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A meshless method for axisymmetric problems in continuously nonhomogeneous saturated porous media
Institution:1. Institution of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia;2. Institute of Applied Mechanics, Graz University of Technology, Graz, Austria;1. LaTICE, School of Science and Technology of Tunis, University of Tunis, 1008 Tunis, Tunisia;2. LERIA, University of Angers, 2 Boulevard Lavoisier, 49045 Angers, France;1. Laboratoire de chimie des matériaux et catalyse, Département de chimie, Faculté des Sciences de Tunis, Université Tunis El Manar, 2092 Tunis, Tunisia;2. IC2MP, UMR 7285 CNRS, “SAMCat Group”, Université de Poitiers, 4, rue Michel Brunet B27, BP 633, 86022 Poitiers Cedex, France;1. College of Pharmacy, Liaoning University of Traditional Chinese Medicine, Shenyang 11660, PR China;2. Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, PR China;3. Institute of Materia Medica, Chinese Academy of Medical Science & Peking Union Medical College, Beijing 100050, PR China;4. Institute of Process Engineering and Chinese Academy of Sciences, Beijing 100190, PR China;5. College of Chemistry and Materials, Hebei Normal University, Shijiazhuang 050016, PR China;6. Department of Materials Science and Engineering, University of Delaware, Newark, DE 19716, United States;1. VIRTUAL VEHICLE Research Center, Graz, Austria;2. Erich Schmidt Institute of Materials Science (ESI ÖAW), Leoben, Austria
Abstract:A meshless method based on the local Petrov–Galerkin approach is proposed to analyze 3-d axisymmetric problems in porous functionally graded materials. Constitutive equations for porous materials possess a coupling between mechanical displacements for solid and fluid phases. The work is based on the u–u formulation and the incognita fields of the coupled analysis in focus are the solid skeleton displacements and the fluid displacements. Independent spatial discretization is considered for each phase of the model, rendering a more flexible and efficient methodology. Both displacements are approximated by the moving least-squares (MLS) scheme. The paper presents in the first time a general meshless method for the numerical analysis of axisymmetric problems in continuously nonhomogeneous saturated porous media. Numerical results are given for boreholes in continuously nonhomogeneous porous medium with prescribed misfit and exponential variation of material parameters in the excavation zone.
Keywords:Solid and fluid phases  Coupled problem  Meshless local Petrov–Galerkin method (MLPG)  Moving least-squares approximation  3D axisymmetric problem  Borehole
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