A non-intrusive model-order reduction of geometrically nonlinear structural dynamics using modal derivatives

Non-intrusive model-order reduction methods are beneficial for reducing the computational costs of dynamic analysis of nonlinear finite element models, developed in programs that do not release nonlinear element forces and Jacobians (e.g., commercial software). One of the key aspects for developing a displacement-based non-intrusive reduced order model is a proper construction of the reduction basis, which has to be small in size, easy to compute, and must span the subspace in which the full solution lives. In this paper, we propose a non-intrusive model order reduction method based on modal derivatives stemming from a selected set of vibration modes of the linearized system. By definition, modal derivatives do not require the knowledge of the applied load. We name this load-independent basis. The method we propose is also simulation-free, meaning that no nonlinear dynamic simulations of the full model are required to construct the reduction basis. The method is tested with three examples of increasing complexity.