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Arbitrary Geometry Cellular Automata for Elastodynamics

[+] Author Affiliations
Ryan K. Hopman, Michael J. Leamy

Georgia Institute of Technology, Atlanta, GA

Paper No. IMECE2009-11222, pp. 535-547; 13 pages
doi:10.1115/IMECE2009-11222
From:
  • ASME 2009 International Mechanical Engineering Congress and Exposition
  • Volume 15: Sound, Vibration and Design
  • Lake Buena Vista, Florida, USA, November 13–19, 2009
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4388-8 | eISBN: 978-0-7918-3863-1
  • Copyright © 2009 by ASME

abstract

This study extends a recently-developed [1] cellular automata (CA) elastodynamic modeling approach to arbitrary two-dimensional geometries through development of a rule set appropriate for triangular cells. The approach is fully object-oriented (OO) and exploits OO conventions to produce compact, general, and easily-extended CA classes. Meshes composed of triangular cells allow the elastodynamic response of arbitrary two-dimensional geometries to be computed accurately and efficiently. As in the previous rectangular CA method, each cell represents a state machine which updates in a stepped-manner using a local “bottom-up” rule set and state input from neighboring cells. The approach avoids the need to develop partial differential equations and the complexity therein. Several advantages result from the method’s discrete, local and object-oriented nature, including the ability to compute on a massively-parallel basis and to easily add or subtract cells in a multi-resolution manner. The extended approach is used to generate the elastodynamic responses of a variety of general geometries and loading cases (Dirichlet and Neumann), which are compared to previous results and/or comparison results generated using the commercial finite element code, COMSOL. These include harmonic interior plate loading, uniform boundary traction, and ramped boundary displacement. Favorable results are reported in all cases, with the CA approach requiring fewer degrees of freedom to achieve similar accuracy, and considerably less code development.

Copyright © 2009 by ASME

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