Finite element meshing approached as a global minimization process

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The ability to generate a suitable finite element mesh in an automatic fashion is becoming the key to being able to automate the entire engineering analysis process. However, placing an all-hexahedron mesh in a general three-dimensional body continues to be an elusive goal. The approach investigated in this research is fundamentally different from any other that is known of by the authors. A physical analogy viewpoint is used to formulate the actual meshing problem which constructs a global mathematical description of the problem. The analogy used was that of minimizing the electrical potential of a system charged particles within a ... continued below

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Medium: P; Size: 135 pages

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WITKOWSKI,WALTER R.; JUNG,JOSEPH; DOHRMANN,CLARK R. & LEUNG,VITUS J. March 1, 2000.

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  • Sandia National Laboratories
    Publisher Info: Sandia National Labs., Albuquerque, NM, and Livermore, CA (United States)
    Place of Publication: Albuquerque, New Mexico

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Description

The ability to generate a suitable finite element mesh in an automatic fashion is becoming the key to being able to automate the entire engineering analysis process. However, placing an all-hexahedron mesh in a general three-dimensional body continues to be an elusive goal. The approach investigated in this research is fundamentally different from any other that is known of by the authors. A physical analogy viewpoint is used to formulate the actual meshing problem which constructs a global mathematical description of the problem. The analogy used was that of minimizing the electrical potential of a system charged particles within a charged domain. The particles in the presented analogy represent duals to mesh elements (i.e., quads or hexes). Particle movement is governed by a mathematical functional which accounts for inter-particles repulsive, attractive and alignment forces. This functional is minimized to find the optimal location and orientation of each particle. After the particles are connected a mesh can be easily resolved. The mathematical description for this problem is as easy to formulate in three-dimensions as it is in two- or one-dimensions. The meshing algorithm was developed within CoMeT. It can solve the two-dimensional meshing problem for convex and concave geometries in a purely automated fashion. Investigation of the robustness of the technique has shown a success rate of approximately 99% for the two-dimensional geometries tested. Run times to mesh a 100 element complex geometry were typically in the 10 minute range. Efficiency of the technique is still an issue that needs to be addressed. Performance is an issue that is critical for most engineers generating meshes. It was not for this project. The primary focus of this work was to investigate and evaluate a meshing algorithm/philosophy with efficiency issues being secondary. The algorithm was also extended to mesh three-dimensional geometries. Unfortunately, only simple geometries were tested before this project ended. The primary complexity in the extension was in the connectivity problem formulation. Defining all of the interparticle interactions that occur in three-dimensions and expressing them in mathematical relationships is very difficult.

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Medium: P; Size: 135 pages

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OSTI as DE00752528

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  • Other Information: PBD: 1 Mar 2000

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  • Report No.: SAND2000-0579
  • Grant Number: AC04-94AL85000
  • DOI: 10.2172/752528 | External Link
  • Office of Scientific & Technical Information Report Number: 752528
  • Archival Resource Key: ark:/67531/metadc707649

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  • March 1, 2000

Added to The UNT Digital Library

  • Sept. 12, 2015, 6:31 a.m.

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  • April 12, 2016, 4:37 p.m.

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WITKOWSKI,WALTER R.; JUNG,JOSEPH; DOHRMANN,CLARK R. & LEUNG,VITUS J. Finite element meshing approached as a global minimization process, report, March 1, 2000; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc707649/: accessed August 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.