Harmonic Convergence Estimation Through Strain Energy Superconvergence

Abstract

Grid convergence in finite element analysis (FEA), despite a wide variety of tools available to date, remains an elusive and challenging task. Due to the complex and time-consuming process of remeshing and solving the finite element model (FEM), convergence studies can be a part of the most arduous portion of the modeling process and can even be impossible with FEMs unassociated with CAD. Existing a posteriori methods, such as relative error in the energy norm, provide a near arbitrary indication of the model convergence for eigenfrequencies. This paper proposes a new approach to evaluate the harmonic convergence of an existing model without conducting a convergence study. Strain energy superconvergence (SES) takes advantage of superconvergence points within a FEM and accurately recovers the strain energy within the model using polyharmonic splines, thus providing a more accurate estimate of the system's eigenfrequencies without modification of the FEM. Accurate eigenfrequencies are critical for designing for airfoil resonance avoidance and mistuned rotor response prediction. Traditional error estimation strategies fail to capture harmonic convergence as effectively as SES, potentially leading to a less accurate airfoil resonance and rotor mistuning prediction.