Highly stable kinematic nonlinear simulations using a Taylor basis

The simulation of kinematic nonlinear systems is typically very time-consuming. The computational cost is primarily related to a time-consuming evaluation of the internal restoring forces performed before each integration step. Using basis projection is a way to reduce the computational cost and, thereby, the simulation time. The present work considers a novel Taylor basis that can significantly improve the stability of the central difference time integration scheme for kinematic nonlinear simulations. It is illustrated that the time step stability limit for a kinematic nonlinear simulation using Taylor basis projection is more or less identical to the analytical stability limit derived for linear systems. Furthermore, an example
shows that the time step stability limit in simulations using Taylor basis projection can be two orders of magnitude higher than the stability limit of a standard kinematic nonlinear simulation. Thus, Taylor basis projection has the potential to significantly reduce the number of time steps and, thereby, the computational cost.