A non-intrusive nonlinear structural ROM for partitioned two-way fluid–structure interaction computations

This paper introduces a nonlinear structural reduced order model (ROM) specifically developed for fluid–structure interaction (FSI) simulations involving high impact loads and large deflections, such as those arising in water slamming of flexible structures. The model is based on a nonlinear modal expansion trained offline using prestressed eigenfrequency analyses performed by nonlinear full-order computational structural dynamics based on finite elements. The training uses the eigenfrequencies as a function of the deflection and is non-intrusive, which means that the knowledge of the system's full-order matrices is not required. Eigenfrequencies and deflections are evaluated under a prescribed set of static loads, which are derived from fully transient computational fluid dynamics (CFD) simulations. The resulting ROM is coupled with CFD using partitioned one- and two-way FSI schemes. Focusing on the impact of an elastic aluminum plate onto still water, the research investigates scenarios with varied horizontal and vertical velocities in three distinct experimental conditions, which cover moderate to strong hydroelastic interactions. Namely, the proposed nonlinear ROM and its linear counterpart are assessed against two FSI benchmark sets. The first set consists in comparing the ROM versus the full-order model (FOM) under prescribed external load, via one-way FSI coupling. The second set consists in comparing the ROM versus experimental data, via two-way tightly-coupled FSI. Comparisons of the nonlinear ROM versus the FOM under prescribed loads achieve an average error equal to 2.7%. Comparisons of the nonlinear ROM under two-way tightly-coupled FSI versus experiments show an average error equal to 4.5%. Comparisons of nonlinear versus linear ROM highlight the need for nonlinear models to accurately capture peak values and trends, especially in scenarios with large deflections.