Ensuring the Accuracy of FE-based Nonlinear Dynamic Reduced-order Models

Abstract

Numerous powerful methods exist for developing Reduced-order Models (ROMs) using Finite Element (FE) models. Ensuring the accuracy of these ROMs is essential; however, the validation using dynamic responses is expensive. In this work, we propose a method to ensure the accuracy of ROMs without extra dynamic FE simulations. It has been shown that the well-established Implicit Condensation and Expansion (ICE) method can produce an accurate ROM when the FE model's static behaviours are captured accurately. However, this is achieved via a fitting procedure, which may be sensitive to the selection of load cases and ROM's order, especially in the multi-mode case. To alleviate this difficulty, we define an error metric that can evaluate the ROM's fitting error efficiently within the displacement range, specified by a given energy level. Based on the fitting result, the proposed method provides a strategy to enrich the static dataset, i.e. additional load cases are found until the ROM's accuracy reaches the required level. Extending this to the higher-order and multi-mode cases, some extra constraints are incorporated into the standard fitting procedure to make the proposed method more robust. A clamped-clamped beam is utilised to validate the proposed method, and the results show that the method can robustly ensure the accuracy of the static fitting of ROMs.