Dynamic Error Estimation in Higher-Order Finite Elements

Abstract

The Finite Element Method (FEM) has emerged as a powerful tool for predicting the behavior of industrial products, including those with complex geometries or uncommon materials. Finite Element Analysis (FEA) is widely used to study structural vibration-related aspects such as stress, displacement, and velocity. Modal analysis, a standard technique for characterizing the vibrational behavior of structures, is essential for identifying resonance frequencies, optimizing component design, and assessing structural integrity. Finite Elements (FE) modal analysis enables engineers to evaluate numerically the modal parameters, whereas model order reduction (MOR) schemes are exploited to achieve a balance between computational efficiency and accuracy, enabling a more efficient solution for computing transient dynamic analysis. Assessing the accuracy and reliability of FE solutions is a crucial aspect of the design cycle, and model-updating procedures are commonly employed to maximize the correlation between measured and predicted dynamic behavior. This study investigated the accuracy and computational efficiency of linear, quadratic, and cubic hexahedral FE formulations for modal analysis and transient dynamic solutions. More specifically, the documented results demonstrate the profitable use of the eigenenergy norm obtained in eigen solutions as a valid predictor of the accuracy reported using either the time response assurance criterion (TRAC) or the frequency response assurance criterion (FRAC), measured in transient dynamic cases. Moreover, our results also highlight the superior computational efficiency of higher-order formulations for both the eigen and transient dynamic solutions.