Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam Structures

The aim of this contribution is to present numerical comparisons model-order reduction methods for geometrically nonlinear structures in the general framework finite element (FE) procedures. Three different are compared: implicit condensation and expansion (ICE), quadratic manifold computed from modal derivatives (MD), direct normal form (DNF) procedure, latter expressing reduced dynamics an invariant-based span phase space. first presented order underline their common points differences, highlighting particular that ICE MD use subspaces not invariant. A simple analytical example then used analyze how treatments nonlinearities by three can affect predictions. Finally, beam examples emphasize ability handle curvature (on a curved beam), 1:1 internal resonance clamped-clamped with two polarizations), inertia nonlinearity cantilever beam).