Triangular Cellular Automata for Computing Two-Dimensional Elastodynamic Response on Arbitrary Domains

摘要

This study extends a recently developed cellular automata (CA) modeling approachn(Leamy, 2008, “Application of Cellular Automata Modeling to Seismic Elastodynamics,”nInt. J. Solids Struct., 45(17), pp. 4835–4849) to arbitrary two-dimensional geometries vianthe development of a rule set governing triangular automata (cells). As in the previousnrectangular CA method, each cell represents a state machine, which updates in a steppednmanner using a local “bottom-up” rule set and state input from neighboring cells. No-ntably, the approach avoids the need to develop and solve partial differential equationsnand the complexity therein. The elastodynamic responses of several general geometriesnand loading cases (interior, Neumann, and Dirichlet) are computed with the method andnthen compared with results generated using the earlier rectangular CA and finite elementnapproaches. Favorable results are reported in all cases with numerical experiments in-ndicating that the extended CA method avoids, importantly, spurious oscillations at thenfront of sharp wave fronts. u0001DOI: 10.1115/1.4002614