Abstract
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.
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