Semi-Discrete and Fully Discrete Partial Projection Finite Element Methods for the Vibrating Timoshenko Beam (Journal of Computational Mathematics, 1999)
In this paper, the partial projection finite element method is applied to the time-dependent problem – the damped vibrating Timoshenko beam model. It is proved that this method allows some new combinations of interpolations for stress and displacement fields. When assuming that a smooth solution exists, we obtain optimal convergence rates with constants independent of the beam thickness.
Keywords: Timoshenko beam; Finite element.