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Keywords = implicit condensation and expansion

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19 pages, 6653 KB  
Article
A Substructure Synthesis Method with Nonlinear ROM Including Geometric Nonlinearities
by Chao An, Yang Meng, Changchuan Xie and Chao Yang
Aerospace 2021, 8(11), 344; https://doi.org/10.3390/aerospace8110344 - 14 Nov 2021
Cited by 2 | Viewed by 2614
Abstract
Large flexible aircraft are often accompanied by large deformations during flight leading to obvious geometric nonlinearities in response. Geometric nonlinear dynamic response simulations based on full-order models often carry unbearable computing burden. Meanwhile, geometric nonlinearities are caused by large flexible wings in most [...] Read more.
Large flexible aircraft are often accompanied by large deformations during flight leading to obvious geometric nonlinearities in response. Geometric nonlinear dynamic response simulations based on full-order models often carry unbearable computing burden. Meanwhile, geometric nonlinearities are caused by large flexible wings in most cases and the deformation of fuselages is small. Analyzing the whole aircraft as a nonlinear structure will greatly increase the analysis complexity and cost. The analysis of complicated aircraft structures can be more efficient and simplified if subcomponents can be divided and treated. This paper aims to develop a hybrid interface substructure synthesis method by expanding the nonlinear reduced-order model (ROM) with the implicit condensation and expansion (ICE) approach, to estimate the dynamic transient response for aircraft structures including geometric nonlinearities. A small number of linear modes are used to construct a nonlinear ROM for substructures with large deformation, and linear substructures with small deformation can also be assembled comprehensively. The method proposed is compatible with finite element method (FEM), allowing for realistic engineering model analysis. Numerical examples with large flexible aircraft models are calculated to validate the accuracy and efficiency of this method contrasted with nonlinear FEM. Full article
(This article belongs to the Section Aeronautics)
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30 pages, 4493 KB  
Article
Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam Structures
by Yichang Shen, Alessandra Vizzaccaro, Nassim Kesmia, Ting Yu, Loïc Salles, Olivier Thomas and Cyril Touzé
Vibration 2021, 4(1), 175-204; https://doi.org/10.3390/vibration4010014 - 4 Mar 2021
Cited by 42 | Viewed by 5566
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 [...] Read more.
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). Full article
(This article belongs to the Special Issue Model Order Reduction of Nonlinear Systems)
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