Critical time-step for central difference integration schemes in discrete methods: Translational and rotational degrees of freedom

Abstract

Abstract The explicit central-difference time integration scheme is widely used in discrete methods. However, restrictions on the size of the time step apply. We revisit the problem of a network of particles with translational and rotational degrees of freedom. We apply a discrete Fourier transform to the equations of motion. By studying the eigenvalues of the amplification matrix, we derived a closed form, sharp stability limit that applies to any network. The time-step limit is compared with previous work (Otsubo et\xa0al. 2017 and O’Sullivan et\xa0al. 2004) for common network configurations. Numerical simulation is used for a certain class of networks in two-dimensional and three-dimensional spaces, and good agreement is observed between the analytical critical time-step and the numerical solutions.