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Finite Strip With Rigid Ends And Edge NotchesErozkan, Deniz 01 August 2009 (has links) (PDF)
This study considers a symmetrical finite strip with a length of 2L and a width of 2h containing two collinear edge cracks located at the center of the strip. Each edge crack has a width h& / #8211 / a. Two ends of the finite strip are bonded to two rigid plates through which uniformly distributed axial tensile loads of intensity p0 are applied. The finite strip is assumed to be made of a linearly elastic and isotropic material. For the solution of the finite strip problem, an infinite strip of width 2h containing two internal cracks of width b& / #8211 / a at y=0 and two rigid inclusions of width 2c at y=± / L is considered. When the width of rigid inclusions approach the width of the strip, the portion of the infinite strip between the inclusions becomes identical with the finite strip problem. When the outer edges of the internal cracks approach the edge of the strip, they become edge cracks (notches). Governing equations are solved by using Fourier transform technique and these equations are reduced to a system of three singular integral equations. By using Gauss-Lobatto and Gauss-Jacobi integration formulas, these three singular integral equations are converted to a system of linear algebraic equations which is solved numerically.
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Axisymmetric Finite Cylinder With Rigid Ends And A Circumferential Edge CrackDurucan, Ayse Rusen 01 August 2010 (has links) (PDF)
An axisymmetric finite cylinder with rigid ends and a circumferential edge crack is considered in this study. The finite cylinder is under the action of uniformly distributed loads at two rigid ends. Material of the finite cylinder is assumed to be linearly elastic and isotropic. This finite cylinder problem is solved by considering an infinite cylinder containing an internal ring-shaped crack located at z=0 plane and two penny-shaped rigid inclusions located at z=± / L planes. General expressions of the infinite cylinder problem are obtained by solving Navier equations with Fourier and Hankel transforms. This infinite cylinder problem is then converted to the target problem by letting the radius of the rigid inclusions approach the radius of the cylinder and letting the outer edge of the crack approach the surface of the cylinder. Consequently, these rigid inclusions form the rigid ends and internal crack form the circumferential edge crack resulting in the problem of a finite cylinder with rigid ends having an edge crack. The problem is reduced to a set of three singular integral equations. These singular integral equations are converted to a system of linear algebraic equations with the aid of Gauss-Lobatto and Gauss-Jacobi integration formulas and are solved numerically.
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Cracked Semi-infinite Cylinder And Finite Cylinder ProblemsKaman, Mete Onur 01 May 2006 (has links) (PDF)
This work considers a cracked semi-infinite cylinder and a finite cylinder. Material of the cylinder is linearly elastic and isotropic. One end of the cylinder is bonded to a fixed support while the other end is subject to axial tension. Solution for this problem can be obtained from the solution for an infinite cylinder having a penny-shaped rigid inclusion at z = 0 and two penny-shaped cracks at z = ± / L. General expressions for this problem are obtained by solving Navier equations using Fourier and Hankel transforms. When the radius of the inclusion approaches the radius of the cylinder, the end at z = 0 becomes fixed and when the radius of the cracks approaches the radius of the cylinder, the ends at z = ± / L become cut and subject to uniformly distributed tensile load. Formulation of the problem is reduced to a system of three singular integral equations. By using Gauss-Lobatto and Gauss-Jacobi integration formulas, these three singular integral equations are converted to a system of linear algebraic equations which is solved numerically.
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3D modelling of Soft soil Improvement by Rigid Inclusions - Complex and Cyclic loading / Modélisation tridimensionnelle de l'amélioration des sols par des inclusions rigides - Chargement complexe et cycliquePham, Van Hung 17 September 2018 (has links)
Le but de cette étude est d'étudier le renforcement des sols par inclusions rigides sous chargement complexe et cyclique. L'effet de certains paramètres liés à la définition d’un chargement complexe et cyclique sur le comportement du système est mis en évidence.Du point de vue des chargements statiques complexes, des semelles de fondation posées sur un sol compressible renforcé par inclusions rigides sans matelas soumis à des charges centrées, excentrées verticales et horizontales et à quelques cycles de charge ont été étudiées. Des approches numériques et expérimentales sont présentées. Les résultats des mesures expérimentales et numériques permettent de mettre en évidence le comportement de ces systèmes en termes de contrainte sur la tête d'inclusion et sur le sol compressible, de déplacements verticaux et latéraux de la semelle et du déplacement latéral de l'inclusion. L'efficacité de la semelle renforcée est comparée à celle d’une semelle non renforcée.Une modélisation 3D de solutions de fondations pour les éoliennes est étudiée. La combinaison d’un chargement vertical et de différents moments appliqués à la fondation est prise en compte. Le sol compressible renforcé par inclusions rigides est considéré comme une option qui est comparée à d’autres solutions plus classiques (fondation superficielle et radier sur pieux). Les résultats obtenus permettent de présenter l’impact sur le tassement du sol, la rotation de la fondation, les efforts axiaux et les moments fléchissants dans les inclusions rigides. Les résultats numériques indiquent enfin que la technique d'amélioration du sol par inclusions rigides peut être une solution appropriée pour les fondations d'éoliennes.En ce qui concerne les aspects cycliques, trois points principaux sont abordés. Dans un premier temps, la modélisation numérique d’essais en laboratoire d’un renforcement de sol par inclusions rigides soumis à des chargements monotones et des cycles limités de chargement mise en œuvre. Le modèle hypoplastique (HYP) est utilisé pour modéliser le comportement de la plate-forme de transfert de charge. Les résultats numériques sont validés à la fois par rapport aux données expérimentales et numériques de Houda (2016). L'influence des conditions aux limites et de l'état du sol compressible est mise en évidence. Les résultats numériques indiquent qu'il est possible de considérer le comportement cyclique du sol renforcé par inclusions rigides en utilisant le modèle HYP.Dans un second temps, un remblai renforcé par des inclusions rigides sous un nombre élevé de chargement cyclique est étudié. Deux niveaux de complexité différents pour le modèle constitutif (HYP et le modèle élastique linéaire parfaitement plastique avec un critère de rupture de type Mohr-Coulomb) ont été pris en compte pour étudier le comportement de la LTP et analyser le comportement cyclique du système. Le modèle HYP est proposé pour la suite des études car il permet de bien capturer la décroissance et l’accumulation des tassements avec le nombre de cycles de charge. L'effet des paramètres qui sont le nombre de cycles de charge, l'amplitude et la fréquence (induite par la vitesse du trafic) et la hauteur du remblai est également présentée.Finalement, une étude sur la réponse cyclique d'un remblai de GRPS est menée. En comparant le remblai renforcé par des géosynthétiques (GRPS) avec le remblai renforcé par inclusions (PE), le rôle du géosynthétique est mis en évidence sous des chargements statiques et cycliques. L'influence du nombre de cycles de chargement et du nombre de géosynthétiques sur l'effet de voute et les tassements cumulés est également discutée. / The aim of the study is to investigate the soil improvement by rigid inclusions under complex and cyclic loadings, and to highlight the effect of some parameters related to complex and cyclic loading on the system behavior.Concerning the static complex loading, footings over rigid inclusion-reinforced soil without mattress subjected to centered, eccentrically vertical and horizontal loads, and load cycles are first studied. Numerical and experimental approaches are presented. Monitored and numerical results permit to show the behavior of these reinforced systems in terms of stresses on the inclusion head and soft soil, vertical and lateral displacements of the footings and lateral displacement of the inclusions. The efficiency of the reinforced footing is also presented and compared to the unreinforced one.A 3D modeling of the foundation solutions for wind turbines is presented. The combination of vertical loading and different moments applied to the foundation is taken into account. The inclusion-improved soft soil under footing is considered as a foundation option and, compared to classical ones (shallow foundation and piled raft). The obtained results are illustrated concerning the ground surface settlements, the foundation rotations, the axial forces and bending moments of the reinforcements. The numerical results indicate that the soil improvement technique by rigid inclusions can be an appropriate solution for the wind turbine foundations.With regard to the cyclic aspects, three main concerns are studied. Firstly, the numerical modeling of laboratory tests on a soil improvement by rigid inclusions subjected to monotonic loading and a limited load cycles is carried out, in which the hypoplasticity (HYP) model is used to model the load transfer platform (LTP). The numerical results are validated against both the experimental data and numerical ones of Houda (2016). The influence of the boundary condition and soft soil state are figured out. The numerical results indicate that it is possible to address the cyclic behavior of the rigid inclusion-reinforced soil by using the HYP model.Secondly, a piled embankment under a high number of cyclic loadings is studied. Two different levels of complexity for the constitutive models are used (HYP and a simpler one the linear elastic perfectly plastic constitutive model with a shear criteria of Mohr-Coulomb). These models were considered to model the behavior of the LTP and analyze the cyclic behavior of the system. The HYP model is then suggested for the following studies since it can capture well the arching decrease and the cumulated settlements under the load cycles number. The effect of the parameters that are load cycles number, amplitude and frequency (induced by traffic speed), and embankment height is illustrated as well.Finally, a study on the cyclic response of a GRPS embankment is conducted. By comparing the geosynthetic-reinforced pile-supported (GRPS) embankment with the piled embankment (PE), the role of the geosynthetic is verified under static and cyclic loading aspects. The influence of the load cycles number and the geosynthetic layers number on the arching effect and cumulative settlements is shown as well.
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