Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam Structures
Article dans une revue avec comité de lecture
Author
SHEN, Yichang
421305 Institut des Sciences de la mécanique et Applications industrielles [IMSIA - UMR 9219]
421305 Institut des Sciences de la mécanique et Applications industrielles [IMSIA - UMR 9219]
VIZZACCARO, Alessandra
69530 Imperial College London
235079 Department of Mechanical Engineering [Imperial College London]
69530 Imperial College London
235079 Department of Mechanical Engineering [Imperial College London]
KESMIA, Nassim
421305 Institut des Sciences de la mécanique et Applications industrielles [IMSIA - UMR 9219]
421305 Institut des Sciences de la mécanique et Applications industrielles [IMSIA - UMR 9219]
Abstract
The aim of this contribution is to present numerical comparisons of model-order reduction methods for geometrically nonlinear structures in the general framework of finite element (FE) procedures. Three different methods are compared: the implicit condensation and expansion (ICE), the quadratic manifold computed from modal derivatives (MD), and the direct normal form (DNF) procedure, the latter expressing the reduced dynamics in an invariant-based span of the phase space. The methods are first presented in order to underline their common points and differences, highlighting in particular that ICE and MD use reduction subspaces that are not invariant. A simple analytical example is then used in order to analyze how the different treatments of quadratic nonlinearities by the three methods can affect the predictions. Finally, three beam examples are used to emphasize the ability of the methods to handle curvature (on a curved beam), 1:1 internal resonance (on a clamped-clamped beam with two polarizations), and inertia nonlinearity (on a cantilever beam).
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