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Christian Soize - One of the best experts on this subject based on the ideXlab platform.
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Uncertainty quantification for elasto-acoustic nonlinear Reduced-Order Model computational Model
2017Co-Authors: Evangéline Capiez-Lernout, Christian Soize, Roger OhayonAbstract:The present research concerns the numerical analysis of an uncertain coupled fluid-structure dynamical system, for which the geometrical nonlinearities of the structure induced by the large deformations and the large displacements are taken into account. The structure is coupled with an internal cavity filled with a linear inviscid compressible fluid. The formulation is carried out in terms of displacements and pressure unknowns. The modal basis is made up of the structural modes of the structure and the acoustic modes of the fluid. A nonlinear-Reduced Order Model is then numerically constructed in Order to reduce the size of the problem. The uncertainties are then implemented by using the nonparametric probabilistic framework. Note that a peculiar attention that allows the uncertainties on the nonlinear part to be coherently taken into account by preventing the presence of a too large number of random variables used for generating the stochastic Model is made. A numerical application is presented.
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Uncertainty propagation in a nonlinear Reduced-Order Model in internal elasto-acoustics
2017Co-Authors: Evangéline Capiez-Lernout, Christian Soize, Quentin Akkaoui, Roger OhayonAbstract:The present research concerns the uncertainty propagation in elasto-acoustics, taking into account the geometrical nonlinearities induced by the large displacements/deformations of the structure and assuming the internal acoustic fluid occupying an internal cavity coupled to the structure to remain in a linear range of vibration. The problem is formulated with structural displacements and fluid pressures unknowns. Uncertainties are implemented from a mean nonlinear Reduced-Order Model using the non-parametric probabilistic approach. More particularly, a dedicated stiffness operator self-containing all the information concerning both linear and nonlinear stiffness terms is constructed. A particular attention concerns the Modeling of such stiffness operator through a second local reduction so that the size of the random germ be of reasonable size and be identical whether uncertainties are investigated on only linear or nonlinear stiffness terms. A numerical application is presented.
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Stochastic Reduced-Order Model for dynamical structures having numerous local elastic modes in the low-frequency range
2017Co-Authors: Anas Batou, Christian SoizeAbstract:We propose a method to construct a stochastic Reduced-Order Model using only the global modes and in taking into account the local elastic modes with a probabilistic approach. The "global elastic modes" and the "local elastic modes" are calculated separately using a new formulation solving two generalized eigenvalue problems. The union of these two families constitutes a basis of the admissible space. Then, the Reduced-Order Model is constructed by projection of the dynamical equation on the global elastic modes. The apparent damping generated in this Reduced-Order Model by the powerflow of the mechanical energy from the global modes to the local modes is constructed by a statistical approach.
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Multilevel stochastic Reduced-Order Model in linear structural dynamics for complex structures
2017Co-Authors: O. Ezvan, Anas Batou, Christian SoizeAbstract:We present the construction of a multilevel stochastic Reduced-Order Model devoted to the robust prediction of frequency response functions of complex linear dy-namical systems that are characterized by the presence of several structural scales in which there are local displacements in addition to the usual global displacements, and which are associated with the distinct low-, medium-, and high-frequency bands. As the levels of uncertainties are different in the three frequency bands, a multilevel stochastic Reduced-Order Model using several orthogonal subspaces associated with the several types of displacements is developed. The objective of the paper is to demonstrate the capability of the multilevel stochastic Reduced-Order Model to adapt the stochastic Modeling of uncertainties to each one of the three frequency bands.
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Computational dynamics in low- and medium-frequency ranges. Reduced-Order Model and uncertainty quantification
2017Co-Authors: Christian Soize, Evangéline Capiez-Lernout, Adrien Arnoux, Anas Batou, Marc P. Mignolet, Moustapha Mbaye, Laurent Gagliardini, Javier Avalos, N De Brie, I. E. PoloskovAbstract:Reduced-Order Models, substructuring techniques and uncertainty quantification are important aspects in computational dynamics, fluid-structure interactions, vibrations and vibroacoustics. In this framework, we will present the following new aspects: (i) Stochastic Reduced-Order Model in low-frequency dynamics in presence of numerous local elastic modes, for which the high modal density makes the use of the classical modal analysis method not suitable; (ii) New ingredients useful for the nonparametric stochastic Modeling of uncertainties (a) for structures with uncertain boundary conditions and/or coupling between substructures and (b) for linear viscoelastic structures in the medium-frequency range; (iii) Bayesian posteriors of uncertainty quantification in computational structural dynamics for low- and medium-frequency ranges. In addition to some illustrations which will be given, three industrial applications will be presented.
Roger Ohayon - One of the best experts on this subject based on the ideXlab platform.
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Uncertainty quantification for elasto-acoustic nonlinear Reduced-Order Model computational Model
2017Co-Authors: Evangéline Capiez-Lernout, Christian Soize, Roger OhayonAbstract:The present research concerns the numerical analysis of an uncertain coupled fluid-structure dynamical system, for which the geometrical nonlinearities of the structure induced by the large deformations and the large displacements are taken into account. The structure is coupled with an internal cavity filled with a linear inviscid compressible fluid. The formulation is carried out in terms of displacements and pressure unknowns. The modal basis is made up of the structural modes of the structure and the acoustic modes of the fluid. A nonlinear-Reduced Order Model is then numerically constructed in Order to reduce the size of the problem. The uncertainties are then implemented by using the nonparametric probabilistic framework. Note that a peculiar attention that allows the uncertainties on the nonlinear part to be coherently taken into account by preventing the presence of a too large number of random variables used for generating the stochastic Model is made. A numerical application is presented.
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Uncertainty propagation in a nonlinear Reduced-Order Model in internal elasto-acoustics
2017Co-Authors: Evangéline Capiez-Lernout, Christian Soize, Quentin Akkaoui, Roger OhayonAbstract:The present research concerns the uncertainty propagation in elasto-acoustics, taking into account the geometrical nonlinearities induced by the large displacements/deformations of the structure and assuming the internal acoustic fluid occupying an internal cavity coupled to the structure to remain in a linear range of vibration. The problem is formulated with structural displacements and fluid pressures unknowns. Uncertainties are implemented from a mean nonlinear Reduced-Order Model using the non-parametric probabilistic approach. More particularly, a dedicated stiffness operator self-containing all the information concerning both linear and nonlinear stiffness terms is constructed. A particular attention concerns the Modeling of such stiffness operator through a second local reduction so that the size of the random germ be of reasonable size and be identical whether uncertainties are investigated on only linear or nonlinear stiffness terms. A numerical application is presented.
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Vibration of structures containing compressible liquids with surface tension and sloshing effects. Reduced-Order Model
Computational Mechanics, 2017Co-Authors: Roger Ohayon, Christian SoizeAbstract:This paper deals with the development of the linear vibration of a general viscoelastic structure, with a local wall acoustic impedance, containing an inviscid compressible liquid (but with an additional volume dissipative term), with surface tension (capillarity) and sloshing effects, and neglecting the effects of internal gravity waves and the elas-togravity operator. The sloshing problems of incompressible liquids with capillarity effects in elastic structures exhibit a major difficulty induced by the boundary contact conditions on the triple line because the capillarity forces are forces per unit length while the elastic forces are forces per unit surface. The proposed framework has the following novel features: (i) introducing a new appropriate boundary condition for the contact angle condition compatible with a deformable structure considered here as viscoelastic, (ii) considering a compressible liquid while incompressibility hypothesis is generally used for FSI problems including capillarity phenomena, and (iii) constructing a Reduced-Order Model for the computational coupled problem.
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Variational-based Reduced-Order Model in dynamic substructuring of coupled structures through a dissipative physical interface: Recent advances
Archives of Computational Methods in Engineering, 2017Co-Authors: Roger Ohayon, Christian Soize, R. SampaioAbstract:This paper deals with a variational-based Reduced-Order Model in dynamic substructuring of two coupled structures through a physical dissipative flexible interface. We consider the linear elastodynamic of a dissipative structure composed of two main dissipative substructures perfectly connected through interfaces by a linking substructure. The linking substructure is flexible and is Modeled in the context of the general linear viscoelasticity theory, yielding damping and stiffness operators depending on the frequency, while the two main dissipative substructures are Modeled in the context of linear elasticity with an additional classical viscous damping Modeling which is assumed to be independent of the frequency. We present an appropriate review that we carry out on the different methods used in dynamic substructuring. The method proposed consists in constructing a Reduced-Order Model using the free-interface elastic modes of the two main substructures and, for the linking substructure, an appropriate elastostatic lifting operator and the frequency-dependent fixed-interface vector basis.
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Vibro-Acoustic Analysis of Laminated Double-Wall: Finite Element Formulation and Reduced-Order Model
Applied Condition Monitoring, 2014Co-Authors: Walid Larbi, Roger OhayonAbstract:This paper presents a finite element Model for sound transmission analysis through a double sandwich panels with viscoelastic core inserted in an infinite baffle. The proposed Model is derived from a multi-field variational principle involving structural displacement of the panels and acoustic pressure inside the fluid cavity. To solve the vibro-acoustic problem, the plate displacements are expanded as a modal summation of the plate’s real eigenfunctions in vacuo. Similarly, the cavity pressure is expanded as a summation over the modes of the cavity with rigid boundaries. Then, an appropriate Reduced-Order Model with mode acceleration method by adding quasi-static corrections is introduced. The structure is excited by a plane wave. The radiated sound power is calculated by means of a discrete solution of the Rayleigh Integral. Fluid loading is neglected. Various results are presented in Order to validate and illustrate the efficiency of the proposed Reduced finite element formulation.
Saba Pasha - One of the best experts on this subject based on the ideXlab platform.
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A Reduced-Order Model of the spine to study pediatric scoliosis
Biomechanics and Modeling in Mechanobiology, 2020Co-Authors: Sunder Neelakantan, Prashant K. Purohit, Saba PashaAbstract:The S-shaped curvature of the spine has been hypothesized as the underlying mechanical cause of adolescent idiopathic scoliosis. In earlier work, we proposed a Reduced-Order Model in which the spine was viewed as an S-shaped elastic rod under torsion and bending. Here, we simulate the deformation of S-shaped rods of a wide range of curvatures and inflection points under a fixed mechanical loading. Our analysis determines three distinct axial projection patterns of these S-shaped rods: two loop (in opposite directions) patterns and one Lemniscate pattern. We further identify the curve characteristics associated with each deformation pattern, showing that for rods deforming in a Loop1 shape the position of the inflection point is the highest and the curvature of the rod is smaller compared to the other two types. For rods deforming in the Loop2 shape, the position of the inflection point is the lowest (closer to the fixed base) and the curvatures are higher than the other two types. These patterns matched the common clinically observed scoliotic curves—Lenke 1 and Lenke 5. Our S-shaped elastic rod Model generates deformations that are similar to those of a pediatric spine with the same sagittal curvature characteristics and it can differentiate between the clinically observed deformation patterns.
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a Reduced Order Model of the spine to study pediatric scoliosis
bioRxiv, 2020Co-Authors: Sunder Neelakantan, Prashant K. Purohit, Saba PashaAbstract:The S-shaped curvature of the spine has been hypothesized as the underlying mechanical cause of adolescent idiopathic scoliosis. In earlier work we proposed a Reduced Order Model in which the spine was viewed as an S-shaped elastic rod under torsion and bending. Here, we simulate the deformation of S-shaped rods of a wide range of curvatures and inflection points under a fixed mechanical loading. Our analysis determines three distinct axial projection patterns of these S-shaped rods: two loop (in opposite directions) patterns and one lemniscate pattern. We further identify the curve characteristics associated with each deformation pattern showing that for rods deforming in a loop 1 shape the position of the inflection point is the highest and the curvature of the rod is smaller compared to the other two types. For rods deforming in the loop 2 shape the position of the inflection point is the lowest (closer to the fixed base) and the curvatures are higher than the other two types. These patterns matched the common clinically observed scoliotic curves - Lenke 1 and Lenke 5. Our elastic rod Model predicts deformations that are similar to those of a pediatric spine and it can differentiate between the clinically observed deformation patterns. This provides validation to the hypothesis that changes in the sagittal profile of the spine can be a mechanical factor in parthenogenesis of pediatric idiopathic scoliosis.
Anas Batou - One of the best experts on this subject based on the ideXlab platform.
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Stochastic Reduced-Order Model for dynamical structures having numerous local elastic modes in the low-frequency range
2017Co-Authors: Anas Batou, Christian SoizeAbstract:We propose a method to construct a stochastic Reduced-Order Model using only the global modes and in taking into account the local elastic modes with a probabilistic approach. The "global elastic modes" and the "local elastic modes" are calculated separately using a new formulation solving two generalized eigenvalue problems. The union of these two families constitutes a basis of the admissible space. Then, the Reduced-Order Model is constructed by projection of the dynamical equation on the global elastic modes. The apparent damping generated in this Reduced-Order Model by the powerflow of the mechanical energy from the global modes to the local modes is constructed by a statistical approach.
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Multilevel stochastic Reduced-Order Model in linear structural dynamics for complex structures
2017Co-Authors: O. Ezvan, Anas Batou, Christian SoizeAbstract:We present the construction of a multilevel stochastic Reduced-Order Model devoted to the robust prediction of frequency response functions of complex linear dy-namical systems that are characterized by the presence of several structural scales in which there are local displacements in addition to the usual global displacements, and which are associated with the distinct low-, medium-, and high-frequency bands. As the levels of uncertainties are different in the three frequency bands, a multilevel stochastic Reduced-Order Model using several orthogonal subspaces associated with the several types of displacements is developed. The objective of the paper is to demonstrate the capability of the multilevel stochastic Reduced-Order Model to adapt the stochastic Modeling of uncertainties to each one of the three frequency bands.
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Stochastic Reduced-Order Model in low frequency dynamics in presence of numerous local elastic modes
2017Co-Authors: Anas Batou, Christian SoizeAbstract:This paper concerns the non usual case in structural dynamics for which a complex structure exhibits both the usual global elastic modes and numerous local elastic modes in the low-frequency range. Despite the presence of these local elastic modes, we are interested in constructing a stochastic Reduced-Order Model using only the global modes and in taking into account the local elastic modes with a probabilistic approach. The "global elastic modes" and the "local elastic modes" are calculated separately using a new formulation solving two generalized eigenvalue problems. The union of these two families constitutes a basis of the admissible space. Then, the Reduced-Order Model is constructed by projection of the dynamical equation on the global elastic modes. The apparent damping generated in this Reduced-Order Model by the power flow of the mechanical energy from the global modes to the local modes is constructed by a statistical approach. The theory is presented and is validated through an application.
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Stochastic Reduced-Order Model for quasi-periodic beam structures having numerous local elastic modes in the low-frequency range
2017Co-Authors: Anas Batou, Christian SoizeAbstract:The problem considered here concerns the construction of a stochastic Reduced-Order Model for quasi-periodic beam structures having numerous local elastic modes in the low-frequency range. The classical methods used for the low-frequency range to construct a Reduced-Order Model are not adapted in this case. We then use a recently proposed method which consists in constructing a basis of the global displacements and a basis of the local displacements by solving two separate eigenvalue problems. We then construct a stochastic Reduced-Order Model using the basis of the global displacements and the contribution of the local displacements is taken into account using a probabilistic approach. The theory is presented and is validated through an application.
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Stochastic Reduced-Order Model for dynamical structures with high modal density in the low-frequency range
2017Co-Authors: Anas Batou, Christian SoizeAbstract:The problem considered here concerns the construction of a stochastic Reduced-Order Model for dynamical structures having a high modal density in the low frequency range. The classical methods used for the low-frequency range to construct a Reduced-Order Model are not adapted in this case. We then use a recently proposed method which consists in constructing a basis of the global displacements and a basis of the local displacements by solving two separate eigenvalue problems. We then construct a stochastic Reduced-Order Model using the basis of the global displacements and the contribution of the local displacements is taken into account using a probabilistic approach. The theory is presented and is applied to tube bundles structures which is are quasi-periodic structures for which the dynamical response is characterized by ensemble (global) displacements and more local displacements.
R. Sampaio - One of the best experts on this subject based on the ideXlab platform.
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Variational-based Reduced-Order Model in dynamic substructuring of coupled structures through a dissipative physical interface: Recent advances
Archives of Computational Methods in Engineering, 2017Co-Authors: Roger Ohayon, Christian Soize, R. SampaioAbstract:This paper deals with a variational-based Reduced-Order Model in dynamic substructuring of two coupled structures through a physical dissipative flexible interface. We consider the linear elastodynamic of a dissipative structure composed of two main dissipative substructures perfectly connected through interfaces by a linking substructure. The linking substructure is flexible and is Modeled in the context of the general linear viscoelasticity theory, yielding damping and stiffness operators depending on the frequency, while the two main dissipative substructures are Modeled in the context of linear elasticity with an additional classical viscous damping Modeling which is assumed to be independent of the frequency. We present an appropriate review that we carry out on the different methods used in dynamic substructuring. The method proposed consists in constructing a Reduced-Order Model using the free-interface elastic modes of the two main substructures and, for the linking substructure, an appropriate elastostatic lifting operator and the frequency-dependent fixed-interface vector basis.
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Variational-Based Reduced-Order Model in Dynamic Substructuring of Coupled Structures Through a Dissipative Physical Interface: Recent Advances
Archives of Computational Methods in Engineering, 2014Co-Authors: Roger Ohayon, Christian Soize, R. SampaioAbstract:This paper deals with a variational-based Reduced-Order Model in dynamic substructuring of two coupled structures through a physical dissipative flexible interface. We consider the linear elastodynamic of a dissipative structure composed of two main dissipative substructures perfectly connected through interfaces by a linking substructure. The linking substructure is flexible and is Modeled in the context of the general linear viscoelasticity theory, yielding damping and stiffness operators depending on the frequency, while the two main dissipative substructures are Modeled in the context of linear elasticity with an additional classical viscous damping Modeling which is assumed to be independent of the frequency. We present recent advances adapted to such a situation, which is positioned with respect to an appropriate review that we carry out on the different methods used in dynamic substructuring. It consists in constructing a Reduced-Order Model using the free-interface elastic modes of the two main substructures and, for the linking substructure, an appropriate frequency-independent elastostatic lifting operator and the frequency-dependent fixed-interface vector basis.
