Partition of Unity Finite Element Method for the Modeling of Structural Vibrations

Overview & Synopsis

The Partition of Unity Finite Element Method (PUFEM) is adapted to calculate the vibrational response of uniform and tapered Timoshenko beams subject to a time-harmonic loading. This method allows easy incorporation of additional functions into the finite element framework to better cope with the wave oscillation behaviour in the beam and the wave modulation phenomenon due to the structural thickness variation. The PUFEM beam elements can be constructed by using different enrichment functions, such as wave functions and polynomials. The numerical performance of these enriched elements is illustrated in terms of computational accuracy and solution convergence. It is found that the PUFEM offers very accurate predictions by using a limited number of degrees of freedom and a much higher convergence rate than classical FEM. This study is currently extended to thin beams, thin plates, and thick plates. Available results of this ongoing work will also be presented.