Performance of the Partition of Unity Finite Element Method for the modeling of Timoshenko beams

The Partition of Unity Finite Element Method (PUFEM) is developed and applied to compute the vibrational response of a Timoshenko beam subject to a uniformly distributed harmonic loading. In the proposed method, classical finite elements are enriched with three types of special functions: propagating and evanescent wave functions, a Fourier-type series and a polynomial enrichment. Different formulations are first assessed through comparisons on the frequency response functions at a specific point on the beam. The computational performance, in terms of both accuracy and data reduction, is then illustrated through convergence analyses. It is found that, by using a very limited number of degrees of freedom, the wave enrichment offers highly accurate results with a convergence rate which is much higher than other formulations. Evanescent waves and the constant term in the wave basis are also shown to play an important role. In all cases, the proposed PUFEM formulations clearly outperform classical finite element method in terms of computational efficiency.