Energy dissipative time finite elements for classical mechanics

摘要

Based upon the temporal discretisation of Hamilton's canonical equations by means of the continuous Galerkin method, a Petrov―Galerkin time finite element formulation is presented to analyse non-linear mechanical systems for long time integration with the presence of dissipation. The time-stepping scheme features a correct estimation of physical dissipative energy for mechanical systems with weak dissipation. This enables to introduce a moderate numerical dissipation to damp out undesired spurious high frequency modes in a controllable manner. Numerical examples are performed to demonstrate that the proposed scheme allows us to obtain a correct amount by which the energy changes over the integration run.