically removed using local modifications [11]. All-quadrilateral mesh generation uses similar techniques [12] [13]. These operations also play an important role in adaptive mesh refinement on tetrahedral meshes [14].…”

Section: Introductionmentioning

confidence: 99%

Local topological modification of hexahedral meshes. Part I: A set of dual-based operations

2008

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Abstract. For hexahedral meshes, it is difficult to make topological modifications which preserve conformal property and which are local to the modified elements. This is most easily understood in how changes affect the dual surfaces ("sheets") and lines ("chords"), which have non-local extent in hexahedral meshes. A set of three operations is proposed which represent distinct local changes to the hex mesh and its dual. These operations are shown to compose the larger set of "flipping" operations described by Bern et. al. The relation between these dual-based operations and the insertion of a Boy surface in the dual, described by Bern, is also discussed. . INTRODUCTIONFinite element analysis and other methods for numerical solution of PDE's require the decomposition of space into a "mesh" (a polyhedral complex where each polyhedron has a prescribed topology). Such decompositions are often required to be conformal [1], where elements fill space, constitute a topology, and whose intersections are either empty or consist of lowerdimensional elements of the topology. Two types of elements are most common in FEA, hexahedra and tetrahedra. Hexahedral meshes are preferred for some kinds of analysis because of their accuracy for a given amount of compute cost [2] [3] 4 A general-purpose method for generating allhexahedral meshes of suitable geometric quality for FEA has not yet been demonstrated. We assert that an important part of any reliable method will be the ability to locally modify the connectivity of the hex mesh; we refer to this as "local hex mesh modification". Previous efforts to describe hex mesh modification have been either ad-hoc or have not described the relation to the hex mesh dual. In this paper, a set of dual-based hex mesh modification operations are described. We demonstrate how other known modifications can be composed from our set of operations. The paper concludes with a discussion of the Boy surface and how it relates to these operations.Body-fitted hexahedral mesh generation has been a topic of study for over ten years. Algorithms can be loosely classified into two groups. "Inside-out" algorithms start by filling a solid with a prescribed regular mesh, usually cartesian, then trim the mesh to match the boundary geometry and topology [4][5]. These meshes often have poor quality near the boundary which, for some applications, is precisely where good quality is most needed. These algorithms also tend to produce more hex elements than is strictly necessary. Inside-out algorithms are not widely used for these reasons. "Outside-in" or advancing-front algorithms start with a prescribed quadrilateral boundary mesh, and seek to fill the interior with hex elements. Methods have been investigated for doing this geometrically [6] or based on connectivity [7], with some of the connectivity-based methods making some boundary modifications [8] or losing some advancing front qualities [9][10] in order to improve chances of closing the mesh. Where mesh closure was reliably achieved [9], mesh quality typically...

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“…In the meantime this and related problems have been approached by several people working in computer science or combinatorics of polytopes (see [4,7,9,20,29]). Notice also that the 2-dimensional case of the sphere S 2 was actually solved earlier by Thurston (see [30]).…”

Section: Introduction and Statementsmentioning

confidence: 99%