Non-Intrusive Data-Free Parametric Reduced Order Model for Geometrically Nonlinear Structures

Abstract

We present a fully non-intrusive parametric reduced-order modeling (PROM) framework for geometrically nonlinear structures subject to geometric variations. The method builds upon equation-driven Galerkin ROMs constructed from vibration modes and modal-derivative companion vectors, while nonlinear reduced tensors are identified from standard finite element outputs. A database of such ROMs is generated over a set of training samples, and all reduced operators-including the linear stiffness matrix, the quadratic and cubic nonlinear tensors, the Rayleigh damping parameters, and the reduction basis-are interpolated using Radial Basis Functions (RBFs). A global reduced basis is obtained through a two-level POD compression, combined with a MAC-guided reordering strategy to ensure parametric smoothness. The resulting PROM preserves the symmetry and polynomial structure of the reduced equations, enabling robust and efficient adaptation to new parameter values. Analytical parameter sensitivities follow directly from the interpolation model. The approach is demonstrated on a parametrically curved panel and a wing-box with geometric variations, showing excellent agreement with high-fidelity simulations and enabling substantial reductions in computational cost for parametric analyses.