Suppressing local particle oscillations in the hamiltonian particle method for elasticity

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.