This study extends a recently developed cellular automata (CA) modeling approach (Leamy, 2008, “Application of Cellular Automata Modeling to Seismic Elastodynamics,” Int. J. Solids Struct., 45(17), pp. 4835–4849) to arbitrary two-dimensional geometries via the development of a rule set governing triangular automata (cells). 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. Notably, the approach avoids the need to develop and solve partial differential equations and the complexity therein. The elastodynamic responses of several general geometries and loading cases (interior, Neumann, and Dirichlet) are computed with the method and then compared with results generated using the earlier rectangular CA and finite element approaches. Favorable results are reported in all cases with numerical experiments indicating that the extended CA method avoids, importantly, spurious oscillations at the front of sharp wave fronts.
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March 2011
Research Papers
Triangular Cellular Automata for Computing Two-Dimensional Elastodynamic Response on Arbitrary Domains
Ryan K. Hopman,
Ryan K. Hopman
Research Assistant
George W. Woodruff School of Mechanical Engineering,
Georgia Institute of Technology
, Atlanta, GA 30332-0405
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Michael J. Leamy
Michael J. Leamy
Assistant Professor
George W. Woodruff School of Mechanical Engineering,
e-mail: michael.leamy@me.gatech.edu
Georgia Institute of Technology
, Atlanta, GA 30332-0405
Search for other works by this author on:
Ryan K. Hopman
Research Assistant
George W. Woodruff School of Mechanical Engineering,
Georgia Institute of Technology
, Atlanta, GA 30332-0405
Michael J. Leamy
Assistant Professor
George W. Woodruff School of Mechanical Engineering,
Georgia Institute of Technology
, Atlanta, GA 30332-0405e-mail: michael.leamy@me.gatech.edu
J. Appl. Mech. Mar 2011, 78(2): 021020 (10 pages)
Published Online: December 20, 2010
Article history
Received:
November 13, 2009
Revised:
September 21, 2010
Posted:
September 24, 2010
Published:
December 20, 2010
Online:
December 20, 2010
Citation
Hopman, R. K., and Leamy, M. J. (December 20, 2010). "Triangular Cellular Automata for Computing Two-Dimensional Elastodynamic Response on Arbitrary Domains." ASME. J. Appl. Mech. March 2011; 78(2): 021020. https://doi.org/10.1115/1.4002614
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