Non-intrusive reduced order modelling for the dynamics of geometrically nonlinear flat structures using three-dimensional finite elements

Vizzaccaro, Alessandra; Givois, Arthur; Longobardi, Pierluigi; Shen, Yichang; Deü, Jean-François; Salles, Loïc; Touzé, Cyril; Thomas, Olivier

doi:10.1007/s00466-020-01902-5

Cited by 51 publications

(78 citation statements)

References 48 publications

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“…where Ξ stands for the quadratic nonlinear mapping, and Φ is the N × m matrix of the master eigenvectors only, i.e., it is the restriction of P φ to the m selected master modes; Θ ij = (Θ ij + Θ ji )/2 is the symmetrized MD. The reduced-order dynamics are obtained by applying the second-order nonlinear mapping (10) to the original equations of motion (1).…”

Section: Reduction With the Quadratic Manifoldmentioning

confidence: 99%

“…Model reduction methods have been investigated for a long time for thin structures experiencing large-amplitude vibrations with geometric nonlinearities [1,2]. The two main identified difficulties are that the nonlinearity is distributed, and that the dynamical phenomena displayed by these nonlinear vibrations are numerous, including jump phenomena [3], bifurcations of solutions [4,5], internal resonance and modal interactions [6][7][8][9], strong couplings [10], transition to chaos [11,12], and wave turbulence [13]. Consequently, deriving accurate and predictive reduced-order models (ROMs) requires tackling these two problems in such a manner that the possible dynamics of the ROM can mimic all of the complexity of the full-order solution.…”

Section: Introductionmentioning

confidence: 99%

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Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam Structures

et al. 2021

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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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Section: Reduction With the Quadratic Manifoldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam Structures

et al. 2021

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“…[4,5] to cite only two examples. Unfortunately, the loss of invariance of linear eigenspaces, expressed through important nonlinear coupling terms that may happen with high-frequency modes [6], makes this approach not efficient in terms of accuracy [7,8,9,2,10]. The Proper Orthogonal Decomposition (POD) method offers a gain since being able to modify slightly the orientation of the subspaces to better fit the curvatures of the nonlinear data, but it is still restricted to the use of linear orthogonal subspaces [11,12,13,14].…”

Section: Introductionmentioning

confidence: 99%

Model Order Reduction based on Direct Normal Form: Application to Large Finite Element MEMS Structures Featuring Internal Resonance

Opreni

Vizzaccaro

Frangi

et al. 2021

Preprint

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Dimensionality reduction in mechanical vibratory systems poses challenges for distributed structures including geometric nonlinearities, mainly because of the lack of invariance of the linear subspaces. A reduction method based on direct normal form computation for large finite element (FE) models is here detailed. The main advantage resides in operating directly from the physical space, hence avoiding the computation of the complete eigenfunctions spectrum. Explicit solutions are given, thus enabling a fully non-intrusive version of the reduction method. The reduced dynamics is obtained from the normal form of the geometrically nonlinear mechanical problem, free of non-resonant monomials, and truncated to the selected master coordinates, thus making a direct link with the parametrisation of invariant manifolds. The method is fully expressed with a complex-valued formalism by detailing the homological equations in a systematic manner, and the link with real-valued expressions is established. A special emphasis is put on the treatment of second-order internal resonances and the specific case of a 1:2 resonance is made explicit. Finally, applications to large-scale models of Micro-Electro-Mechanical structures featuring 1:2 and 1:3 resonances are reported, along with considerations on computational efficiency.

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“…Stress values and numerical solutions of hooks under static and dynamic loads are commonly performed today with ABAQUS and ANSYS analysis programs. For deriving reduced models for geometrically nonlinear structures nearly twenty years in a sequential, predetermined displacements of a finite element static and dynamic applications in the finite element method has been used [42]. In Figure 14-15-16-17-18, studies on some FEM were examined.…”

Section: Finite Element Methods (Fem)mentioning

confidence: 99%

An Evaluation on Computer Aided Design, Analysis and Mechanical Properties of Hatch Cover Opening Hooks

Şengül¹,

Kam²

2020

IJAEFEA

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Warehouses inside the ship are of great importance in maritime transport. Due to the adverse weather conditions in maritime transport, hatch covers must be manufactured appropriately and installed on ships. In this study, Computer Aided Design (CAD), manufacture, analysis, and mechanical properties of hatch cover opening hooks used to close stock type warehouse lids in maritime transport were examined. In literature studies, the mechanical properties of St-37, St-52, St-44, St-70, AISI 4140, Weldox 700, Hardox 600 steels, and Aluminum 6061 materials used as hook materials were examined. In the studies, it is seen that curved crane hooks and the same materials are preferred in these hooks. It was concluded that it would be appropriate to use St-37 from structural steels, AISI 4140 steel from tempered steels and high strength Weldox 700 steels as hook material. There is a need for the design and manufacture of special hooks for cranes made to open and close the hatch covers. Hook design -analysis by Finite Element Method (FEM) should be done and stress values should be examined. Accretion stress points should be determined by this FEM and a reliable manufacturing should be done. In addition, optimum conditions will be achieved by designing and manufacturing hooks with economical, long life and high mechanical properties.

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Non-intrusive reduced order modelling for the dynamics of geometrically nonlinear flat structures using three-dimensional finite elements

Cited by 51 publications

References 48 publications

Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam Structures

Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam Structures

Model Order Reduction based on Direct Normal Form: Application to Large Finite Element MEMS Structures Featuring Internal Resonance

An Evaluation on Computer Aided Design, Analysis and Mechanical Properties of Hatch Cover Opening Hooks

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