Evaluating applied force reduced-order models: verification

Indirect Reduced-Order Models (ROMs) aim to dramatically reduce the cost of simulating nonlinear dynamic behaviour in large nonlinear finite element systems. Applied force based methods, most notably implicit condensation and expansion, are a classical approach. This work summarises and critiques the past 25 years of development whilst making the case for the continued relevance of the method in the context of the more recent and mathematically rigorous invariant manifold based reduction approach. To facilitate this, a novel applied force framework is developed: the Applied Force Reduction (AFR) method. This includes a more precise approach to evaluate the general accuracy of indirect ROMs through the distinction between verification (the correct implementation of the method) and validation (evaluating the accuracy of the ROM in replicating the full-order system). The former is the focus of this work, and a general verification algorithm is presented which is implemented in the new open source AFR Tool software package. The verification process involves studying the convergence of the underlying polynomial models to select an optimal dataset that minimises interaction with the FE model. This process is completely automated and allows for the efficient construction of ROMs capturing the dynamic behaviour of large systems. This efficiency is demonstrated through consideration of a curved double arch with over 1,000,000 degrees-of-freedom. A two degree-of-freedom ROM is constructed and verified in 60 minutes, on a desktop computer, and is able to accurately reproduce the internal resonance found in the full-order system.