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See detailNon-linear aeroelastic prediction for aircraft applications
Henshaw, M.J. de C.; Badcock, Ken J.; Vio, G. A. et al

in Progress in Aerospace Sciences (2007), 434(4-6), 65-137

Current industrial practice for the prediction and analysis of flutter relies heavily on linear methods and this has led to overly conservative design and envelope restrictions for aircraft. Although the ... [more ▼]

Current industrial practice for the prediction and analysis of flutter relies heavily on linear methods and this has led to overly conservative design and envelope restrictions for aircraft. Although the methods have served the industry well, it is clear that for a number of reasons the inclusion of non-linearity in the mathematical and computational aeroelastic prediction tools is highly desirable. The increase in available and affordable computational resources, together with major advances in algorithms, mean that non-linear aeroelastic tools are now viable within the aircraft design and qualification environment. The Partnership for Unsteady Methods in Aerodynamics (PUMA) Defence and Aerospace Research Partnership (DARP) was sponsored in 2002 to conduct research into non-linear aeroelastic prediction methods and an academic, industry, and government consortium collaborated to address the following objectives: (1) To develop useable methodologies to model and predict non-linear aeroelastic behaviour of complete aircraft. (2) To evaluate the methodologies on real aircraft problems. (3) To investigate the effect of non-linearities on aeroelastic behaviour and to determine which have the greatest effect on the flutter qualification process. These aims have been very effectively met during the course of the programme and the research outputs include: (a) New methods available to industry for use in the flutter prediction process, together with the appropriate coaching of industry engineers. (b) Interesting results in both linear and non-linear aeroelastics, with comprehensive comparison of methods and approaches for challenging problems. (c) Additional embryonic techniques that, with further research, will further improve aeroelastics capability. This paper describes the methods that have been developed and how they are deployable within the industrial environment. We present a thorough review of the PUMA aeroelastics programme together with a comprehensive review of the relevant research in this domain. This is set within the context of a generic industrial process and the requirements of UK and US aeroelastic qualification. A range of test cases, from simple small DOF cases to full aircraft, have been used to evaluate and validate the non-linear methods developed and to make comparison with the linear methods in everyday use. These have focused mainly on aerodynamic non-linearity, although some results for structural non-linearity are also presented. The challenges associated with time domain (coupled computational fluid dynamics–computational structural model (CFD–CSM)) methods have been addressed through the development of grid movement, fluid–structure coupling, and control surface movement technologies. Conclusions regarding the accuracy and computational cost of these are presented. The computational cost of time-domain methods, despite substantial improvements in efficiency, remains high. However, significant advances have been made in reduced order methods, that allow non-linear behaviour to be modelled, but at a cost comparable with that of the regular linear methods. Of particular note is a method based on Hopf bifurcation that has reached an appropriate maturity for deployment on real aircraft configurations, though only limited results are presented herein. Results are also presented for dynamically linearised CFD approaches that hold out the possibility of non-linear results at a fraction of the cost of time coupled CFD–CSM methods. Local linearisation approaches (higher order harmonic balance and continuation method) are also presented; these have the advantage that no prior assumption of the nature of the aeroelastic instability is required, but currently these methods are limited to low DOF problems and it is thought that these will not reach a level of maturity appropriate to real aircraft problems for some years to come. Nevertheless, guidance on the most likely approaches has been derived and this forms the basis for ongoing research. It is important to recognise that the aeroelastic design and qualification requires a variety of methods applicable at different stages of the process. The methods reported herein are mapped to the process, so that their applicability and complementarity may be understood. Overall, the programme has provided a suite of methods that allow realistic consideration of non-linearity in the aeroelastic design and qualification of aircraft. Deployment of these methods is underway in the industrial environment, but full realisation of the benefit of these approaches will require appropriate engagement with the standards community so that safety standards may take proper account of the inclusion of non-linearity. [less ▲]

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See detailNon-linear generalization of principal component analysis: From a global to a local approach
Kerschen, Gaëtan ULg; Golinval, Jean-Claude ULg

in Journal of Sound & Vibration (2002), 254(5), 867-876

Principal component analysis (PCA), also known as proper orthogonal decomposition or Karhunen-Loeve transform, is commonly used to reduce the dimensionality of a data set with a large number of ... [more ▼]

Principal component analysis (PCA), also known as proper orthogonal decomposition or Karhunen-Loeve transform, is commonly used to reduce the dimensionality of a data set with a large number of interdependent variables. PCA is the optimal linear transformation with respect to minimizing the mean square reconstruction error but it only considers second-order statistics. If the data have non-linear dependencies, an important issue is to develop a technique which takes higher order statistics into account and which can eliminate dependencies not removed by PCA. Recognizing the shortcomings of PCA, researchers in the field of statistics and neural networks have developed non-linear extensions of PCA. The purpose of this paper is to present a non-linear generalization of PCA, called VQPCA. This algorithm builds local linear models by combining PCA with clustering of the input space. This paper concludes by observing from two illustrative examples that VQPCA is potentially a more effective tool than conventional PCA. (C) 2002 Elsevier Science Ltd. All rights reserved. [less ▲]

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See detailA non-linear homogeneous model for bone-like materials under compressive load.
Mengoni, Marlène ULg; Voide, Romain; Toye, Dominique ULg et al

in Nithiarasu, P.; Löhner, R.; van Loon, R. (Eds.) et al Conference Proceedings - 2nd International Conference on Computational & Mathematical Biomedical Engineering (2011)

Using morphological data provided by computed tomography, finite element (FE) models can be used to compute the mechanical response of bone and bone-like materials without describing the complex local ... [more ▼]

Using morphological data provided by computed tomography, finite element (FE) models can be used to compute the mechanical response of bone and bone-like materials without describing the complex local microarchitecture. A constitutive law is here developed and proposed for this purpose. It captures the non-linear structural behavior of bone-like materials through the use of fabric tensors. It also allows for irreversible strains using a plastic material model, allowing hardening of the yield parameters. These characteristics are expressed in a constitutive law based on the anisotropic continuum damage theory coupled with isotropic elastoplasticity in a finite strains framework. This law is implemented into Metafor, a non-linear FE software. Simulations of cylindrical samples undergoing stepwise compression are presented. [less ▲]

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See detailA non-linear homogeneous model for bone-like materials under compressive load.
Mengoni, Marlène ULg; Voide, Romain; de Bien, Charlotte ULg et al

in International Journal for Numerical Methods in Biomedical Engineering (2012), 28(2), 334-348

Finite element (FE) models accurately compute the mechanical response of bone and bone-like materials when the models include their detailed microstructure. In order to simulate non-linear behavior, which ... [more ▼]

Finite element (FE) models accurately compute the mechanical response of bone and bone-like materials when the models include their detailed microstructure. In order to simulate non-linear behavior, which currently is only feasible at the expense of extremely high computational costs, coarser models can be used if the local morphology has been linked to the apparent mechanical behavior. The aim of this paper is to implement and validate such a constitutive law. This law is able to capture the non-linear structural behavior of bone-like materials through the use of fabric tensors. It also allows for irreversible strains using an elastoplastic material model incorporating hardening. These features are expressed in a constitutive law based on the anisotropic continuum damage theory coupled with isotropic elastoplasticity in a finite strains framework. This material model was implemented into Metafor, a non-linear FE software. The implementation was validated against experimental data of cylindrical samples subjected to compression. Three materials with bone-like microstructure were tested : aluminum foams of variable density (ERG, Oakland, CA), PLA (polylactic acid) foam (CERM, University of Liège) and cancellous bone tissue of a deer antler (Faculty of Veterinary Medicine, University of Liège). [less ▲]

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See detailNon-Linear Identification in Modal Space Using a Genetic Algorithm Approach for Model Selection
Platten, Michael F; Wright, Jan Robert; Worden, Keith et al

in International Journal of Applied Mathematics & Mechanics (2007), 3(1), 72-89

The Non-Linear Resonant Decay Method is an approach for the identification of non-linear systems with large numbers of degrees of freedom. The identified non-linear model is expressed in linear modal ... [more ▼]

The Non-Linear Resonant Decay Method is an approach for the identification of non-linear systems with large numbers of degrees of freedom. The identified non-linear model is expressed in linear modal space and comprises the modal model of the underlying linear system with additional terms representing the non-linear behaviour. Potentially, a large number of these non-linear terms will exist but not all of them will be significant. The problem of deciding which and how many terms are required for an accurate identification has previously been addressed using the Forward Selection and Backward Elimination techniques. In this paper, a Genetic Algorithm optimisation is proposed as an alternative to those methods. A simulated lumped parameter non-linear dynamic system is used to demonstrate the proposed optimisation. The use of separate data sets for the identification and validation of the modal model is also investigated. It is found that the Genetic Algorithm approach yields significantly better results than the Backward Elimination and Forward Selection algorithms in many cases. [less ▲]

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See detailNon-Linear Identification Using a Genetic Algorithm Approach for Model Selection
Platten, Michael F; Wright, Jan Robert; Worden, Keith et al

in Proceedings of the 23rd International Modal Analysis Conference (2005, January)

The Non-Linear Resonant Decay Method is an approach for the identification of non-linear systems with large numbers of degrees of freedom. The identified non-linear model is expressed in linear modal ... [more ▼]

The Non-Linear Resonant Decay Method is an approach for the identification of non-linear systems with large numbers of degrees of freedom. The identified non-linear model is expressed in linear modal space and comprises the modal model of the underlying linear system with additional terms representing the non-linear behaviour. Potentially, a large number of these non-linear terms will exist but not all of them will be significant. The problem of deciding which and how many terms are required for an accurate identification has previously been addressed using the Forward Selection and Backward Elimination techniques. In this paper, a Genetic Algorithm optimisation is proposed as an alternative to those methods. A simulated 5-DOF lumped parameter non-linear system is used to demonstrate the proposed optimisation. The use of separate data sets for the identification and validation of the modal model is also investigated. It is found that the Genetic Algorithm approach yields significantly better results than the Backward Elimination and Forward Selection algorithms in many cases. [less ▲]

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See detailNon-linear loudspeaker simulation. Guitar loudspeaker.
Schmitz, Thomas ULg; Embrechts, Jean-Jacques ULg

Conference (2012, June 06)

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See detailNon-linear magnetic model refinement via a finite element subproblem method
Dular, Patrick ULg; V Sabariego, Ruth ULg; Gyselinck, Johan et al

in Proceedings of the XXI Symposium on Electromagnetic Phenomena in Nonlinear Circuits (EPNC 2010) (2010, June)

Model refinements of non-linear magnetic circuits are performed via a finite element subproblem method. A complete problem is split into subproblems to allow a progression from 1- D to 3-D including ... [more ▼]

Model refinements of non-linear magnetic circuits are performed via a finite element subproblem method. A complete problem is split into subproblems to allow a progression from 1- D to 3-D including linear to non-linear model corrections. Its solution is then expressed as the sum of the subproblem solutions supported by different meshes. A convenient and robust correction procedure is proposed allowing independent overlapping meshes for both source and reaction fields. The procedure simplifies both meshing and solving processes, and quantifies the gain given by each model refinement on both local fields and global quantities. [less ▲]

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See detailNon-linear mechanical solvers for GMSH
Noels, Ludovic ULg; Becker; Nguyen, Van Dung ULg et al

Scientific conference (2012, March)

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See detailNon-linear neural networks forecasting of sea level anomaly in the Alboran Sea
Rixen, M.; Barth, Alexander ULg; Beckers, Jean-Marie ULg

Conference (2002)

Forecasts based on artificial intelligence (AI) concepts exploit past time series of satellite images to infer near future ocean conditions at the surface by feed-forward non-linear neural networks. The ... [more ▼]

Forecasts based on artificial intelligence (AI) concepts exploit past time series of satellite images to infer near future ocean conditions at the surface by feed-forward non-linear neural networks. The size of the AI problem is drastically reduced by splitting the spatio-temporal variability contained in the remote sensing data by using empirical orthogonal function (EOF) decomposition. The problem of forecasting the dynamics of a two-dimensional surface field can thus be reduced by selecting the most relevant empirical modes, and non-linear time series predictors are then applied on the time independent amplitudes only. In the present case study, we use altimetric maps of the Mediterranean Sea and the Alboran Sea, combining TOPEX-POSEIDON and ERS-1/2 data for the period October 1992 to March 2000. The learning procedure is applied to each mode individually. The final forecast is then reconstructed from the EOFs and the forecasted amplitudes, and compared to the real observed field, the persistence and linear forecasts for validation purposes. [less ▲]

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See detailNon-linear optical measurements and crystalline characterization of CdTe nanoparticles produces by thes electropulse technique
Loicq, Jerôme ULg; Renotte, Yvon ULg; Delplancke, Jean-Luc

in New Journal of Physics (2004), 6(32),

We propose to extend the ‘electropulse’ technique to synthesize CdTe nanoparticles for optical components. To do so, we create nuclei of the expected material on a titanium electrode immersed in an ... [more ▼]

We propose to extend the ‘electropulse’ technique to synthesize CdTe nanoparticles for optical components. To do so, we create nuclei of the expected material on a titanium electrode immersed in an electrolytic solution by using an electrochemical pulse. The nanoparticles are expelled from the titanium horn surface by cavitation bubbles, which are produced in the solution by a high intensity ultrasound pulse generated by a piezoelectric crystal. Optical absorption spectra and third-order non-linear optical properties of a colloidal solution of CdTe particles produced by this technique are presented. The non-linear refractive index was characterized using the single-beam z-scan technique, and measurements were carried out at several incidence intensities. Non-linear indices of refraction between −1.2×10−7 and −2×10−8 cm2W−1 were measured. [less ▲]

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See detailThe non-linear refractive index of colloidal PbSe nanocrystals:Spectroscopy and saturation behaviour
Moreels, Iwan; Kockaert, Pascal; Van Deun, Rick et al

in Journal of Luminescence (2006), 121

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See detailNon-linear structures
Newerla, A.; Kerschen, Gaëtan ULg

in Calvi, A.; Roy, N. (Eds.) Spacecraft Loads Analysis (2012)

Non-linearity is a frequent occurrence in engineering structures including spacecraft structures. It can take different forms, and it is at the origin of various dynamical phenomena with no linear ... [more ▼]

Non-linearity is a frequent occurrence in engineering structures including spacecraft structures. It can take different forms, and it is at the origin of various dynamical phenomena with no linear counterpart. These phenomena include jumps, harmonics, bifurcation and non-unicity of the solutions. Even when they are local, non-linearities can affect the global dynamical behaviour of a structure and have a substantial impact on spacecraft loads. What makes non-linear dynamics challenging to analyse and model is the well-known result that the principle of linear superposition does not (generally) apply to non-linear systems. Even if linearisation may suffice in some cases, the rigorous analysis of non-linear structures requires adequate and dedicated numerical and experimental methodologies. The main objective of this chapter is to describe how to handle non-linearities for an accurate estimation of loads in spacecraft structures. Specifically, guidelines for both modeling and testing are provided. [less ▲]

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See detailNon-local Damage-Enhanced MFH for Multiscale Simulations of Composites
Wu, Ling ULg; Noels, Ludovic ULg; Adam, Laurent et al

in Patterson, Eann; Backman, David; Cloud, Gary (Eds.) Composite Materials and Joining Technologies for Composites, Volume 7 (2013)

In this work, a gradient-enhanced mean-field homogenization (MFH) procedure is proposed for fiber reinforced materials. In this approach, the fibers are assumed to remain linear elastic while the matrix ... [more ▼]

In this work, a gradient-enhanced mean-field homogenization (MFH) procedure is proposed for fiber reinforced materials. In this approach, the fibers are assumed to remain linear elastic while the matrix material obeys an elasto-plastic behavior enhanced by a damage model. As classical finite element simulations face the problems of losing uniqueness and strain localization when strain softening of materials is involved, we develop the mean-field homogenization in a non-local way. Toward this end we use the so-called non-local implicit approach, reformulated in an anisotropic way to describe the damage in the matrix. As a result we have a multi-scale model that can be used to study the damage process at the meso-scale, and in particular the damaging of plies in a composite stack, in an efficient comput0ational way. As a demonstration a stack with a hole is studied and it is shown that the model predicts the damaging process in bands oriented with the fiber directions. [less ▲]

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See detailNon-local damage-enhanced MFH for multiscale simulations of composites
Wu, Ling ULg; Noels, Ludovic ULg; Adam, Laurent et al

in Proceedings of the XII SEM International Conference & Exposition on Experimental and Applied Mechanics (2012)

In this work, a gradient-enhanced mean-field homogenization (MFH) procedure is proposed for fiber reinforced materials. In this approach, the fibers are assumed to remain linear elastic while the matrix ... [more ▼]

In this work, a gradient-enhanced mean-field homogenization (MFH) procedure is proposed for fiber reinforced materials. In this approach, the fibers are assumed to remain linear elastic while the matrix material obeys an elasto-plastic behavior enhanced by a damage model. As classical finite element simulations face the problems of losing uniqueness and strain localization when strain softening of materials is involved, we develop the mean-field homogenization in a non-local way. Toward this end we use the so-called non-local implicit approach, reformulated in an anisotropic way to describe the damage in the matrix. As a result we have a multi-scale model that can be used to study the damage process at the meso-scale, and in particular the damaging of plies in a composite stack, in an efficient computational way. As a demonstration a stack with a hole is studied and it is shown that the model predicts the damaging process in bands oriented with the fiber directions. [less ▲]

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See detailNon-Local Incremental-Secant Mean-Field-Homogenization of Damage-Enhanced Elasto-Plastic Composites
Wu, Ling ULg; Noels, Ludovic ULg; Adam, Laurent et al

Conference (2013, December)

An anisotropic gradient–enhanced continuum damage model is herein embedded in a mean–field homogenization (MFH) process for elasto-plastic composites. The homogenization procedure is based on the newly ... [more ▼]

An anisotropic gradient–enhanced continuum damage model is herein embedded in a mean–field homogenization (MFH) process for elasto-plastic composites. The homogenization procedure is based on the newly developed incremental secant mean-field homogenization formulation, for which the residual stress and strain states reached in the phases upon a fictitious elastic unloading are considered as starting point to apply the secant method. The mean stress fields in the phases are then computed using isotropic secant tensors, which are naturally used to define the Linear Comparison–Composite The resulting multi– scale model is then applied to study the damage process at the meso–scale of laminates, and in particular the damaging of plies in a composite stack. By using the gradient–enhanced continuum damage model, the problem of losing uniqueness upon strain softening is avoided. [less ▲]

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See detailA non-local MLT treatment fitting 3D simulations
Dupret, Marc-Antoine ULg; Goupil, M*-J; Samadi, R. et al

in Proceedings of SOHO 18/GONG 2006/HELAS I, Beyond the spherical Sun (2006, October 01)

Not Available

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See detailNon-local multiscale analyzes of composite laminates based on a damage-enhanced mean–field homogenization formulation
Wu, Ling ULg; Noels, Ludovic ULg; Adam, Laurent et al

Conference (2013, June)

Properties of carbon fiber reinforced epoxy laminates are studied using an anisotropic gradient–enhanced continuum damage model embedded in a mean–field homogenization (MFH) procedure. The fibers are ... [more ▼]

Properties of carbon fiber reinforced epoxy laminates are studied using an anisotropic gradient–enhanced continuum damage model embedded in a mean–field homogenization (MFH) procedure. The fibers are assumed to remain elastic, and the matrix material obeys an elasto–plastic behavior enhanced by the proposed damage model. The resulting multi– scale model is then applied to study the damage process at the meso–scale of laminates, and in particular the damaging of plies in a composite stack. By using the gradient–enhanced continuum damage model, the problem of losing uniqueness and strain localization, which happens in classical finite element simulations when strain softening of materials is involved, is avoided. As a demonstration a stack with a hole is studied and it is shown that the model predicts the damaging process in bands oriented with the fiber directions, accordingly to the conducted experimental results. [less ▲]

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See detailNon-local time-dependent treatments of convection in A-G type stars
Dupret, Marc-Antoine ULg; Samadi, R.; Grigahcene, A. et al

in Communications in Asteroseismology (2006), 147

Time-Dependent Convection (TDC) models obtained by combining the local treatment of Gabriel (1996) and Grigahcene et al. (2005) and the non-local prescriptions of Spiegel (1963) are presented. We show ... [more ▼]

Time-Dependent Convection (TDC) models obtained by combining the local treatment of Gabriel (1996) and Grigahcene et al. (2005) and the non-local prescriptions of Spiegel (1963) are presented. We show that in the stationary unperturbed case, these non-local treatments can be constrained by the results of 3D hydrodynamic simulations (Stein & Nordlund 1998). We consider here the case of solar-type stars with a large convective envelope and A-F type stars with two very thin surface convection zones. [less ▲]

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See detailNon-Lte Effects and Abundance Analyses of Halo Stars
Magain, Pierre ULg

in Cayrel de Strobel, G.; Spite, M. (Eds.) The Impact of Very High S/N Spectroscopy on Stellar Physics (1988)

The possible existence of departures from LTE affecting the abundance analyses of halo dwarfs and subgiants is analysed from the observational point of view, and illustrated by the case of the ... [more ▼]

The possible existence of departures from LTE affecting the abundance analyses of halo dwarfs and subgiants is analysed from the observational point of view, and illustrated by the case of the intermediate halo subgiant HD 76932. [less ▲]

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