scholarly journals Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

2021 ◽  
Author(s):  
Cyril Touzé ◽  
Alessandra Vizzaccaro ◽  
Olivier Thomas
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Geometrically Nonlinear ◽  
Nonlinear Structures ◽  
Model Order ◽  
Reduction Methods

scholarly journals Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam Structures

Vibration ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 175-204
Author(s):  
Yichang Shen ◽  
Alessandra Vizzaccaro ◽  
Nassim Kesmia ◽  
Ting Yu ◽  
Loïc Salles ◽  
...  
Keyword(s):  
Finite Element ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Geometrically Nonlinear ◽  
Nonlinear Structures ◽  
Model Order ◽  
Nonlinear Beam ◽  
Quadratic Nonlinearities ◽  
Reduction Methods ◽  
Modal Derivatives

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).

THE NEW ALGORITHM OF SOLVING HARMONIC BALANCE EQUATIONS

2019 ◽  
Author(s):  
Vladimir Lantsov ◽  
A. Papulina
Keyword(s):  
Harmonic Balance ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Balance Equations ◽  
Model Order ◽  
Cad Systems ◽  
Computational Costs ◽  
Reduction Methods ◽  
Model Equations

The new algorithm of solving harmonic balance equations which used in electronic CAD systems is presented. The new algorithm is based on implementation to harmonic balance equations the ideas of model order reduction methods. This algorithm allows significantly reduce the size of memory for storing of model equations and reduce of computational costs.

scholarly journals Comparison of model order reduction methods for optimal sensor placement for thermo-elastic models

2018 ◽  
Vol 51 (3) ◽  
pp. 465-483 ◽  
Author(s):  
Peter Benner ◽  
Roland Herzog ◽  
Norman Lang ◽  
Ilka Riedel ◽  
Jens Saak
Keyword(s):  
Model Order Reduction ◽  
Sensor Placement ◽  
Order Reduction ◽  
Optimal Sensor Placement ◽  
Model Order ◽  
Reduction Methods

Recent Advances in Computational Methods for Microsystems

2013 ◽  
Vol 745 ◽  
pp. 13-25 ◽  
Author(s):  
Alberto Corigliano ◽  
Martino Dossi ◽  
Stefano Mariani
Keyword(s):  
Model Order Reduction ◽  
Computing Time ◽  
Order Reduction ◽  
Orthogonal Decomposition ◽  
Coupled Problems ◽  
Strong Reduction ◽  
Model Order ◽  
Solution Strategies ◽  
Reduction Methods ◽  
Proper Orthogonal

An algorithm, which combines the use of Domain Decomposition and Model Order Reduction methods based on Proper Orthogonal Decomposition, is proposed. The algorithm allows for the efficient handling of electro-mechanical coupled problems in MEMS, with a strong reduction of computing time with respect to standard monolithic or staggered solution strategies. Examples of coupled electro-mechanical problems, concerning a vibrating beam subject to variable electrostatic forces, are presented and discussed.

Model order reduction methods applied to a welding model

2012 ◽  
Vol 226 (7) ◽  
pp. 972-984
Author(s):  
Fredrik Sikström ◽  
Anna-Karin Christiansson ◽  
Bengt Lennartson
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Model Order ◽  
Reduction Methods
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