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Dissertations / Theses on the topic 'Elastodynamics'
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Rachele, Lizabeth. "An inverse problem in elastodynamics /." Thesis, Connect to this title online; UW restricted, 1996. http://hdl.handle.net/1773/5735.
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Gross, Michael. "Conserving time integrators for nonlinear elastodynamics." [S.l.] : [s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=970706081.
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Hopman, Ryan. "Aribitrary geometry cellular automata for elastodynamics." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29742.
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Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2010.<br>Committee Chair: Dr. Michael Leamy; Committee Member: Dr. Karim Sabra; Committee Member: Dr. Aldo Ferri. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Pramanik, Ramkrishna. "Some crack and inclusion problem in Elastodynamics." Thesis, University of North Bengal, 2001. http://hdl.handle.net/123456789/644.
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Das, Apurba Narayan. "Some boundary value problems in linear elastodynamics." Thesis, University of North Bengal, 1993. http://hdl.handle.net/123456789/630.
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Pal, Subhas Chandra. "Some extended source and crack problems in elastodynamics." Thesis, University of North Bengal, 1996. http://hdl.handle.net/123456789/632.
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Mandal, Subhas Chandra. "Some mixed boundary value problems in elastodynamics." Thesis, University of North Bengal, 1992. http://hdl.handle.net/123456789/628.
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Mahinzaeim, Mahyar. "Feedback control and stabilisability in problems of elastodynamics." Thesis, University of Newcastle upon Tyne, 2013. http://hdl.handle.net/10443/3064.
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Isakari, Hiroshi. "Periodic FMMs and Calderon's preconditioning in acoustics and elastodynamics." 京都大学 (Kyoto University), 2012. http://hdl.handle.net/2433/157517.
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He, Lisha. "Improvement and application of smoothed particle hydrodynamics in elastodynamics." Thesis, Durham University, 2015. http://etheses.dur.ac.uk/11314/.
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This thesis explores the mesh-free numerical method, Smooth Particle Hydrodynamics (SPH), presents improvements to the algorithm and studies its application in solid mechanics problems. The basic concept of the SPH method is introduced and the governing equations are discretised using the SPH method to simulate the elastic solid problems. Special treatments are discussed to improve the stability of the method, such as the treatment for boundary problems, artificial viscosity and tensile instability. In order to improve the stability and efficiency, (i) the classical SPH method has been combined with the Runge-Kutta Chebyshev scheme and (ii) a new time-space Adaptive Smooth Particle Hydrodynamics (ASPH) algorithm has been developed in this thesis. The SPH method employs a purely meshless Lagrangian numerical technique for spatial discretisation of the domain and it avoids many numerical difficulties related to re-meshing in mesh-based methods such as the finite element method. The explicit Runge-Kutta Chebyshev (RKC) scheme is developed to accurately capture the dynamics in elastic materials for the SPH method in the study. Numerical results are presented for several test examples applied by the RKC-SPH method compared with other different time stepping scheme. It is found that the proposed RKC scheme offers a robust and accurate approach for solving elastodynamics using SPH techniques. The new time-space ASPH algorithm which is combining the previous ASPH method and the RKC schemes can achieve not only the adaptivity of the particle distribution during the simulation, but also the adaptivity of the number of stage in one fixed time step. Numerical results are presented for a shock wave propagation problem using the time-space ASPH method compared with the analytical solution and the results of standard SPH. It is found that using the dynamic adaptive particle refinement procedure with adequate refinement criterion, instead of adopting a fine discretisation for the whole domain, can achieve a substantial reduction in memory and computational time, and similar accuracy is achieved.
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Mazzieri, Ilario. "Non-conforming high order methods for the elastodynamics equation." Nice, 2012. http://www.theses.fr/2012NICE4014.
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Dans cette thèse, on présente une nouvelle approche de discrétization qui combine les méthodes aux éléments spectraux Discontinuous Galerkin (DGSE) and Mortar (MSE) avec des méthodes convenables de discretization en temps pour la simulation de la propagation des ondes élastiques dans les milieux hétérogènes. Pour surmonter les limites des approches existantes on applique le paradigme non conforme au niveau des sous domaines. On montre que les formulations obtenues sont stables, ont des propriétés d’approximation optimales, et souffrent d’erreurs de dispersion et dissipation négligeables. Les méthodes DGSE et MSE sont finalement utilisées pour résoudre de vrais problèmes sismiques dans des domaines tridimensionnels<br>In this thesis, we present a new discretization approach to combine the Discontinuous Galerkin Spectral Element (DGSE) and the Mortar Spectral Element (MSE) methods with suitable time advancing schemes for the simulation of the elastic wave propagation in heterogeneous media. To overcome the limitations of the existing approaches we apply the non-conforming paradigm only at the subdomain level. We show that the resulting formulations are stable, enjoy optimal approximation properties, and suffer from low dispersion and dissipation errors. Applications of the DGSE and MSE methods to simulate realistic seismic wave propagation problems in three dimensions are also considered
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Korkut, Fuat. "Generalized Finite Difference Method In Elastodynamics Using Perfectly Matched Layer." Phd thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614476/index.pdf.
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This study deals with the use of the generalized finite difference method (GFDM) in perfectly matched layer (PML) analysis of the problems in wave mechanics, in particular, in elastodynamics. It is known that PML plays the role of an absorbing layer, for an unbounded domain, eliminating reflections of waves for all directions of incidence and frequencies. The study is initiated for purpose of detecting any possible advantages of using GFDM in PML analysis: GFDM is a meshless method suitable for any geometry of the domain, handling the boundary conditions properly and having an easy implementation for PML analysis. In the study, first, a bounded 2D fictitious plane strain problem is solved by GFDM to determine its appropriate parameters (weighting function, radius of influence, etc.). Then, a 1D semi-infinite rod on elastic foundation is considered to estimate PML parameters for GFDM. Finally, the proposed procedure, that is, the use of GFDM in PML analysis, is assessed by considering the compliance functions (in frequency domain) of surface and embedded rigid strip foundations. The surface foundation is assumed to be supported by three types of soil medium: rigid strip foundation on half space (HS), on soil layer overlying rigid bedrock, and on soil layer overlying HS. For the embedded rigid strip foundation, the supporting soil medium is taken as HS. In addition of frequency space analyses stated above, the direct time domain analysis is also performed for the reaction forces of rigid strip foundation over HS. The results of GFDM for both frequency and time spaces are compared with those of finite element method (FEM) with PML and boundary element method (BEM), when possible, also with those of other studies. The excellent matches observed in the results show the reliability of the proposed procedure in PML analysis (that is, of using GFDM in PML analysis).
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Franke, Marlon [Verfasser]. "Discretisation techniques for large deformation computational contact elastodynamics / Marlon Franke." Karlsruhe : KIT Scientific Publishing, 2014. http://www.ksp.kit.edu.
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Desiderio, Luca. "H-matrix based Solver for 3D Elastodynamics Boundary Integral Equations." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLY002/document.
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Cette thèse porte sur l'étude théorique et numérique des méthodes rapides pour résoudre les équations de l'élastodynamique 3D en domaine fréquentiel, et se place dans le cadre d'une collaboration avec la société Shell en vue d'optimiser la convergence des problèmes d'inversion sismique. La méthode repose sur l'utilisation des éléments finis de frontière (BEM) pour la discrétisation et sur les techniques de matrices hiérarchiques (H-matrices) pour l'accélération de la résolution du système linéaire. Dans le cadre de cette thèse on a développé un solveur direct pour les BEMs en utilisant une factorisation LU et un stockage hiérarchique. Si le concept des H-matrices est simple à comprendre, sa mise en oeuvre requiert des développements algorithmiques importants tels que la gestion de la multiplication de matrices représentées par des structures différentes (compressées ou non) qui ne comprend pas mois de 27 sous-cas. Un autre point délicat est l'utilisation des méthodes d'approximations par matrices compressées (de rang faible) dans le cadre des problèmes vectoriels. Une étude algorithmique a donc été faite pour mettre en oeuvre la méthode des H-matrices. Nous avons par ailleurs estimé théoriquement le rang faible attendu pour les noyaux oscillants, ce qui constitue une nouveauté, et montré que la méthode est utilisable en élastodynamique. En outre on a étudié l'influence des divers paramètres de la méthode en acoustique et en élastodynamique 3D, à fin de calibrer leur valeurs numériques optimales. Dans le cadre de la collaboration avec Shell, un cas test spécifique a été étudié. Il s'agit d'un problème de propagation d'une onde sismique dans un demi-espace élastique soumis à une force ponctuelle en surface. Enfin le solveur direct développé a été intégré au code COFFEE développé a POEMS (environ 25000 lignes en Fortran 90)<br>This thesis focuses on the theoretical and numerical study of fast methods to solve the equations of 3D elastodynamics in frequency-domain. We use the Boundary Element Method (BEM) as discretization technique, in association with the hierarchical matrices (H-matrices) technique for the fast solution of the resulting linear system. The BEM is based on a boundary integral formulation which requires the discretization of the only domain boundaries. Thus, this method is well suited to treat seismic wave propagation problems. A major drawback of classical BEM is that it results in dense matrices, which leads to high memory requirement (O (N 2 ), if N is the number of degrees of freedom) and computational costs.Therefore, the simulation of realistic problems is limited by the number of degrees of freedom. Several fast BEMs have been developed to improve the computational efficiency. We propose a fast H-matrix based direct BEM solver
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Desiderio, Luca. "H-matrix based Solver for 3D Elastodynamics Boundary Integral Equations." Electronic Thesis or Diss., Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLY002.
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Cette thèse porte sur l'étude théorique et numérique des méthodes rapides pour résoudre les équations de l'élastodynamique 3D en domaine fréquentiel, et se place dans le cadre d'une collaboration avec la société Shell en vue d'optimiser la convergence des problèmes d'inversion sismique. La méthode repose sur l'utilisation des éléments finis de frontière (BEM) pour la discrétisation et sur les techniques de matrices hiérarchiques (H-matrices) pour l'accélération de la résolution du système linéaire. Dans le cadre de cette thèse on a développé un solveur direct pour les BEMs en utilisant une factorisation LU et un stockage hiérarchique. Si le concept des H-matrices est simple à comprendre, sa mise en oeuvre requiert des développements algorithmiques importants tels que la gestion de la multiplication de matrices représentées par des structures différentes (compressées ou non) qui ne comprend pas mois de 27 sous-cas. Un autre point délicat est l'utilisation des méthodes d'approximations par matrices compressées (de rang faible) dans le cadre des problèmes vectoriels. Une étude algorithmique a donc été faite pour mettre en oeuvre la méthode des H-matrices. Nous avons par ailleurs estimé théoriquement le rang faible attendu pour les noyaux oscillants, ce qui constitue une nouveauté, et montré que la méthode est utilisable en élastodynamique. En outre on a étudié l'influence des divers paramètres de la méthode en acoustique et en élastodynamique 3D, à fin de calibrer leur valeurs numériques optimales. Dans le cadre de la collaboration avec Shell, un cas test spécifique a été étudié. Il s'agit d'un problème de propagation d'une onde sismique dans un demi-espace élastique soumis à une force ponctuelle en surface. Enfin le solveur direct développé a été intégré au code COFFEE développé a POEMS (environ 25000 lignes en Fortran 90)<br>This thesis focuses on the theoretical and numerical study of fast methods to solve the equations of 3D elastodynamics in frequency-domain. We use the Boundary Element Method (BEM) as discretization technique, in association with the hierarchical matrices (H-matrices) technique for the fast solution of the resulting linear system. The BEM is based on a boundary integral formulation which requires the discretization of the only domain boundaries. Thus, this method is well suited to treat seismic wave propagation problems. A major drawback of classical BEM is that it results in dense matrices, which leads to high memory requirement (O (N 2 ), if N is the number of degrees of freedom) and computational costs.Therefore, the simulation of realistic problems is limited by the number of degrees of freedom. Several fast BEMs have been developed to improve the computational efficiency. We propose a fast H-matrix based direct BEM solver
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Mbanga, Badel L. "HYBRID PARTICLE-FINITE ELEMENT ELASTODYNAMICS SIMULATIONS OF NEMATIC LIQUID CRYSTAL ELASTOMERS." Kent State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=kent1334607477.
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Chatzis, Ilias. "Boundary integral equation method in transient elastodynamics : techniques to reduce computational costs." Thesis, Imperial College London, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249633.
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Kitahara, Michihiro. "Boundary integral equation methods in eigenvalue problems of elastodynamics and thin plates /." Amsterdam ; New York : Elsevier, 1985. http://catalog.hathitrust.org/api/volumes/oclc/11650624.html.
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Miao, Jinghong. "Linear and nonlinear inverse scattering algorithms applied in 2-D electromagnetics and elastodynamics /." Kassel : Kassel Univ. Press, 2008. http://d-nb.info/989004627/04.
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Zhou, Joseph Xu. "An adaptive space-time boundary element method for impulsive wave propagation in elastodynamics." Thesis, University of Glasgow, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.443409.
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Yu, Peng. "Isogeometric analysis with local adaptivity based on a posteriori error estimation for elastodynamics." Thesis, Cardiff University, 2019. http://orca.cf.ac.uk/119867/.
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IsoGeometric Analysis (IGA) was invented to integrate the Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE) into a unified process. According to the recent research, IGA performs a super convergence in case of vibration, and especially, it perfectly addresses the Gibbs phenomenon (fluctuation) occurring in discrete spectra when using standard Finite Element Method (FEM). However, due to the tensor-product structure of Non-Uniform Rational B-Splines (NURBS), it fails to achieve the local refinement, which restricts its application to engineering fields performing local characteristics that require local refinement, such as sharp geometrical feature and/or varying material properties. In this context, the first goal of thesis is to extend the recently proposed paradigm, called Geometry Independent Field approximaTion (GIFT), to be applied in the scheme of dynamics. The GIFT methodology allows geometry of structure to be described within the NURBS provided directly by the existing CAD software, and solution field to be approximated by the Polynomial splines over Hierarchical Tmeshes (PHT) with the feature of local refinement meanwhile. Subsequently, in the framework of GIFT, an adaptivity technique based on hierarchical a posteriori error estimation on the modal vector is established for the free vibration of thick plate. The proposed adaptive mesh achieves a faster convergence than uniform refinement. Especially, the employment of Modal Assurance Criterion (MAC)-style strategy is able to better determine the modal correspondence between coarse and fine discretizations than Frequency Error Criterion (FEC) method. Furthermore, based on hierarchical a posteriori error estimation strategy, three types of adaptivity algorithms are constructed to deal with the space-time refinement. Specially, unidirectional multi-level space-time adaptive GIFT/Newmark (UM-STAGN) well catches stress wave propagation but fails in error information transfer. Energybased space-time adaptive GIFT/Newmark (E-STAGN) can reassess the error but cannot uncover the source of error. Dual weighted residual adaptive GIFT/Newmark (DWR-STAGN) methods are error-sensitive so that it leads to the best convergence among these three approaches.
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Fang, Chih. "A reduced-order meshless energy (ROME) model for the elastodynamics of mistuned bladed disks." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/12457.
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Lowe, Robert Lindsey. "Finite-Deformation Modeling of Elastodynamics and Smart Materials with Nonlinear Electro-Magneto-Elastic Coupling." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1433276487.
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Miao, Jinghong [Verfasser]. "Linear and Nonlinear Inverse Scattering Algorithms Applied in 2-D Electromagnetics and Elastodynamics / Miao Jinghong." Kassel : Kassel University Press, 2008. http://d-nb.info/1006916105/34.
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Nassar, Hussein. "Elastodynamic homogenization of periodic media." Thesis, Paris Est, 2015. http://www.theses.fr/2015PESC1151/document.
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La problématique récente de la conception de métamatériaux a renouvelé l'intérêt dans les théories de l'homogénéisation en régime dynamique. En particulier, la théorie de l'homogénéisation élastodynamique initiée par J.R. Willis a reçu une attention particulière suite à des travaux sur l'invisibilité élastique. La présente thèse reformule la théorie de Willis dans le cas des milieux périodiques, examine ses implications et évalue sa pertinence physique au sens de quelques ``conditions d'homogénéisabilité'' qui sont suggérées. En se basant sur les résultats de cette première partie, des développements asymptotiques approximatifs de la théorie de Willis sont explorés en relation avec les théories à gradient. Une condition nécessaire de convergence montre alors que toutes les branches optiques de la courbe de dispersion sont omises quand des développements asymptotiques de Taylor de basse fréquence et de longue longueur d'onde sont déployés. Enfin, une nouvelle théorie de l'homogénéisation est proposée. On montre qu'elle généralise la théorie de Willis et qu'elle l'améliore en moyenne fréquence de sorte qu'on retrouve certaines branches optiques omises auparavant. On montre également que le milieu homogène effectif défini par la nouvelle théorie est un milieu généralisé dont les champs satisfont une version élastodynamique généralisée du lemme de Hill-Mandel<br>The recent issue of metamaterials design has renewed the interest in homogenization theories under dynamic loadings. In particular, the elastodynamic homogenization theory initiated by J.R. Willis has gained special attention while studying elastic cloaking. The present thesis reformulates Willis theory for periodic media, investigates its outcome and assesses its physical suitability in the sense of a few suggested ``homogenizability conditions''. Based on the results of this first part, approximate asymptotic expansions of Willis theory are explored in connection with strain-gradient media. A necessary convergence condition then shows that all optical dispersion branches are lost when long-wavelength low-frequency Taylor asymptotic expansions are carried out. Finally, a new homogenization theory is proposed to generalize Willis theory and improve it at finite frequencies in such a way that selected optical branches, formerly lost, are recovered. It is also proven that the outcome of the new theory is an effective homogeneous generalized continuum satisfying a generalized elastodynamic version of Hill-Mandel lemma
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Chehade, Samar. "Modelling of the 3D scattering of elastic waves by complex structures for specimen echoes calculation. Application to ultrasonic NDT simulation." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLS273/document.
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Le sujet de la thèse s’inscrit dans le cadre du développement de modèles pour la simulation du contrôle non-destructif (CND) par ultrasons. L'objectif à long terme est la mise au point, par une méthode de rayons, d’un outil complet de simulation des échos issus de la géométrie (surfaces d’entrée, de fond…) ou des structures internes des pièces inspectées. La thèse vise plus précisément à intégrer le phénomène de diffraction par les dièdres à un modèle existant dérivant de l’acoustique géométrique et qui prend uniquement en compte les réflexions sur les faces.Pour cela, la méthode dite des fonctions spectrales, développée initialement pour le cas d'un dièdre immergé, est développée et validée dans un premier temps dans le cas des ondes acoustiques pour des conditions aux limites de type Dirichlet ou Neumann. La méthode est ensuite étendue à la diffraction des ondes élastiques par des dièdres infinis à faces libres et d'angles quelconques, pour une incidence 2D puis pour une incidence 3D. Cette méthode est semi-analytique puisque les solutions recherchées s'écrivent sous la forme d'une somme d'une fonction singulière, qui est déterminée analytiquement à l'aide d'un algorithme récursif, et d'une fonction régulière, qui est approchée numériquement.Les codes correspondants sont validés par comparaison à une solution exacte dans le cas acoustique et par comparaison à d'autres codes (semi-analytiques et numériques) dans le cas élastique. Des validations expérimentales du modèle élastodynamique sont également proposées<br>This thesis falls into the framework of model development for simulation of ultrasonic non-destructive testing (NDT). The long-term goal is to develop, using ray methods, a complete simulation tool of specimen echoes (input, back-wall surfaces...) or echoes of inner structures of inspected parts. The thesis aims more specifically to integrate the phenomenon of diffraction by wedges to an existing model derived from geometrical acoustics, which only accounts for reflections on the wedge faces.To this end, a method called the spectral functions method, which was initially developed for immersed wedges, is developed and validated as a first step in the case of acoustic waves with Dirichlet or Neumann boundary conditions. The method is then extended to elastic wave diffraction by infinite stress-free wedges of arbitrary angles, for 2D and 3D incidences. This method is semi-analytic since the unknown solutions are expressed as the sum of a singular function, determined analytically using a recursive algorithm, and a regular function which is approached numerically.The corresponding codes are validated by comparison to an exact solution in the acoustic case and by comparison to other codes (semi-analytic and numerical) in the elastic case. Experimental validations of the elastodynamic model are also proposed
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Baker, Christopher E. "The effect of transient dynamics of the internal combustion compression ring upon its tribological performance." Thesis, Loughborough University, 2014. https://dspace.lboro.ac.uk/2134/14068.
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The losses in an internal combustion engine are dominated by thermal and parasitic sources. The latter arises from mechanical inefficiencies inherent within the system, particularly friction in load bearing conjunctions such as the piston assembly. During idle and at low engine speeds, frictional losses are the major contributor to the overall engine losses as opposed to the dominant contribution of thermal losses under other driving conditions. Given the relatively small size and simple structure of the top compression ring, it has a disproportionate contribution to the total frictional losses. This suggests further analysis would be required to understand the underlying causes of compression ring behaviour throughout the engine cycle. The available literature on tribological analyses of compression rings does not account for the transient ring elastodynamics. They usually assume a rigid ring for film thickness and power loss predictions, which is not representative of the ring's dynamic response. A combined study of ring elastodynamic behaviour and its tribological conjunction is a comprehensive approach.
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Rieger, Marc Oliver. "Nonconvex Dynamical Problems." Doctoral thesis, Universitätsbibliothek Leipzig, 2004. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-37269.
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Many problems in continuum mechanics, especially in the theory of elastic materials, lead to nonlinear partial differential equations. The nonconvexity of their underlying energy potential is a challenge for mathematical analysis, since convexity plays an important role in the classical theories of existence and regularity. In the last years one main point of interest was to develop techniques to circumvent these difficulties. One approach was to use different notions of convexity like quasi-- or polyconvexity, but most of the work was done only for static (time independent) equations. In this thesis we want to make some contributions concerning existence, regularity and numerical approximation of nonconvex dynamical problems.
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Guerder, Pierre-Yves. "Theoretical and Numerical Study of Nonlinear Phononic Crystals." Diss., The University of Arizona, 2015. http://hdl.handle.net/10150/555837.
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This work is dedicated to the theoretical and numerical study of nonlinear phononic crystals. The studied nonlinearities are those due to the second (quadratic) and third (cubic) order elastic constants of the materials that constitute the crystals. Nonlinear effects are studied by the means of finite element methods, used to simulate the propagation of an elastic wave through the crystals. A first research project concerns the study of a bone structure, namely the dispersion of elastic waves in a structure composed of collagen and hydroxy apatite alternate constituent layers. Simulations showed that it exists a strong link between bones hydration and their ability to dissipate the energy. The second study relates to an elastic resonator. A structure composed of steel inclusions in a silica matrix shows a switch behavior when the cubic nonlinearities of steel are taken into account. This strong nonlinear effect appears when the amplitude of the incident wave reaches a threshold. A full analytical model is provided. The last study demonstrates the design of composite materials with both strong cubic nonlinearities and weak quadratic nonlinearities. The derivation of the mixing laws of the elastic parameters of a nonlinear material inside a linear one is performed up to order three. Equations show a strong amplification of the nonlinear parameters of the material for some concentrations. Numerical simulations allow to conclude that the above mentioned resonator can be produced. For this thesis, an innovative tool based on the Discontinuous Galerkin (DG) finite element method is developed for the simulation of elastic wave propagation, in linear and nonlinear systems and in finite and semi-infinite media. The implementation of this DG code for 2D and 3D simulations benefits from the efficient exploitation of modern computer infrastructure (GPU units, clusters) using the property of massive parallelization of DG algorithms. This thesis is part of a joint agreement for an international Ph.D. degree between École Centrale de Lille and the Materials Science and Engineering department of the University of Arizona at Tucson.
Ce travail porte sur l'étude théorique et numérique des cristaux phononiques non-linéaires. Les non-linéarités étudiées sont celles dues aux constantes élastiques d'ordre deux (quadratiques) et trois (cubiques) des matériaux constituant les cristaux. Les effets non-linéaires sont étudiés grâce á des méthodes d'éléments finis en simulant la propagation d'une onde élastique á travers les cristaux. Un premier projet de recherche a porté sur l'étude d'une structure osseuse, et plus spécifiquement sur la dispersion des ondes élastiques dans une structure constituée d'une alternance de couches de collagène et d'hydroxy apatite. Les simulations montrent qu'il existe un lien étroit entre l'hydratation des os et leur capacité à dissiper l'énergie. La seconde étude réalisée concerne un résonateur élastique. Une structure constituée d'inclusions d'acier dans de la silice présente un comportement de commutateur (switch) lorsque les non-linéarités cubiques de l'acier sont prises en compte. Cet effet fortement non-linéaire apparaît lorsque l'amplitude de l'onde incidente dépasse un certain seuil. Un modèle analytique complet est fourni. La dernière étude réalisée montre la conception de matériaux composites possédant de fortes non-linéarités cubiques mais de faibles non-linéarités quadratiques. La dérivation des lois de mélange des paramètres élastiques d'un matériau non-linéaire dans un matériau linéaire est effectuée à l'ordre trois. Les équations montrent une forte amplification des paramètres non-linéaires du matériau résultant pour certaines concentrations. Les simulations permettent de conclure que le résonateur mentionné ci-dessus peut effectivement étre réalisé. Pour cette thèse, un outil numérique innovant basé sur la méthode des éléments finis de type Galerkin Discontinu (DG) est développé pour la simulation de la propagation d'ondes élastiques, dans des systèmes linéaires et non-linéaires et dans des milieux finis et semi-infinis. L'implémentation de ce code DG pour des simulations 2D et 3D tire parti des infrastructures de calcul actuelles (processeurs graphiques, clusters) grâce à la propriété de parallélisation massive des algorithmes DG. Cette thèse s'est déroulée dans le cadre d'une cotutelle entre l'École Centrale de Lille et le département de Science et ingénierie des matériaux de l'Université d'Arizona, à Tucson.
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Dang, Tran Thang. "Méthodes numériques pour l’homogénéisation élastodynamique des matériaux hétérogènes périodiques." Thesis, Paris Est, 2015. http://www.theses.fr/2015PEST1046/document.
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La théorie d'homogénéisation élastodynamique des matériaux hétérogènes initiée par J.R. Willis il y a environ une trentaine d'années a récemment reçu une très grande attention. D'après cette théorie qui est mathématiquement exacte, la loi constitutive homogénéisée est non locale en espace et en temps ; le tenseur des contraintes dépend non seulement du tenseur des déformations mais aussi de la vitesse ; la quantité du mouvement dépend à la fois de la vitesse et du tenseur des déformations, faisant apparaître en général une masse anisotrope. Ces propriétés constitutives effectives, qui pourraient être surprenantes d'un point de vue mécanique classique, se révèlent en fait très utiles pour la conception de métamatériaux acoustiques et de capes acoustiques. Ce travail de thèse consiste essentiellement à proposer et développer deux méthodes numériques efficaces pour déterminer les propriétés élastodynamiques effectives des matériaux périodiquement hétérogènes. La première méthode relève de la méthode des éléments finis alors que la deuxième méthode est basée sur la transformée de Fourier rapide. Ces deux méthodes sont d'abord élaborées pour une microstructure périodique 3D quelconque et ensuite implantées pour une microstructure périodique 2D quelconque. Les avantages et les inconvénients de chacune de ces deux méthodes sont comparés et discutés. A l'aide des méthodes numériques élaborées, la théorie de Willis est appliquée au calcul élastodynamique sur un milieu infini hétérogène et celui homogénéisé. Les différents cas d'homogénéisabilité et de non-homogénéisabilité sont discutés<br>The elastodynamic homogenization theory of heterogeneous materials initiated by J.R. Willis about thirty years ago has recently received considerable attention. According to this theory which is mathematically exact, the homogenized constitutive law is non-local in space and time; the stress tensor depends not only on the strain tensor but also on the velocity; the linear momentum depends on both the velocity and the strain tensor, making appear an anisotropic mass tensor in general. These effective constitutive properties, which may be surprising from a classical mechanical point of view, turn out in fact to be very useful for the design of acoustic metamaterials and acoustic cloaks. The present work is essentially to propose and develop two efficient numerical methods for determining the effective elastodynamic properties of periodically heterogeneous materials. The first method belongs to the finite element method while the second method is based on the fast Fourier transform. These two methods are first developed for any 3D periodic microstructure and then implanted for any 2D periodic microstructure. The advantages and disadvantages of each of these two methods are compared and discussed. Using the elaborated numerical methods, the Willis theory is applied to the elastodynamic computation over the infinite heterogeneous medium and the homogenized one. The various cases of homogeneisability and non-homogeneisability are discussed
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Mehta, Harsh. "Elastodynamic Analysis of Vehicle Suspension Uprights." Thesis, Virginia Tech, 2018. http://hdl.handle.net/10919/83531.
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The ability of a Formula SAE sports car to negotiate a turn in a race is influenced by many parameters which include car's overall geometry, its shape, weight distribution, type of suspension used, spring and shock absorber characteristics that are used in the tire properties, static and dynamic loading. Steady-state cornering implies that the forces acting on the vehicle are unchanging for a given time. The suspension uprights form a connection between the wheel assembly and the suspension linkages. The criticality of the upright is that it is considered an un-suspended body, but in fact, it is subjected to very high stresses. The dynamic load imposed on the vehicle from various road conditions, cornering, braking and suspension assembly constraints generate stress on the upright body.
The equations of motion generally govern vehicle dynamics. For a kinematic and rigid body dynamics analysis, a multibody dynamics (MBD) approach is popular. The results of the dynamic analysis yield internal loads which are used to analyze suspension components for structural stiffness and strength. Automotive companies with relatively lower structural loads have made the MBD approach popular because it is supposed to be computationally less expensive. Elastodynamics is an alternative approach to solving dynamics equations while considering the components to be elastic. This approach can capture the inertial and elastic responses of the components and the load path with varying positions of the components in a mechanism.
In this research, a quarter-car suspension is modeled in a finite element code (Abaqus®), focusing on the vehicle upright but still modeling the connections and interactions of the quarter-car suspension system of a FSAE vehicle. The BEAM element modeling used for the suspension members captures the bending response. The overall model is created by making computationally conscious decisions, debugging and refining the interactions and connections to be representative. The modeling technique to create elastodynamic models is explored and established with a versatile set of suspension components and interactions providing a good experience with finite element modeling. The models are created with incremental steps and early steps are verified with hand calculations. A further vehicle verification and validation plan is the next immediate priority to gain confidence in the model for accurate simulations which can be used to predict accurate structural and dynamic results. With extending the model capabilities and computational capabilities, a quarter-car suspension model is powerful enough to run the entire track simulations for formula races and even durability load cases for commercial vehicles. Fatigue loading and abusive test cases would be the load cases to investigate possible failure modes.
The quarter-car suspension model is a framework with different interactions, connections, components, boundary conditions and loads that are representative for different suspension configurations in different vehicles. The best practices of this modeling exercise are established and scalability to defeature or add details while preserving the connection behavior is achieved.<br>Master of Science
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Chang, O. V. "Boundary elements applied to three dimensional elastodynamic problems." Thesis, University of Southampton, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.373572.
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Athale, Madhura Athale. "Elastodynamic Characterization of Material Interfaces Using Spring Models." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1503262542890538.
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Cornaggia, Rémi. "Développement et utilisation de méthodes asymptotiques d'ordre élevé pour la résolution de problèmes de diffraction inverse." Electronic Thesis or Diss., Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLY012.
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L'objectif de ce travail fut le développement de nouvelles méthodes pour aborder certains problèmes inverses en élasticité, en tirant parti de la présence d'un petit paramètre dans ces problèmes pour construire des approximation asymptotiques d'ordre élevé. La première partie est consacrée à l'identification de la taille et la position d'une inhomogénéité Bᵗʳᵘᵉ enfouie dans un domaine élastique tridimensionnel. Nous nous concentrons sur l'étude de fonctions-coûts ��(Bₐ) quantifiant l'écart entre Bᵗʳᵘᵉ et une hétérogénéité ``test'' Bₐ. Une telle fonction-coût peut en effet être minimisée par rapport à tout ou partie des caractéristiques de l'inclusion ``test'' Bₐ (position, taille, propriétés mécaniques ...) pour établir la meilleure correspondance possible entre Bₐ et Bᵗʳᵘᵉ. A cet effet, nous produisons un développement asymptotique de �� en la taille a de Bₐ, qui en constitue une approximation polynomiale plus aisée à minimiser. Ce développement, établi jusqu'à l'ordre O(a⁶), est justifié par une estimation du résidu. Une méthode d'identification adaptée est ensuite présentée et illustrée par des exemples numériques portant sur des obstacles de formes simples dans l'espace libre ℝ³.L'objet de la seconde partie est de caractériser une inclusion microstructurée de longueur L, modélisée en une dimension, composée de couches de deux matériaux alternés périodiquement, en supposant que les plus basses de ses fréquences propres de transmission (TEs) sont connues. Ces fréquences sont les valeurs propres d'un problème dit de transmission intérieur (ITP). Afin de disposer d'un modèle propice à l'inversion, tout en prenant en compte les effets de la microstructure, nous nous reposons sur des approximations de l'ITP exact obtenues par homogénéisation. A partir du modèle homogénéisé d'ordre 0, nous établissons tout d'abord une méthode simple pour déterminer les paramètres macroscopiques (L et contrastes matériaux)d'une telle inclusion. Pour avoir accès à la période de la microstructure, nous nous intéressons ensuite à des modèles homogénéisés d'ordre élevé, pour lesquels nous soulignons le besoin de conditions aux limites adaptées<br>The purpose of this work was to develop new methods to address inverse problems in elasticity,taking advantage of the presence of a small parameter in the considered problems by means of higher-order asymptoticexpansions.The first part is dedicated to the localization and size identification of a buried inhomogeneity Bᵗʳᵘᵉ in a 3Delastic domain. In this goal, we focused on the study of functionals ��(Bₐ) quantifying the misfit between Bᵗʳᵘᵉ and a trial homogeneity Bₐ. Such functionals are to be minimized w.r.t. some or all the characteristics of the trial inclusion Bₐ (location, size, mechanical properties ...) to find the best agreement with Bᵗʳᵘᵉ. To this end, we produced an expansion of �� with respect to the size a of Bₐ, providing a polynomial approximation easier to minimize. This expansion, established up to O(a⁶) in a volume integral equations framework, is justified by an estimate of the residual. A suited identification procedure is then given and supported by numerical illustrations for simple obstacles in full-space ℝ³.The main purpose of this second part is to characterize a microstructured two-phases layered1D inclusion of length L, supposing we already know its low-frequency transmission eigenvalues (TEs). Those are computed as the eigen values of the so-called interior transmission problem (ITP). To provide a convenient invertible model, while accounting for the microstructure effects, we then relied on homogenized approximations of the exact ITP for the periodic inclusion. Focusing on the leading-order homogenized ITP, we first provide a straightforward method tore cover the macroscopic parameters (L and material contrast) of such inclusion. To access to the period of themicrostructure, higher-order homogenization is finally addressed, with emphasis on the need for suitable boundary conditions
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Zhuang, Wei. "Numerical modeling for elastodynamic problems in laminated composite cylinders." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ35049.pdf.
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Cho, Hwankee. "Elastodynamic thermal shock stresses in orthotropic thick cylindrical shells." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/12357.
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Aannaque, Abdeslam. "Kineto-elastodynamic analysis of high-speed four-bar mechanism." Thesis, Aston University, 1996. http://publications.aston.ac.uk/15261/.
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This thesis addresses the kineto-elastodynamic analysis of a four-bar mechanism running at high-speed where all links are assumed to be flexible. First, the mechanism, at static configurations, is considered as structure. Two methods are used to model the system, namely the finite element method (FEM) and the dynamic stiffness method. The natural frequencies and mode shapes at different positions from both methods are calculated and compared. The FEM is used to model the mechanism running at high-speed. The governing equations of motion are derived using Hamilton's principle. The equations obtained are a set of stiff ordinary differential equations with periodic coefficients. A model is developed whereby the FEM and the dynamic stiffness method are used conjointly to provide high-precision results with only one element per link. The principal concern of the mechanism designer is the behaviour of the mechanism at steady-state. Few algorithms have been developed to deliver the steady-state solution without resorting to costly time marching simulation. In this study two algorithms are developed to overcome the limitations of the existing algorithms. The superiority of the new algorithms is demonstrated. The notion of critical speeds is clarified and a distinction is drawn between "critical speeds", where stresses are at a local maximum, and "unstable bands" where the mechanism deflections will grow boundlessly. Floquet theory is used to assess the stability of the system. A simple method to locate the critical speeds is derived. It is shown that the critical speeds of the mechanism coincide with the local maxima of the eigenvalues of the transition matrix with respect to the rotational speed of the mechanism.
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Fooladi, Samaneh, and Samaneh Fooladi. "Numerical Implementation of Elastodynamic Green's Function for Anisotropic Media." Thesis, The University of Arizona, 2016. http://hdl.handle.net/10150/623144.
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Displacement Green's function is the building block for some semi-analytical methods like Boundary Element Method (BEM), Distributed Point Source Method (DPCM), etc. In this thesis, the displacement Green`s function in anisotropic media due to a time harmonic point force is studied. Unlike the isotropic media, the Green's function in anisotropic media does not have a closed form solution. The dynamic Green's function for an anisotropic medium can be written as a summation of singular and non-singular or regular parts. The singular part, being similar to the result of static Green's function, is in the form of an integral over an oblique circular path in 3D. This integral can be evaluated either by a numerical integration technique or can be converted to a summation of algebraic terms via the calculus of residue. The other part, which is the regular part, is in the form of an integral over the surface of a unit sphere. This integral needs to be evaluated numerically and its evaluation is considerably more time consuming than the singular part. Obtaining dynamic Green's function and its spatial derivatives involves calculation of these two types of integrals. The spatial derivatives of Green's function are important in calculating quantities like stress and stain tensors. The contribution of this thesis can be divided into two parts. In the first part, different integration techniques including Gauss Quadrature, Simpson's, Chebyshev, and Lebedev integration techniques are tried out and compared for evaluation of dynamic Green’s function. In addition the solution from the residue theorem is included for the singular part. The accuracy and performance of numerical implementation is studied in detail via different numerical examples. Convergence plots are used to analyze the numerical error for both Green's function and its derivatives. The second part of contribution of this thesis relates to the mathematical derivations. As mentioned above, the regular part of dynamic Green's function, being an integral over the surface of a unit sphere, is responsible for the majority of computational time. From symmetry properties, this integration domain can be reduced to a hemisphere, but no more simplification seems to be possible for a general anisotropic medium. In this thesis, the integration domain for regular part is further reduced to a quarter of a sphere for the particular case of transversely isotropic material. This reduction proposed for the first time in this thesis nearly halves the number of integration points for the evaluation of regular part of dynamic Green's function. It significantly reduces the computational time.
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Pratap, Rudra 1964. "A NEW RESIDUAL FINITE-ELEMENT FORMULATION FOR ELASTODYNAMIC PROBLEMS." Thesis, The University of Arizona, 1987. http://hdl.handle.net/10150/276552.
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In the research undertaken a finite element formulation has been developed for an elastodynamic problem using a least squares approach. The special requirements of the problem demanded a study of suitability of various elements. The emergence of the final element is a result of both theoretical and numerical study of three different elements. The approximation function is assumed on the basis of the order of the governing differential equations. Then the square of the error resulting from the approximate solution is minimized over the entire domain as well as the boundaries in the same functional. The element equation emerging from the formulation does not yield a singular stiffness matrix, since the boundary conditions are already taken into account in the element equation. The formulation presented in this thesis is only for the normal propagation of phi-wave. A finite element code has been developed based on the new formulation.
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Danan, David. "Modélisation, analyse et simulations numériques de quelques problèmes de contact." Thesis, Perpignan, 2016. http://www.theses.fr/2016PERP0015/document.
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Les phénomènes de contact entre les corps, déformables ou non, sont omniprésents dans la vie courante. Leurs modélisations requièrent des outils mathématiques faisant appel à des systèmes d'équations aux dérivées partielles incluant des conditions aux limites non triviales pour décrire le contact. Si les aspects physiques de la mécanique du contact sont connus depuis longtemps, la théorie mathématique qui lui est dédiée reste relativement récente laissant ainsi place à de nombreux problèmes à investiguer. Ce travail porte sur la modélisation, l'analyse et la simulation numérique de tels problèmes. Il se situe à mi-chemin entre la mécanique du contact et les aspects mathématiques inhérents au type de problème qui en découle. L'objectif est ici d'étudier certaines catégories de problèmes faisant intervenir des conditions originales de contact (avec et sans frottement) à la fois d'un point de vue mathématique et numérique, afin d'apporter une contribution à la théorie mathématique, puis de mettre en avant quelques méthodes numériques adaptées à leur résolution dans un cadre spécifique<br>Contact phenomena between bodies, whether they are deformable or not, abound in everyday life. Their modellings require mathematical tools using systems of partial differential equations and involving complex boundary conditions, in order to describe the contact. While the physical aspects of such phenomena have been known for a long time, the mathematical theory remains relatively recent which leaves room for numerous problems. This work focuses on the modelling, the analysis and the numerical simulations of such problems. It is located halfway between contact mechanics and the mathematical aspects inherent to the mechanical questions involved. Our aim is to study several groups of problems that include original contact conditions (with or without friction), both from a mathematical and numerical point of view, in order to contribute to the theory, and also to highlight several numerical methods used to solve specific contact problems
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da, Costa Filho Carlos Alberto. "Elastodynamic Green's function retrieval : theory and applications in exploration geophysics." Thesis, University of Edinburgh, 2017. http://hdl.handle.net/1842/28760.
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The ability to synthesize recordings from surface data as if they had come from subsurface sources has allowed geophysicists to estimate subsurface properties. Either in the form of classical seismic migration which creates structural maps of the subsurface, to the more recent seismic interferometry which turns seismic sources into receivers and vice-versa, this ability has provided a rich trove of methods with which to probe the Earth's interior. While powerful, both of these techniques suffer from well-known issues. Standard migration requires data without multiply-scattered waves (multiples). Seismic interferometry, on the other hand, can be applied to full recorded data (containing multiples and other wave types), but requires sources (receivers) to be physically placed at the location from (to) one wishes to estimate responses. The Marchenko method, developed recently for the seismic setting, circumvents both of these restrictions: it creates responses from virtual subsurface sources as if measured at the surface. It requires only single-sided surface data, and a smooth estimate of the subsurface velocities. Initially developed for acoustic media, this thesis contributes the first elastic formulation of the Marchenko method, providing a more suitable setting for applications for the solid Earth. In another development, this thesis shows how the obtained virtual recordings may be used for migration. With these two contributions, this thesis shows that for elastic surface seismic data, the main drawbacks of migration and interferometry can be overcome using the Marchenko method: multiples do not harm migrated images, and sources (receivers) need not be physically placed in the medium for their responses to be accessible. In addition to the above methods, generating images devoid of multiple-related artifacts can be achieved in several other different ways. Two approaches to this are the use of a post-imaging filter, and attenuation of internal multiples in the data itself. This thesis contributes one new method using each of these approaches. First, a form of Marchenko imaging is known to create spurious reflectors, as also occurs in standard reverse-time migration (RTM). However, these artifacts usually appear at different locations in RTM and this form of Marchenko imaging. Using this insight, this thesis presents a way to combine pairs of seismic images in such a way that their differences (e.g. artifacts) are attenuated, while similarities (e.g. true reflectors) are preserved. Applying this to RTM and Marchenko-derived images markedly improves image quality. Second, this thesis presents a method to estimate multiples in the data. Multiples can either be migrated on their own to aid in interpretation, or be adaptatively removed from the data to improve image quality. However, because of the nature of adaptive subtraction, this second method may harm primary energy. To avoid this problem, this thesis develops a final method to directly image using only primary energy in the recorded data using only a small number of virtual points. This method bypasses the need for multiple removal and the estimation of subsurface responses at every depth location. In addition, primaries from particular reflectors may be particularly selected such that they can be imaged individually. Overall this thesis provides several new ways to use surface seismic data in such a way that multiples do not hamper the end product of seismic data processing: the seismic image. It demonstrates this use on synthetic and real data, proving their effectiveness.
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Rossi, Marco. "Dynamics and stability of discrete and continuous structures: flutter instability in piecewise-smooth mechanical systems and cloaking for wave propagation in Kirchhoff plates." Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/322240.
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The first part of this Thesis deals with the analysis of piecewise-smooth mechanical systems and the definition of special stability criteria in presence of non-conservative follower forces.
To illustrate the peculiar stability properties of this kind of dynamical system, a reference 2 d.o.f. structure has been considered, composed of a rigid bar, with one and constrained to slide, without friction, along a curved profile, whereas the other and is subject to a follower force. In particular, the curved constraint is assumed to be composed of two circular profiles, with different and opposite curvatures, defining two separated subsystems. Due to this jump in the curvature, located at the junction point between the curved profiles, the entire mechanical structure can be modelled by discontinuous equations of motion, the differential equations valid in each subsystem can be combined, leading to the definition of a piecewise-smooth dynamical system. When a follower force acts on the structure, an unexpected and counterintuitive behaviour may occur: although the two subsystems are stable when analysed separately, the composed structure is unstable and exhibits flutter-like exponentially-growing oscillations. This special form of instability, previously known only from a mathematical point of view, has been analysed in depth from an engineering perspective, thus finding a mechanical interpretation based on the concept of non-conservative follower load. Moreover, the goal of this work is also the definition of some stability criteria that may help the design of these mechanical piecewise-smooth systems, since classical theorems cannot be used for the investigation of equilibrium configurations located at the discontinuity. In the literature, this unusual behaviour has been explained, from a mathematical perspective, through the existence of a discontinuous invariant cone in the phase space. For this reason, starting from the mechanical system described above, the existence of invariant cones in 2 d.o.f. mechanical systems is investigated through Poincaré maps. A complete theoretical analysis on piecewise-smooth dynamical systems is presented and special mathematical properties have been discovered, valid for generic 2~d.o.f. piecewise-smooth mechanical systems, which are useful for the characterisation of the stability of the equilibrium configurations. Numerical tools are implemented for the analysis of a 2~d.o.f. piecewise-smooth mechanical system, valid for piecewise-linear cases and extendible to the nonlinear ones. A numerical code has been developed, with the aim of predicting the stability of a piecewise-linear dynamical system a priori, varying the mechanical parameters. Moreover, “design maps” are produced for a given subset of the parameters space, so that a system with a desired stable or unstable behaviour can easily be designed. The aforementioned results can find applications in soft actuation or energy harvesting. In particular, in systems devoted to exploiting the flutter-like instability, the range of design parameters can be extended by using piecewise-smooth instead of smooth structures, since unstable flutter-like behaviour is possible also when each subsystem is actually stable. The second part of this Thesis deals with the numerical analysis of an elastic cloak for transient flexural waves in Kirchhoff-Love plates and the design of special metamaterials for this goal. In the literature, relevant applications of transformation elastodynamics have revealed that flexural waves in thin elastic plates can be diverted and channelled, with the aim of shielding a given region of the ambient space. However, the theoretical transformations which define the elastic properties of this “invisibility cloak” lead to the presence of a strong compressive prestress, which may be unfeasible for real applications. Moreover, this theoretical cloak must present, at the same time, high bending stiffness and a null twisting rigidity. In this Thesis, an orthotropic meta-structural plate is proposed as an approximated elastic cloak and the presence of the prestress has been neglected in order to be closer to a realistic design. With the aim of estimating the performance of this approximated cloak, a Finite Element code is implemented, based on a sub-parametric technique. The tool allows the investigation of the sensitivity of specific stiffness parameters that may be difficult to match in a real cloak design. Moreover, the Finite Element code is extended to investigate a meta-plate interacting with a Winkler foundation, to analyse how the substrate modulus transforms in the cloak region. This second topic of the Thesis may find applications in the realization of approximated invisibility cloaks, which can be employed to reduce the destructive effects of earthquakes on civil structures or to shield mechanical components from unwanted vibrations.
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Siebrits, Eduard. "Three-dimensional elastodynamic shear fracture propagation and ground motion simulation model." Master's thesis, University of Cape Town, 1986. http://hdl.handle.net/11427/26137.
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Putta, Sriram. "Elastodynamic Numerical Characterization of Adhesive Interfaces Using Spring and Cohesive Zone Models." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu156338398610629.
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Krishnaswamy, Sridhar Rosakis Ares J. "On the domain of dominance of the asymptotic elastodynamic crack-tip fields /." Diss., Pasadena, Calif. : California Institute of Technology, 1989. http://resolver.caltech.edu/CaltechETD:etd-10292003-134326.
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Liu, Yi Lapusta Nadia Lapusta Nadia. "Three-dimensional elastodynamic modeling of frictional sliding with application to intersonic transition /." Diss., Pasadena, Calif. : Caltech, 2009. http://resolver.caltech.edu/CaltechETD:etd-02142009-181805.
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Guerder, Pierre-Yves. "Etude théorique et numérique des cristaux phononiques non linéaires." Thesis, Ecole centrale de Lille, 2015. http://www.theses.fr/2015ECLI0006/document.
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Ce travail porte sur l'étude théorique et numérique des cristaux phononiques non linéaires. Les non linéarités étudiées sont celles dues aux constantes élastiques d'ordre deux (quadratiques) et trois (cubiques) des matériaux constituant les cristaux. Les effets non linéaires sont étudiés grâce à des méthodes d'éléments finis en simulant la propagation d'une onde élastique à travers les cristaux.Un premier projet de recherche a porté sur l'étude d'une structure osseuse, et plus spécifiquement sur la dispersion des ondes élastiques dans une structure constituée d'une alternance de couches de collagène et d'hydroxy apatite. Les simulations montrent qu'il existe un lien étroit entre l'hydratation des os et leur capacité à dissiper l'énergie.La seconde étude réalisée concerne un résonateur élastique. Une structure constituée d'inclusions d'acier dans de la silice présente un comportement de commutateur lorsque les non linéarités cubiques de l'acier sont prises en compte. Cet effet fortement non linéaire apparaît lorsque l'amplitude de l'onde incidente dépasse un certain seuil. Un modèle analytique complet est fourni.La dernière étude réalisée montre la conception de matériaux composites possédant de fortes non linéarités cubiques mais de faibles non linéarités quadratiques. La dérivation des lois de mélange des paramètres élastiques d'un matériau non linéaire dans un matériau linéaire est effectuée à l'ordre trois. Les équations montrent une forte amplification des paramètres non linéaires du matériau résultant pour certaines concentrations. Les simulations permettent de conclure que le résonateur mentionné ci-dessus peut effectivement être réalisé<br>This work is dedicated to the theoretical and numerical study of nonlinear phononic crystals. The studied nonlinearities are those due to the second (quadratic) and third (cubic) order elastic constants of the materials that constitute the crystals. Nonlinear effects are studied by the means of finite element methods, used to simulate the propagation of an elastic wave through the crystals.A first research project concerns the study of a bone structure, namely the dispersion of elastic waves in a structure composed of collagen and hydroxy apatite alternate constituent layers. Simulations showed that it exists a strong link between bones hydration and their ability to dissipate the energy.The second study relates to an elastic resonator. A structure composed of steel inclusions in a silica matrix shows a switch behavior when the cubic nonlinearities of steel are taken into account. This strong nonlinear effect appears when the amplitude of the incident wave reaches a threshold. A full analytical model is provided.The last study demonstrates the design of composite materials with both strong cubic nonlinearities and weak quadratic nonlinearities. The derivation of the mixing laws of the elastic parameters of a nonlinear material inside a linear one is performed up to order three. Equations show a strong amplification of the nonlinear parameters of the material for some concentrations. Numerical simulations allow to conclude that the above mentioned resonator can be produced
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Tjandrawidjaja, Yohanes. "Some contributions to the analysis of the Half-Space Matching Method for scattering problems and extension to 3D elastic plates." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLY012.
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Cette thèse porte sur la Half-Space Matching Method qui a été développée pour traiter certains problèmes de diffraction dans des domaines complexes infinis pour lesquels les méthodes numériques existantes ne s'appliquent pas. En 2D, elle consiste à coupler plusieurs représentations en ondes planes dans des demi-espaces entourant les obstacles et une représentation éléments finis dans un domaine borné. Afin d'assurer la compatibilité entre les différentes représentations, les traces de la solution sont liées par des équations intégrales de Fourier posées sur les frontières infinies des demi-espaces. Dans le cas d'un milieu dissipatif, il a été montré que ce système d'équations intégrales est coercif plus compact dans un cadre L².Dans cette thèse, nous établissons des estimations d'erreur par rapport aux paramètres de discrétisation (à la fois pour les variables spatiales et les variables de Fourier). Pour traiter le cas non-dissipatif, nous proposons une version modifiée de la Half-Space Matching Method, obtenue en appliquant une dilatation complexe aux inconnues afin de retrouver le cadre L².Nous étendons ensuite la Half-Space Matching Method aux problèmes de diffraction dans une plaque élastique infinie 3D en vue d'applications au Contrôle Non Destructif. La difficulté par rapport au cas 2D vient de la décomposition sur les modes de Lamb utilisée dans les représentations de demi-plaque. La relation de bi-orthogonalité des modes des Lamb impose de considérer comme inconnues non seulement le champ de déplacement, mais aussi le champ de contrainte sur les bandes infinies au bord des demi-plaques. Certaines questions théoriques soulevées par cette formulation multi-inconnues sont étudiées dans le cas 2D scalaire. Des connexions avec les méthodes intégrales sont aussi abordées dans le cas où la fonction de Green est connue, au moins partiellement dans chaque sous-domaine.Les différentes versions de la méthode ont été mises en oeuvre dans la bibliothèque XLiFE++ et des résultats numériques sont présentés pour les cas 2D et 3D<br>This thesis focuses on the Half-Space Matching Method which was developed to treat some scattering problems in complex infinite domains, when usual numerical methods are not applicable. In 2D, it consists in coupling several plane-wave representations in half-spaces surrounding the obstacle(s) with a Finite Element computation of the solution in a bounded domain. To ensure the matching of all these representations, the traces of the solution are linked by Fourier-integral equations set on the infinite boundaries of the half-spaces. In the case of a dissipative medium, this system of integral equations was proved to be coercive plus compact in an L² framework.In the present thesis, we derive error estimates with respect to the discretization parameters (both in space and Fourier variables). To handle the non-dissipative case, we propose a modified version of the Half-Space Matching Method, which is obtained by applying a complex-scaling to the unknowns, in order to recover the L² framework.We then extend the Half-Space Matching Method to scattering problems in infinite 3D elastic plates for applications to Non-Destructive Testing. The additional complexity compared to the 2D case comes from the decomposition on Lamb modes used in the half-plate representations. Due to the bi-orthogonality relation of Lamb modes, we have to consider as unknowns not only the displacement, but also the normal stress on the infinite bands limiting the half-plates. Some theoretical questions concerning this multi-unknown formulation involving the trace and the normal trace are studied in a 2D scalar case. Connections with integral methods are also addressed in the case where the Green's function is known, at least partially in each subdomain.The different versions of the method have been implemented in the library XLiFE++ and numerical results are presented for both 2D and 3D cases
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Ricks, David Charles. "Elastodynamic modeling of fluid-loaded cylindrical shells with multiple layers and internal attachments." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/36443.
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Allouko, Amond. "Modélisation hybride modale-éléments finis pour le contrôle ultrasonore d'une plaque élastique. Traitement des intégrales oscillantes de la méthode HSM." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPAST023.
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Cette thèse porte sur la méthode Half-Space Matching (HSM) pour la résolution de problèmes de diffraction dans une plaque élastique non-bornée, en vue de la simulation du contrôle non-destructif de plaques composites. La méthode HSM est une approche hybride qui couple un calcul éléments finis dans une boite contenant les défauts, avec des représentations semi-analytiques dans quatre demi-plaques qui recouvrent la partie saine de la plaque. Les représentations semi-analytiques de demi-plaques font intervenir des tenseurs de Green, exprimés à l'aide d'intégrales de Fourier et de séries modales. Or ces expressions peuvent être délicates à évaluer en pratique (coût et précision), rendant la méthode HSM inexploitable industriellement. Les difficultés sont d'abord analysées dans un cas scalaire bidimensionnel (acoustique). Deux méthodes sont proposées pour une évaluation efficace des intégrales de Fourier : la première exploite une approximation de type champ lointain et la seconde repose sur une déformation du chemin d'intégration dans le plan complexe (méthode de la complexification). Ces deux méthodes sont validées dans les cas scalaires isotrope et anisotrope où l'on dispose des valeurs exactes des intégrales de Fourier exprimées à l'aide de fonctions de Hankel. Elles sont ensuite généralisées au cas tridimensionnel de la plaque élastique. Dans ce cas, la formule de représentation est obtenue en faisant une transformée de Fourier suivant une direction parallèle à la plaque, puis, pour chaque valeur de la variable de Fourier ξ, une décomposition modale dans l'épaisseur. Les modes mis en jeu, appelés ξ-modes, sont étudiés en détail et comparés aux modes classiques (Lamb et SH dans le cas isotrope). Afin d'exploiter la bi-orthogonalité des ξ-modes, la formule de demi-plaque requiert la connaissance à la fois du déplacement et de la contrainte normale sur la frontière. Dans le cas isotrope, les propriétés d'analyticité des ξ-modes permettent de justifier et d'étendre la méthode de la complexification, y compris en présence de modes inverses. Ceci réduit les effets de couplage modal parasite induits par la discrétisation des intégrales de Fourier. La méthode de la complexification est ensuite utilisée pour le calcul des opérateurs intervenant dans la méthode HSM, qui dérivent tous de la formule de demiplaque. Différentes validations de la méthode HSM sont ainsi effectuées dans le cas isotrope. Des résultats préliminaires encourageants sont également obtenus pour une plaque orthotrope. Les améliorations réalisées ont permis à la fois de réduire significativement le temps de calcul et d'assurer une plus grande précision de la méthode HSM, permettant d'envisager son exploitation systématique dans un cadre de simulation industrielle<br>This thesis focuses on the Half-Space Matching (HSM) method for solving scattering problems in an unbounded elastic plate to simulate non-destructive testing of composite plates. The HSM method is a hybrid approach that couples a finite element calculation in a box containing the defects with semi-analytical representations in four half-plates covering the plate's healthy part. Semi-analytical half-plate representations involve Green tensors, expressed with Fourier integrals and modal series. However, these expressions can be challenging to evaluate in practice (cost and accuracy), making the HSM method unusable industrially. The difficulties are first analyzed in a two-dimensional scalar (acoustic) case. Two methods are proposed for an efficient evaluation of Fourier integrals : the first one uses a far-field type approximation, and the second one is based on a deformation of the integration path in the complex plane (complexification method). These two methods are validated in the isotropic and anisotropic scalar cases, where we have the exact values of the Fourier integrals expressed using Hankel functions. They are then generalized to the three-dimensional case of the elastic plate. In this case, the representation formula is obtained by performing a Fourier transform in a direction parallel to the plate, and then, for each value of the Fourier variable ξ, a modal decomposition in the thickness. The modes involved called ξ-modes, are studied in detail and compared to classical modes (Lamb and SH in the isotropic case). In order to exploit the bi-orthogonality of the ξ modes, the half-plate formula requires the knowledge of both the displacement and the normal stress on the boundary. In the isotropic case, the analytic properties of the ξ-modes make it possible to justify and extend the complexification method, including in the presence of inverse modes. This reduces the spurious effects of modal coupling induced by the discretization of Fourier integrals. The complexification method is then used to calculate the operators involved in the HSM method, which derive from the half-plate formula. Different validations of the HSM method are thus carried out in the isotropic case. Encouraging preliminary results are also obtained for an orthotropic plate. The improvements significantly reduce the calculation time and ensure higher accuracy of the HSM method, making it possible to consider its systematic exploitation in an industrial simulation framework