Nonlinear reduced order modeling of isotropic and functionally graded plates
TL;DR: In this article, a non-linear structural dynamic reduced-order model for aircraft panels is proposed, with particular emphasis on aircraft panels, and the model is validated for isotropic/symmetric composite structures and then extended to asymmetric and functionally graded ones.
Abstract: The focus of this investigation is on the development and validation of non-linear structural dynamic reduced order models of structures undergoing large deformations, with particular emphasis on aircraft panels. Significant efforts are devoted to the formulation and assessment of “dual modes” which when combined with the linear transverse modes form an excellent basis for the representation of the displacement and stress fields in the reduced order model. This task is first successfully achieved for isotropic/symmetric composite structures and then extended to asymmetric and functionally graded ones. Examples of application are presented that demonstrate the high accuracy of the proposed reduced order models as compared to full finite element preditions, even with a small number of modes.
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TL;DR: In this article, a review of reduced order modeling techniques for geometrically nonlinear structures, more specifically those techniques that are applicable to structural models constructed using commercial finite element software, is presented.
286 citations
01 Jan 2015
55 citations
TL;DR: In this article, a stochastic nonlinear computational model is constructed as a function of a scalar dispersion parameter, which has to be identified with respect to the nonlinear static experimental response of a very thin cylindrical shell submitted to a static shear load.
54 citations
TL;DR: In this article, a review of nonlinear methods for model order reduction in structures with geometric nonlinearity is presented, with a special emphasis on the techniques based on invariant manifold theory.
Abstract: This paper aims at reviewing nonlinear methods for model order reduction in structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear-based techniques by their use of a nonlinear mapping instead of adding new vectors to enlarge the projection basis. Invariant manifolds have been first introduced in vibration theory within the context of nonlinear normal modes and have been initially computed from the modal basis, using either a graph representation or a normal form approach to compute mappings and reduced dynamics. These developments are first recalled following a historical perspective, where the main applications were first oriented toward structural models that can be expressed thanks to partial differential equations. They are then replaced in the more general context of the parametrisation of invariant manifold that allows unifying the approaches. Then, the specific case of structures discretised with the finite element method is addressed. Implicit condensation, giving rise to a projection onto a stress manifold, and modal derivatives, used in the framework of the quadratic manifold, are first reviewed. Finally, recent developments allowing direct computation of reduced-order models relying on invariant manifolds theory are detailed. Applicative examples are shown and the extension of the methods to deal with further complications are reviewed. Finally, open problems and future directions are highlighted.
54 citations
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Book•
28 Sep 1997TL;DR: Bonet and Wood as discussed by the authors provide a complete, clear, and unified treatment of nonlinear continuum analysis and finite element techniques under one roof, providing an essential resource for postgraduates studying non-linear continuum mechanics and ideal for those in industry requiring an appreciation of the way in which their computer simulation programs work.
Abstract: Designing engineering components that make optimal use of materials requires consideration of the nonlinear characteristics associated with both manufacturing and working environments. The modeling of these characteristics can only be done through numerical formulation and simulation, and this requires an understanding of both the theoretical background and associated computer solution techniques. By presenting both nonlinear continuum analysis and associated finite element techniques under one roof, Bonet and Wood provide, in this edition of this successful text, a complete, clear, and unified treatment of these important subjects. New chapters dealing with hyperelastic plastic behavior are included, and the authors have thoroughly updated the FLagSHyP program, freely accessible at www.flagshyp.com. Worked examples and exercises complete each chapter, making the text an essential resource for postgraduates studying nonlinear continuum mechanics. It is also ideal for those in industry requiring an appreciation of the way in which their computer simulation programs work.
1,859 citations
"Nonlinear reduced order modeling of..." refers background in this paper
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Book•
01 Jun 2001
TL;DR: In this paper, a tensor analysis of strain conservation laws elastic and plastic behaviour of materials linearized theory of elasticity solutions of problems by potentials two-dimensional problems in variational calculus, energy theorems, Saint-Venant's principle Hamilton's principle, wave propagation, applications of generalized co-ordinates elasticity and thermodynamics irreversible thermodynamics and viscoelasticity thermoelasticness visco-elasticy large deformation incremental approach to solving some nonlinear problems.
Abstract: Tensor analysis stress tensor analysis of strain conservation laws elastic and plastic behaviour of materials linearized theory of elasticity solutions of problems in linearized theory of elasticity by potentials two-dimensional problems in linearized theory of elasticity variational calculus, energy theorems, Saint-Venant's principle Hamilton's principle, wave propagation, applications of generalized co-ordinates elasticity and thermodynamics irreversible thermodynamics and viscoelasticity thermoelasticity viscoelasticity large deformation incremental approach to solving some nonlinear problems finite element methods mixed and hybrid formulations finite element methods for plates and shells finite element modelling of nonlinear elasticity, viscoelasticity, plasticity, viscoplasticity and creep.
484 citations
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...see [30,31], summation over repeated indices assumed)...
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TL;DR: In this paper, a method for determining the nonlinear modal stiffness coefficients for an arbitrary finite element model is presented, which is suitable for use with commercial finite element codes having a geometrically nonlinear static capability.
279 citations
"Nonlinear reduced order modeling of..." refers background in this paper
...Further, see the discussion in [33] for the general validity of the restriction of the indices ....
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...( ) ( ) ( ) X U q X U q X u l i r l j i r j r i ) ( ) ( ) ( ) ( ) ( + = , r = 1,2,3, see [33] for details....
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...finite element solutions has been proposed by Muravyov and Rizzi [33]....
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TL;DR: In this article, several methods used to construct the nonlinear modal models are compared using a clamped-clamped beam as an example problem, and the modal equations can then be integrated in the time domain.
174 citations
"Nonlinear reduced order modeling of..." refers background in this paper
...The significant development and validation efforts carried out in particular in [16–19,22–27] have well established the accuracy and efficiency of such non-linear reduced order modeling techniques....
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...A different selection of in-plane basis functions, referred to as ‘‘dual’’ or ‘‘companion’’ modes, has also been proposed [16–19,27] that relies on in-plane static displacements induced by specified transverse loads directly relating to the transverse modes used....
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...buckled or not, see [1–27]....
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TL;DR: In this paper, a non-linearly coupled multi-modal response model is proposed for modeling large deflection beam response involving multiple vibration modes, which can be applied to the case of a homogeneous isotropic beam.
151 citations
Additional excerpts
...buckled or not, see [1–27]....
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