Exact 3D solution for static and damped harmonic response of simply supported general laminates

The state-space method is adapted to obtain three dimensional exact solutions for the static and damped dynamic behaviors of simply supported general laminates. The state-space method is written in a general form that permits to handle both cross-ply and antisymmetric angle-ply laminates. This general form also permits to obtain exact solutions for general laminates, albeit with some constraints. For the general case and for the static behavior, either an additive term is added to the load to simulate simply supported boundary conditions, or the plate bends in a particular way. For the dynamic behavior, the general case leads to pairs of natural frequencies for each order, with associated mode shapes. Finite element simulations have been performed to validate most of the results presented in this study. As the boundary conditions needed for the general case are not so straightforward, a specific discussion has been added. It is shown that these boundary conditions also work for the two aforementioned laminate classes. The damped harmonic response of a non symmetrical isotropic sandwich is studied for different frequencies around the fundamental frequency. The static and undamped dynamic behaviors of the [-15/15], [0/30/0] and [-10/0/40] laminates are studied for various length-to-thickness ratios

Transverse shear warping functions for anisotropic multilayered plates

In this work, transverse shear warping functions for an equivalent single layer plate model are formulated from a variational approach. The part of the strain energy which involves the shear phenomenon is expressed in function of the warping functions and their derivatives. The variational calculus leads to a differential system of equations which warping functions must verify. Solving this system requires the choice of values for the (global) shear strains and their derivatives. A particular choice, which is justified for cross-ply laminates, leads to excellent results. For single layer isotropic and orthotropic plates, an analytical expression of the warping functions is given. They involve hyperbolic trigonometric functions. They differ from the z - 4/3z3 Reddy's formula which has been found to be a limit of present warping functions for isotropic and moderately thick plates. When the h/L and/or the G13/E1 ratios significantly differ from those of isotropic and moderately thick plates, a difference between present warping functions and Reddy's formula can be observed, even for the isotropic single layer plate. Finite element simulations agree perfectly with the present warping functions in these cases. For multilayer cross-ply configurations, the warping functions are determined using a semi-analytical procedure. They have been compared to results of 3D finite element simulations. They are in excellent agreement. For angle-ply laminates, the above process gives warping functions that seem to have relevant shapes, even if the choice for global shear values cannot be justified in this case. No finite element comparison has been presented at this time because it is difficult to propose boundary conditions and prescribed load that permit to isolate the shear phenomenon

A multilayer anisotropic plate model with warping functions for the study of vibrations reformulated from Woodcock's work

In this paper, a plate model suitable for static and dynamic analysis of inhomogeneous anisotropic multilayered plates is described. This model takes transverse shear variation through the thickness of the plate into account by means of warping functions which are determined by enforcing kinematic and static assumptions at the layers interfaces. This model leads to a 10 x 10 behavior matrix in which membrane strains, bending curvatures, and transverse shear x and y-derivatives are coupled, and to a classical 2 x 2 shear behavior matrix. This model has been proven to be very efficient, especially when high ratios -up to 10E5- between the stiffnesses of layers are present. This work is related to Woodcock's model, so it can be seen as a reformulation of his work. However, it propose several enhancements: the displacement field is made explicit; it is reformulated with commonly used plate notations; laminate equations of motion are fully detailed; the place of this model relatively to other plate models is now easy to see and is discussed; the link between this formulation and the original one is completely written with all necessary proofs; misses and errors have been found in the energy coefficients of the original work, and then have been corrected; it is now easy to improve or to adapt the model for specific applications with the choice of refined or specific warping functions

Latin hypercube sampling with inequality constraints

In some studies requiring predictive and CPU-time consuming numerical models, the sampling design of the model input variables has to be chosen with caution. For this purpose, Latin hypercube sampling has a long history and has shown its robustness capabilities. In this paper we propose and discuss a new algorithm to build a Latin hypercube sample (LHS) taking into account inequality constraints between the sampled variables. This technique, called constrained Latin hypercube sampling (cLHS), consists in doing permutations on an initial LHS to honor the desired monotonic constraints. The relevance of this approach is shown on a real example concerning the numerical welding simulation, where the inequality constraints are caused by the physical decreasing of some material properties in function of the temperature

Global sensitivity analysis in welding simulations -- what are the material data you really need ?

International audienceIn this paper, the Sensitivity Analysis methodology is applied to numerical welding simulation in order to rank the importance of input variables on the outputs of the code like distorsions or residual stresses. The numerical welding simulation uses the Finite Element Method, with a thermal computation followed by a mechanical one. Classically, a Local Sensitivity Analysis is performed, hence the validity of the results is limited to the neighborhood of a nominal point, and cross effects cannot be detected. This study implements a Global Sensitivity Analysis which allows to screen the whole material space of the steel family mechanical properties. A set of inputs of the mechanical model --material properties that are temperature-dependent-- is generated with the help of Latin Hypercube Sampling. The same welding simulation is performed with each sampling element as input data. Then, output statistical processing allows us to classify the relative input influences by means of different sensitivity indices estimates. Two different welding configurations are studied. Considering their major differences, they give a different ranking of inputs, but both of them show that only a few parameters are responsible of the variability of the outputs. To prove it a posteriori for the first configuration, two series of computations are performed for a complete sample and for its reduced copy --where all the secondary parameters are set to mean values. They match perfectly, showing a substantial economy can be done by giving to the rest of the inputs mean values. Sensitivity analysis has then provided answers to what we consider one of the probable frequently asked questions regarding welding simulation: for a given welding configuration, which properties must be measured with a good accuracy and which ones can be simply extrapolated or taken from a similar material? That leads us to propose a comprehensive methodology for welding simulations including four sequential steps: a problem characterization, a sensitivity analysis, an experimental campaign, simulations

Comportement vibratoire de structures composites intégrant des éléments amortissants

Ce travail traite de la modélisation de structures composites intégrant des éléments amortissants passifs. Un modèle de plaque "équivalent simple couche" générique utilisant des fonctions de description du cisaillement transverse est présenté. Plusieurs méthodes d'obtention de ces fonctions sont décrites, permettant de retrouver des modèles classiques ou issus de la littérature. Deux nouvelles méthodes d'obtention de ces fonctions sont aussi présentées.Plusieurs méthodes de discrétisation adaptées au modèle générique sont étudiées. La méthode de Navier permet de tester la qualité de chaque modèle associé à un jeu de fonctions de description du cisaillement transverse. La méthode de Rayleigh-Ritz permet l'étude du comportement vibratoire d'une plaque rectangulaire munie d'un ou plusieurs patchs viscocontraints. Plusieurs éléments finis issus de la littérature, adaptés au modèle, sont aussi présentés.À l'aide de la méthode de Navier, une étude numérique du comportement statique et dynamique de plusieurs configurations de plaques permet la comparaison des différents modèles présentés. La méthode de Rayleigh-Ritz est utilisée pour étudier le comportement vibratoire d'une plaque munie d'un patch viscocontraint. Une comparaison des résultats obtenus avec le modèle présenté et ceux issus de calculs éléments finis tridimensionnels permet de valider notre modèle. Une étude énergétique de la plaque patchée permet d'illustrer le comportement du patch. Enfin une méthode inverse d'identification des matériaux viscoélastiques, basées sur une combinaison du modèle décrit et d'un algorithme génétique, montre une application du modèle.This work is on the subject of modelization of structures treated with passive damping elements. A generic "equivalent single layer" plate model using transverse shear warping functions is presented. Several methods to obtain these functions are described, allowing the implementation of classical models and others issued from the litterature. Two new methods for obtaining these functions are also presented.Several discretization methods adapted to the generic plate model are studied. Navier's procedure allows the testing of the quality of each model associated with a set of transverse shear warping functions. Rayleigh-Ritz method allows the study of the vibrational behavior of a rectangular plate treated with one or several constrained damping patches. Several finite elements issued from the literature are also presented.Using Navier's procedure, a numerical study of the static and dynamic behavior of several plate configurations allows the comparison of the different plate models. Rayleigh-Ritz method is used to study the vibrational response of a plate treated with a constrained damping patch. A comparison of the results with those obtained with three dimensional finite element calculations permits the model validation. An energetic study of the patched plate allow us to understand the constrainted damping patch behavior. Finally, an inverse method, allowing the identification of the properties of viscoelastic materials, based on a combination of the presented model and a genetic algorithm, shows a possible application of the model.DIJON-BU Doc.électronique (212319901) / SudocSudocFranceF

Measurement of jet-substructure observables in top quark, W boson and light jet production in proton-proton collisions at √s=13 TeV with the ATLAS detector

A measurement of jet substructure observables is presented using data collected in 2016 by the ATLAS experiment at the LHC with proton-proton collisions at s√ = 13 TeV. Large-radius jets groomed with the trimming and soft-drop algorithms are studied. Dedicated event selections are used to study jets produced by light quarks or gluons, and hadronically decaying top quarks and W bosons. The observables measured are sensitive to substructure, and therefore are typically used for tagging large-radius jets from boosted massive particles. These include the energy correlation functions and the N-subjettiness variables. The number of subjets and the Les Houches angularity are also considered. The distributions of the substructure variables, corrected for detector effects, are compared to the predictions of various Monte Carlo event generators. They are also compared between the large-radius jets originating from light quarks or gluons, and hadronically decaying top quarks and W bosons

Two multilayered plate models with transverse shear warping functions issued from three dimensional elasticity equations

International audienceA multilayered plate theory which uses transverse shear warping functions issued from three-dimensional elasticity is presented. Two methods to obtain these transverse shear warping functions are detailed. The warping functions are issued from the variations of transverse shear stresses computed at special location points for a simply supported bending problem. The first method considers an exact 3D solution of the problem. The second method uses the solution provided by the model itself: the transverse shear stresses are computed by the integration of equilibrium equations. Hence, an iterative process is applied, the model being updated with the new warping functions, and so on. These two models are compared to other models and to analytical solutions for the bending of simply supported plates. Four different laminates and a sandwich are considered, length-to-thickness values varying from 2 to 100. An additional analytical solution that simulates the behavior of laminates under the plane stress hypothesis - which is retained by all presented models - shows that the iterative model almost gives the exact solution for all laminates and all length-to-thickness ratio values