Applications of multifidelity reduced order modeling to single and multiphysics nonlinear structural problems

The present investigation focuses on the response of uncertain structures that are excited well beyond their linear regime so that significant nonlinear geometric effects take place. Such situations may occur due to the application of large mechanical loads but also, and especially, when the structure is part of a multiphysics problem, e.g., coupled to aerodynamics and/or heating. It is demonstrated here that the computational burden associated with the prediction of the statistics of the response can be dramatically reduced by combining nonlinear reduced order modeling and multifidelity Monte Carlo (MFMC) simulation. The MFMC approach combines the simulations of several different models of different fidelity to accurately estimates the desired statistics. This approach is well suited to reduced order models where different fidelities are easily obtained with different number of basis functions. Three such nonlinear applications are considered the first of which is a purely structural problem. The second one is a multiphysics problem, a panel undergoing a simulated high speed trajectory with aerodynamic-structural-thermal coupling. The third application is also multiphysics and focuses on the limit cycle oscillation behavior of a wing past flutter due to structural nonlinearity. In all of these applications, the MFMC performed very well leading to accurate predictions of the statistics of the response at a reduced/much reduced computational cost.