A novel boundary infinite element

Zienkiewicz, O. C.; Emson, C.R.I.; Bettess, P.

doi:10.1002/nme.1620190307

Cited by 329 publications

(97 citation statements)

References 4 publications

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“…Finally, a node list sub i is generated for the computation of F ij . In¯nite elements [Zienkiewicz et al, 1983] are generated at the bottom and along the side plane of the constructed FE model to approximate the in¯nite boundary condition. Although solving Eq.…”

Section: Methodsmentioning

confidence: 99%

Tsunami Analysis Method with High-Fidelity Crustal Structure and Geometry Model

Ichimura

Agata

Hori

et al. 2017

J. Earthquake and Tsunami

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Higher¯delity sea°oor topography and crustal structure models have become available with accumulation of observation data. Previous studies have shown that the consideration of such high-¯delity models produces signi¯cant e®ects, in some cases, on crustal deformation results that are used as inputs for tsunami analysis. However, it is di±cult to apply high-¯delity model of crustal deformation computations to tsunami computations because of large computational costs. In this paper, we propose a new crustal deformation computation method for estimating inputs for tsunami computations, which is based on a¯nite element analysis method with remarkable reduction of computation costs by e±cient use of the arithmetic space and the solution space. This¯nite element analysis method enables us to conduct 10 2À3 -times crustal deformation computations using high-¯delity models with a degree of freedom on the order of 10 8 for the 2011 Tohoku earthquake example. Tsunami computations with typical settings are conducted as an application example to present the advantages and characteristics of the proposed method. Comparisons between results of the proposed and the conventional method

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Section: Methodsmentioning

confidence: 99%

Tsunami Analysis Method with High-Fidelity Crustal Structure and Geometry Model

Ichimura

Agata

Hori

et al. 2017

J. Earthquake and Tsunami

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“…Figure 10 shows a typical 2-D FE mesh for simulating vertical downward and oblique pipe movement in soil. Infinite elements (Zienkiewicz et al 1983) were used to represent a semi-infinite soil medium. Inside the dashed lines, eight-node bi-quadratic, plane strain, quadrilateral, reduced integration elements (element type CPE8R) represent the soil surrounding the pipe.…”

Section: Finite Element Analysis For Downward Pipe Movementmentioning

confidence: 99%

Multi-directional force–displacement response of underground pipe in sand

2016

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Abstract:A methodology is presented to evaluate multi-directional force-displacement relationships for soil-pipeline interaction analysis and design. Large-scale tests of soil reaction to pipe lateral and uplift movement in dry and partially saturated sand are used to validate plane strain, finite element (FE) soil, and pipe continuum models. The FE models are then used to characterize force versus displacement performance for lateral, vertical upward, vertical downward, and oblique orientations of pipeline movement in soil. Using the force versus displacement relationships, the analytical results for pipeline response to strike-slip fault rupture are shown to compare favorably with the results of large-scale tests in which strike-slip fault movement was imposed on 250 and 400 mm diameter high-density polyethylene pipelines in partially saturated sand. Analytical results normalized with respect to maximum lateral force are provided on 360°plots to predict maximum pipe loads for any movement direction. The resulting methodology and dimensionless plots are applicable for underground pipelines and conduits at any depth, subjected to relative soil movement in any direction in dry or saturated and partially saturated medium to very dense sands.Key words: pipeline, Mohr-Coulomb, soil-pipe interaction, earthquake, liquefaction, ground failure.Résumé : Une méthodologie est présentée afin d'évaluer les relations force-déplacement multidirectionnel pour la conception et l'analyse des interactions sol-pipeline. Des essais à grande échelle de la réaction du sol aux mouvements latéraux ou au soulèvement de tuyau dans le sable sec et partiellement saturé servent à valider les modèles en déformation plane, les sols par élément fini (EF) et le continuum de tuyau. Les modèles EF sont ensuite utilisés pour caractériser les performances de force versus déplacement latéral, pour les orientations verticales, vers le haut, vertical vers le bas et obliques de mouvement du pipeline dans le sol. En utilisant les relations de force versus déplacement, les résultats des analyses pour une réponse à la rupture de faille par décrochement se comparent favorablement avec les résultats des essais à grande échelle, dont le mouvement de faille, par décrochement a été imposé à des pipelines en polyéthylène à haute densité de 250 et de 400 mm de diamètre dans du sable partiellement saturé. Les résultats analytiques normalisés en ce qui concerne la force latérale maximale sont fournis sur des parcelles de 360°pour n'importe quelle direction de mouvement. La méthodologie qui en résulte et les parcelles sans dimension sont applicables pour les pipelines souterrains et les conduits à n'importe quelle profondeur, sujettes à des mouvements de sol relatif dans tous les sens dans un milieu sec ou saturé et partiellement saturé aux sables très denses. [Traduit par la Rédaction] Mots-clés : pipeline, Mohr-Coulomb, interaction sol-tuyau, tremblement de terre, liquéfaction, échec de sol.

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“…Since the solution on the boundary of the "inner" domain is already quite close to the asymptotic value, the gradient in the outer region can be modeled as a simple parametrized function of the scaled coordinate. For more details on this subject, see [18].…”

Section: Model Validationmentioning

confidence: 99%

The Steady-State Convection-Diffusion Equation at High Péclet Numbers for a Cluster of Spheres: An Extension of Levich's Theory

Biello¹,

Samson²,

Sigal³

2016

SIAM J. Appl. Math.

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Abstract. This paper describes an approximate analytical model of competitive effects between members of a dense cluster of absorbing objects, which are modeled as spheres. Neighboring absorbing spheres compete for diffusing species and thereby reduce each other's rate of absorption. Levich's well-known asymptotic (high Péclet number) theory of convection-diffusion considers only the inner region of the concentration boundary layer; it does not describe the wake zone accurately. An extension of the Levich model is constructed for the wake zone. This is used to model intersphere competitive effects. The model demonstrates that for two neighboring spheres aligned along the flow direction, the absorption of the downstream sphere is substantially reduced vis-à-vis the upstream sphere. The model is verified by comparison to numerical simulation studies. Both single-sphere simulations (reported in this paper) and multisphere simulations (taken from existing literature) are considered. In the single-sphere case, the discrepancy between the analytical model and the numerical results is maximally 10% at Pe = 10 and much lower at higher Péclet numbers. An appreciable part of the error stems from the original Levich model itself, rather than from our method of extending the Levich model. In the multisphere case, the difference between the analytical model and the numerical studies is generally less than 30%. At small intersphere separations (say, center-to-center distances < 5 sphere radii), the model tends to overestimate the interference effects. This is related to the fact that flow stagnancy in the space between two closely packed spheres is not taken into account in the model. Key words. diffusion convection mass-transfer AMS subject classifications. 76R50, 76M45DOI. 10.1137/15M10393891. Introduction. Consider a steady-state model of mass transport in which a microscopic species moves toward a collection of macroscopic immobile absorption centers. The motion of the microscopic species consists of a combination of stochastic movements (diffusion) and externally imposed motion by a carrier fluid (convection). The macroscopic absorption centers are assumed to be spheres of which the locations are known and fixed; they are assumed to be all of equal size.In a recent paper [6] we developed an approximate analytical theory for such a system in the case of pure diffusion and in the case of diffusion combined with a relatively weak convective component. It was found that the range of applicability of the former theory in the convection-diffusion (CD) case was very limited; beyond Péclet numbers of about 0.6, our theory was found to be unreliable. (The Péclet number measures the ratio between convective and diffusive fluxes.) As will be shown below (and as is intuitively quite plausible), the reason for this failure at high Péclet numbers is that CD-concentration profiles around a sphere exhibit an extreme degree of fore/aft asymmetry. At the front side of the sphere, the solute is swept up extremely close to the boundary of t...

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A novel boundary infinite element

Cited by 329 publications

References 4 publications

Tsunami Analysis Method with High-Fidelity Crustal Structure and Geometry Model

Tsunami Analysis Method with High-Fidelity Crustal Structure and Geometry Model

Multi-directional force–displacement response of underground pipe in sand

The Steady-State Convection-Diffusion Equation at High Péclet Numbers for a Cluster of Spheres: An Extension of Levich's Theory

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