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Suppressing local particle oscillations in the Hamiltonian particle method for elasticity
Author(s) -
Kondo Masahiro,
Suzuki Yukihito,
Koshizuka Seiichi
Publication year - 2009
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2744
Subject(s) - discretization , hamiltonian (control theory) , cantilever , classical mechanics , hamiltonian system , elasticity (physics) , equations of motion , physics , hamiltonian mechanics , stiffness , mathematics , mathematical analysis , mathematical optimization , engineering , quantum mechanics , phase space , structural engineering , thermodynamics
The governing equation of elasticity is discretized into motion equations of the particles in a Hamiltonian system. A weighted least‐square method is adopted to evaluate the Green–Lagrange strain. Using a symplectic scheme for the Hamiltonian system, we obtain the property of energy conservation in the discretized calculations. However, local particle oscillations occur, and they excessively decrease low frequency motion. In this study, we propose the use of an artificial potential force to suppress the local oscillations. The accuracy of the model with and without the inclusion of the artificial force is examined by analyzing a cantilever beam and wave propagation. With the inclusion of the artificial force, the local oscillations are reduced while energy conservation is maintained. Copyright © 2009 John Wiley & Sons, Ltd.