Relevant bibliographies by topics / Linearized Elasticity

Academic literature on the topic 'Linearized Elasticity'

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Published: 10 December 2022
Last updated: 9 March 2023

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Journal articles on the topic "Linearized Elasticity"

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Slaughter, WS, and J. Petrolito. "Linearized Theory of Elasticity." Applied Mechanics Reviews 55, no. 5 (September 1, 2002): B90—B91. http://dx.doi.org/10.1115/1.1497478.

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Yavari, Arash, and Arkadas Ozakin. "Covariance in linearized elasticity." Zeitschrift für angewandte Mathematik und Physik 59, no. 6 (March 26, 2008): 1081–110. http://dx.doi.org/10.1007/s00033-007-7127-2.

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Bociu, Lorena, Steven Derochers, and Daniel Toundykov. "Linearized hydro-elasticity: A numerical study." Evolution Equations and Control Theory 5, no. 4 (October 2016): 533–59. http://dx.doi.org/10.3934/eect.2016018.

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CIARLET, PHILIPPE G., PATRICK CIARLET, OANA IOSIFESCU, STEFAN SAUTER, and JUN ZOU. "LAGRANGE MULTIPLIERS IN INTRINSIC ELASTICITY." Mathematical Models and Methods in Applied Sciences 21, no. 04 (April 2011): 651–66. http://dx.doi.org/10.1142/s0218202511005167.

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In an intrinsic approach to three-dimensional linearized elasticity, the unknown is the linearized strain tensor field (or equivalently the stress tensor field by means of the constitutive equation), instead of the displacement vector field in the classical approach. We consider here the pure traction problem and the pure displacement problem and we show that, in each case, the intrinsic approach leads to a quadratic minimization problem constrained by Donati-like relations (the form of which depends on the type of boundary conditions considered). Using the Babuška-Brezzi inf-sup condition, we then show that, in each case, the minimizer of the constrained minimization problem found in an intrinsic approach is the first argument of the saddle-point of an ad hoc Lagrangian, so that the second argument of this saddle-point is the Lagrange multiplier associated with the corresponding constraints. Such results have potential applications to the numerical analysis and simulation of the intrinsic approach to three-dimensional linearized elasticity.
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Ciarlet, Philippe G., and Cristinel Mardare. "Intrinsic formulation of the displacement-traction problem in linearized elasticity." Mathematical Models and Methods in Applied Sciences 24, no. 06 (March 28, 2014): 1197–216. http://dx.doi.org/10.1142/s0218202513500814.

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The displacement-traction problem of linearized elasticity is a system of partial differential equations and boundary conditions whose unknown is the displacement field inside a linearly elastic body. We explicitly identify here the corresponding boundary conditions satisfied by the linearized strain tensor field associated with such a displacement field. Using this identification, we are then able to provide an intrinsic formulation of the displacement-traction problem of linearized elasticity, by showing how it can be recast into a boundary value problem whose unknown is the linearized strain tensor field.
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Friedrich, Manuel, and Francesco Solombrino. "Quasistatic crack growth in 2d-linearized elasticity." Annales de l'Institut Henri Poincaré C, Analyse non linéaire 35, no. 1 (January 2018): 27–64. http://dx.doi.org/10.1016/j.anihpc.2017.03.002.

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Ciarlet, Philippe G., Patrick Ciarlet, Oana Iosifescu, Stefan Sauter, and Jun Zou. "A Lagrangian approach to intrinsic linearized elasticity." Comptes Rendus Mathematique 348, no. 9-10 (May 2010): 587–92. http://dx.doi.org/10.1016/j.crma.2010.04.011.

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Serrano, Hélia. "Homogenization of kinetic laminates in linearized elasticity." Mathematical Methods in the Applied Sciences 41, no. 1 (October 5, 2017): 270–80. http://dx.doi.org/10.1002/mma.4611.

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Gussmann, Pascal, and Alexander Mielke. "Linearized elasticity as Mosco limit of finite elasticity in the presence of cracks." Advances in Calculus of Variations 13, no. 1 (January 1, 2020): 33–52. http://dx.doi.org/10.1515/acv-2017-0010.

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AbstractThe small-deformation limit of finite elasticity is considered in presence of a given crack. The rescaled finite energies with the constraint of global injectivity are shown to Γ-converge to the linearized elastic energy with a local constraint of non-interpenetration along the crack.
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Carlson, Donald E. "On the range of applicability of linearized elasticity." Mathematics and Mechanics of Solids 16, no. 5 (April 13, 2011): 467–81. http://dx.doi.org/10.1177/1081286510387527.

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Dissertations / Theses on the topic "Linearized Elasticity"

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Bridgeman, Leila. "Stability and a posteriori error analysis of discontinious Galerkin methods for linearized elasticity." Thesis, McGill University, 2010. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=95054.

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We consider discontinuous Galerkin finite element methods for the discretization of linearized elasticity problems in two space dimensions. Inf-sup stability results on the continuous and discrete level are provided. Furthermore, we derive lower and upper a posteriori error bounds that are robust with respect to nearly incompressible materials, and can easily be implemented within an automatic mesh refinement procedure. The theoretical results are illustrated with a series of numerical experiments.
Nous considérons les méthodes de Galerkin pour la discrétisation des relations déformations-déplacements linéaires en deux dimensions d'espace. Des résultats du stabilité inf-sup sur les niveaux continus et discrets sont fournis. En plus, nous dérivons des limites inférieurs et supérieures pour l'erreur a posteriori qui peuvent être utilisées dans des procédures de maillage automatisées sans difficulté et qui demeurent robustes dans le cas des matériaux qui ne sont presque pas compressibles. Les résultats théoriques sont illustrés par des expériences numériques.
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Dalla, Riva Matteo. "Potential theoretic methods for the analysis of singularly perturbed problems in linearized elasticity." Doctoral thesis, Università degli studi di Padova, 2008. http://hdl.handle.net/11577/3426270.

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The dissertation is made of two chapters. The first chapter is dedicated to the investigation of some properties of the layer potentials of a constant coefficient elliptic partial differential operator. In the second chapter, we focus our attention to the Lamè equations, which are related to the physic of an isotropic homogeneous elastic body. In particular, in the first chapter, we investigate the dependence of the single layer potential upon perturbation of the density, the support and the coefficients of the corresponding operator. Under some more restrictive assumptions on the operator, we prove a real analyticity theorem for the single layer potential and its derivatives. As a first step, we introduce a particular fundamental solution of a given constant coefficient partial differential operator. For this purpose, we exploite the construction of a fundamental solution given by John (1955). We have verified that, if the coefficients of the operator are constrained to a bounded set, then there exist a particular fundamental solution which is a sum of functions which depend real analytically on the coefficients of the operator. Such a result resembles the results of Mantlik (1991, 1992) (see also Tréves (1962)), where more general assumptions on the operator are considered. We observe that it is not a corollary. Indeed, we need a suitably detailed expression for the fundamental solution, which cannot be deduced by Mantlik's results. The next step is to introduce the support of our single layer potentials. It will be a compact sub-manifold of the the n-dimensional euclidean space parametrized by a suitable diffeomorphism defined on the boundary of a fixed domain. Then, we will be ready to state in Theorem 1.7 the main result of this chapter, which is a real analyticity result in the frame of Shauder spaces. The main idea of the proof stems from the papers of Lanza de Cristoforis & Preciso (1999) and by Lanza de Cristoforis & Rossi (2004, 2005) and exploits the Implicit Mapping Theorem for real analytic functions. Indeed, our main Theorem 1.7 is in some sense a natural extension of theorems obtained by Lanza de Cristoforis & Preciso (1999) and by Lanza de Cristoforis & Rossi (2004, 2005), for the Cauchy integral and for the Laplace and Helmholtz operators, respectively. Here we confine our attention to elliptic operators which can be factorized with operators of order 2. In the last section of the first chapter, we consider some applications of Theorem 1.7. In particular, we deduce a real analyticity theorem for the single and double layer potential which arise in the analysis of the boundary value problems for the Lamè equations and for the Stokes system. In the second chapter, we focus our attention to the Lamè equations. We consider some boundary value problems defined in a domain with a small hole. For each of them, we investigate the behavior of the solution and of the corresponding energy integral as the hole shrinks to a point. This kind of problem is not new at all and has been long investigated by the techniques of asymptotic analysis. It is perhaps difficult to give a complete list of contributions. Here we mention the work of Keller, Kozlov, Movchan, Maz'ya, Nazarov, Plamenewskii, Ozawa and Ward. The results that we present are in accordance with the behavior one would expect by looking at the above mentioned literature, but we adopt a different approach proposed by Lanza de Cristoforis (2001, 2002, 2005, 2007.) To do so, we exploit the real analyticity results for the elastic layer potentials obtained in the first chapter. We now briefly outline the main difference between our approach and the one of asymptotic analysis. Let d>0 be a parameter which is proportional to the diameter of the hole, so that the singularity of the domain appears when d=0. By the approach of the asymptotic analysis, we can expect to obtain results which are expressed by means of known functions of d plus an unknown term which is smaller than a positive power of d. Whereas, our results are expressed by means of real analytic functions of d defined in a whole open neighborhood of d=0 and by, possibly singular, but completely known functions of d, such as d^(2-n) or log d. Moreover, not only we can consider the dependence upon d, we can also investigate the dependence of the solution and the corresponding energy integral upon perturbations of the coefficients of the operator, and of the point where the hole is situated, and of the shape of the hole, and of the shape of the outer domain, and of the boundary data on the boundary of the hole, and of the boundary data on the boundary of the outer domain, and of the interior data. Also in this case we obtain results expressed by means of real analytic functions and completely known functions such as d^(2-n) and log d. The first boundary value problem we have studied is a Dirichlet boundary value problem with homogeneous data in the interior. Then, we turned to investigate a Robin boundary value problem with homogeneous data in the interior. In this case we have also described the behavior of the solution and the corresponding energy integral when both the domain and the boundary data display a singularity for d=0. Finally, we have studied a Dirichlet boundary value problem with non-homogeneous data in the interior.
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SOUHAIL, Hicham. "Schema volumes finis : Estimation d'erreur a posteriori hierarchique par elements finis mixtes. Resolution de problemes d'elasticite non-linearie." Phd thesis, Ecole Centrale de Lyon, 2004. http://tel.archives-ouvertes.fr/tel-00005418.

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La partie 1 releve de l'Analyse Numerique. Partant de l'interpretation Element Finis Mixtes des schemas volumes finis classiques, l'estimation a posteriori de l'erreur est analysee dans la hierarchie des elements de Raviart-Thomas. Un estimateur calculable est explicite pour ces schemas volumes finis.
La partie 2 introduit, d'abord un maillage rectangulaire, puis un maillage structure, une famille de schemas volumes finis de type differences finies. Des essais numeriques sur des problemes modeles montrent que l'ordre prevu par l'analyse peut etre atteint.
La partie 3 presente l'application de ces schemas volumes finis a la simulation numerique du comportement d'un bloc de gomme en presence d'une fissure finie. Il s'agit d'un materiau hyperelastique compressible en grandes deformations et differents tenseurs de contraintes, avec tests en quasi-incompressible et des simulations d'endommagement.
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Books on the topic "Linearized Elasticity"

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Linearized theory of elasticity. Boston: Birkhäuser, 2002.

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Slaughter, William S. The Linearized Theory of Elasticity. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0093-2.

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Slaughter, William S. Linearized Theory of Elasticity. Birkhäuser Boston, 2012.

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Slaughter, William S. Linearized Theory of Elasticity. Birkhauser Verlag, 2012.

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Rajagopal, Kumbakonam. Lecture Notes in Engineering: Introduction to Linearized Elasticity. de Gruyter GmbH, Walter, 2022.

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Rajagopal, Kumbakonam. Lecture Notes in Engineering: Introduction to Linearized Elasticity. de Gruyter GmbH, Walter, 2022.

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Rajagopal, Kumbakonam. Lecture Notes in Engineering: Introduction to Linearized Elasticity. de Gruyter GmbH, Walter, 2022.

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Shen, Zhongwei. Layer potentials and boundary value problems for parabolic lame systems of elasticity and a nonstationary linearized system of Navier-Stokes equations in Lipschitz cylinders. 1989.

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Book chapters on the topic "Linearized Elasticity"

1

Kružík, Martin, and Tomáš Roubíček. "Linearized Elasticity." In Interaction of Mechanics and Mathematics, 161–91. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-02065-1_5.

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Slaughter, William S. "Linearized Elasticity Problems." In The Linearized Theory of Elasticity, 221–54. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0093-2_6.

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Slaughter, William S. "Review of Mechanics of Materials." In The Linearized Theory of Elasticity, 1–21. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0093-2_1.

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Slaughter, William S. "Variational Methods." In The Linearized Theory of Elasticity, 387–429. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0093-2_10.

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Slaughter, William S. "Complex Variable Methods." In The Linearized Theory of Elasticity, 431–512. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0093-2_11.

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Slaughter, William S. "Mathematical Preliminaries." In The Linearized Theory of Elasticity, 23–95. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0093-2_2.

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Slaughter, William S. "Kinematics." In The Linearized Theory of Elasticity, 97–155. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0093-2_3.

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Slaughter, William S. "Forces and Stress." In The Linearized Theory of Elasticity, 157–92. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0093-2_4.

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Slaughter, William S. "Constitutive Equations." In The Linearized Theory of Elasticity, 193–220. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0093-2_5.

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Slaughter, William S. "Two-Dimensional Problems." In The Linearized Theory of Elasticity, 255–303. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0093-2_7.

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Conference papers on the topic "Linearized Elasticity"

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Kulvait, Vojtech. "Nonlinear elastic models within linearized elasticity and applications." In XVII International Conference on Nonlinear Elasticity in Materials. ASA, 2012. http://dx.doi.org/10.1121/1.4748242.

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Itou, Hiromichi, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "On Convergent Expansions of Solutions of the Linearized Elasticity Equation near Singular Points." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636764.

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Doostmohammadi, Amin, and Seyyedeh Negin Mortazavi. "Instability of Viscoelastic Fluids in Blasius Flow." In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-24315.

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In this paper, we study the hydrodynamic stability of a viscoelastic Walters B liquid in the Blasius flow. A linearized stability analysis is used and orthogonal polynomials which are related to de Moivre’s formula are implemented to solve Orr–Sommerfeld eigenvalue equation. An analytical approach is used in order to find the conditions of instability for Blasius flow and Critical Reynolds number is found for various combinations of the elasticity number. Based on the results, the destabilizing effect of elasticity on Blasius flow is determined and interpreted.
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Silvestrov, I. "Singular Value Decomposition Analysis Of Linearized Operator Of Dynamic Elasticity For Look-Ahead Prediction Using OVSP Data." In VII Annual International Conference and Exhibition - Galperin Readings 2007. European Association of Geoscientists & Engineers, 2007. http://dx.doi.org/10.3997/2214-4609.201403150.

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Kersken, Hans-Peter, Christian Frey, Christian Voigt, and Graham Ashcroft. "Time-Linearized and Time-Accurate 3D RANS Methods for Aeroelastic Analysis in Turbomachinery." In ASME Turbo Expo 2010: Power for Land, Sea, and Air. ASMEDC, 2010. http://dx.doi.org/10.1115/gt2010-22940.

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A computational method for performing aeroelastic analysis using either a time-linearized or an unsteady time-accurate solver for the compressible Reynolds averaged Navier-Stokes (RANS) equations is described. The time-linearized solver employs the assumption of small time-harmonic perturbations and is implemented via finite differences of the nonlinear flux routines of the time-accurate solver. The resulting linear system is solved using a parallelized Generalized Minimal Residual (GMRES) method with block-local preconditioning. The time accurate solver uses a dual time stepping algorithm for the solution of the unsteady RANS equations on a periodically moving computational grid. For either solver, and both flutter and forced response problems, a mapping algorithm has been developed to map structural eigenmodes, obtained from finite element structural analysis, from the surface mesh of the finite element structural solver to the surface mesh of the finite volume flow solver. Using the surface displacement data an elliptic mesh deformation algorithm, based on linear elasticity theory, is then used to compute the grid deformation vector field. The developed methods are validated first using standard configuration ten. Finally, for an ultra high bypass ratio fan the results of the time-linearized and the unsteady module are compared. The gain in prediction time using the linearized methods is highlighted.
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Aguirre-Rivas, Donovan A., and Karim H. Muci-Küchler. "Accurate Prediction of Strains and Stresses in 2-D Elasticity Using Adini’s Finite Element." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-51647.

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In the interest of obtaining accurate stress predictions in linear elastic problems while keeping the computational cost low, a finite element solution approach using cubic elements that include not only the displacement but also the spatial derivatives of the displacement as nodal degrees of freedom (DOFs) is explored in this paper. The proposed approach has the advantage that the nodal values of the strains, and hence the stresses, can be directly computed from the finite element solution and, as shown in this paper, it is capable of converging faster to the analytical solution than the commonly used reduced integration Serendipity quadratic element. Because the proposed approach is capable of achieving high accuracy using less DOFs, it is possible to use coarser meshes than with conventional elements. This is of particular importance in dynamic problems in which explicit techniques are used and the size of the time step is tied to the element size. Moreover, the proposed approach can be beneficial in non-linear problems in which stepping techniques are used to solve a linearized problem and the strains or stresses of the current step are used as input for the following step.
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Hall, Kevin J., Fang Zhu, and Christopher D. Rahn. "Three Dimensional Vibration of a Ballooning String." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0542.

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Abstract In many textile manufacturing processes, yarn is rotated at high speed forming a balloon. In this paper, Hamilton’s principle is used to derive the nonlinear partial differential equations of a ballooning string. Jacobian elliptical sine functions satisfy the nonlinear steady state equations. The steady state eyelet tension is related to the string length for a constant balloon height. For high tension and low string length cases, single loop balloons occur. As the string length increases, tension decreases and multiple loop solutions are obtained. The nonlinear partial differential equations are linearized about the steady state solutions, resulting in three coupled equations with spatially varying coefficients. The equations involve a positive definite mass matrix operator, skew symmetric gyroscopic matrix operator, and symmetric stiffness matrix operator. It is shown using a Galerkin approach that only single loop balloons are stable for practical yarn elasticity. The natural frequencies of the single loop balloon increase with decreasing balloon size and increasing yam stiffness. The effect of yarn elasticity on the first three vibration modes of a single loop balloon is analyzed. The steady state and stability analyses are experimentally verified.
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Yahnioglu, Nazmiye, and Ulku Babuscu Yesil. "Concentration of Stress Around the Cylindrical Hole in an Initial Stressed Rectangular Orthotropic Thick Plate." In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-24698.

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An orthotropic pre-stressed thick plate with a cylindrical hole under additional static loading on the upper face-plane of the plate have been studied within the framework of the Three-Dimensional Linearized Theory of Elasticity (TDLTE) in Initially Stressed Bodies. The corresponding problem formulation is presented and, in order to find the solution to this problem, the 3D finite element method is employed. The numerical results on the concentration of the stress around the cylindrical hole and the influence of the initial forces, geometrical and mechanical parameters on these concentrations are presented in graphical form and discussed. According to these results, in particular it is established that the stress distributions around the cylindrical hole changed significantly with the initial stretching or compressing forces.
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Rahmati, M. T. "Frequency and Time Domain Methods for Forced Vibration Analysis of an Oscillating Cascade." In ASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/omae2016-55054.

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Unsteady flow around an oscillating plate cascade has been computationally studied, aimed at examining the predictive ability of a non-linear frequency solution method for hydro-elasticity analysis compared with a standard analytical solution. The comparison of computational and analytical solutions for flow around an oscillating plate configuration demonstrates the capabilities of the frequency domain method compared with the analytical solution in capturing the unsteady flow. It also shows the great advantage of significant CPU time saving by the frequency methods over the nonlinear time method. This approach is based on casting the unsteady flow equations into a set of steady-like equations at a series of phases of a period of unsteadiness. So, One of the advantages of this method compared with other conventional time-linearized frequency domain methods is that any steady flow solution method can be easily used in a straightforward simple method for modelling unsteady perturbations.
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Salwa, Tomasz, Onno Bokhove, and Mark A. Kelmanson. "Variational Modelling of Wave-Structure Interactions for Offshore Wind Turbines." In ASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/omae2016-54897.

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We consider the development of a mathematical model of water waves interacting with the mast of an offshore wind turbine. A variational approach is used for which the starting point is an action functional describing a dual system comprising a potential-flow fluid, a solid structure modelled with (linear) elasticity, and the coupling between them. The variational principle is applied and discretized directly using Galerkin finite elements that are continuous in space and dis/continuous in time. We develop a linearized model of the fluid-structure or wave-mast coupling, which is a linearization of the variational principle for the fully coupled nonlinear model. Our numerical results indicate that our variational approach yields a stable numerical discretization of a fully coupled model of water waves and a linear elastic beam. The energy exchange between the subsystems is seen to be in balance, yielding a total energy that shows only small and bounded oscillations whose amplitude tends to zero as the timestep goes to zero.
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