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Two Dimensional Stress and Displacement Wave Propagation Under Shock Loading in Saturated Porous Materials with Two Dimensional Functionally Graded Materails Using MLPG Method | ||
| AUT Journal of Civil Engineering | ||
| مقاله 8، دوره 1، شماره 2، اسفند 2017، صفحه 167-176 اصل مقاله (1.55 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22060/ceej.2017.12762.5262 | ||
| نویسندگان | ||
| H. Kazemi1؛ F. Shahabian* 1؛ S. M. Hosseini2 | ||
| 1Civil Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran | ||
| 2Industrial Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad,Mashhad, Iran | ||
| چکیده | ||
| The meshless local Petrov-Galerkin (MLPG) method is employed for dynamic analysis of fully saturated porous materials under shock loading considering two directional functionally grading patterns in constitutive mechanical properties. To approximate the trial functions in the radial point interpolation method (RPIM), the radial basis functions (RBFs) are utilized. The mechanical properties are simulated using a non-linear grading model with the radial and axial exponent. The 2D propagation of displacement and stresses are tracked through radial and axial direction in a two dimensional domain for various grading patterns at different time instants. By employing the presented meshless technique, the effects of various grading patterns on maximum values of stresses and displacements are studied in detail. The variation in the value of radial exponent has a significant effect on the dynamic behavior of radial displacement and radial stress comparing to the variation in the value of axial exponent. The MLPG method has a high capability to track the stress and displacement wave fronts at every arbitrary time instant in 2D domain. | ||
تازه های تحقیق | ||
[1] K. Terzaghi, Erdbaumechanik auf bodenphysikalischer Grundlage, (1925). [2] M.A. Biot, General theory of three.dimensional consolidation, Journal of applied physics, 12(2) (1941) 155-164. [3] A.P. Selvadurai, Mechanics of poroelastic media, Springer Science & Business Media, 2013. [4] M. Schanz, Poroelastodynamics: linear models, analytical solutions, and numerical methods, Applied mechanics reviews, 62(3) (2009) 030803. [5] M. Schanz, A.-D. Cheng, Transient wave propagation in a one-dimensional poroelastic column, Acta Mechanica, 145(1-4) (2000) 1-18. [6] M.H.G. Rad, F. Shahabian, S.M. Hosseini, A meshless local Petrov–Galerkin method for nonlinear dynamic analyses of hyper-elastic FG thick hollow cylinder with Rayleigh damping, Acta Mechanica, 226(5) (2015) 1497-1513. [7] X. Lai, M. Cai, F. Ren, M. Xie, T. Esaki, Assessment of rock mass characteristics and the excavation disturbed zone in the Lingxin Coal Mine beneath the Xitian river, China, International Journal of Rock Mechanics and Mining Sciences, 43(4) (2006) 572-581. [8] S. Kwon, C. Lee, S. Cho, S. Jeon, W. Cho, An investigation of the excavation damaged zone at the KAERI underground research tunnel, Tunnelling and underground space technology, 24(1) (2009) 1-13. [9] W. Kaewjuea, Poroelastic solutions for borehole and cylinder, Chulalongkorn University, 2010. [10] J. Sladek, V. Sladek, C. Zhang, M. Schanz, Meshless local Petrov-Galerkin method for continuously nonhomogeneous linear viscoelastic solids, Computational Mechanics, 37(3) (2006) 279-289. [11] S. Moussavinezhad, F. Shahabian, S.M. Hosseini, Two-dimensional stress-wave propagation in finite-length FG cylinders with two-directional nonlinear grading patterns using the MLPG method, Journal of Engineering Mechanics, 140(3) (2013) 575-592. [12] S. Chen, C. Xu, G. Tong, A meshless local natural neighbour interpolation method to modeling of functionally graded viscoelastic materials, Engineering Analysis with Boundary Elements, 52 (2015) 92-98. [13] J. Sladek, V. Sladek, M. Schanz, A meshless method for axisymmetric problems in continuously nonhomogeneous saturated porous media, Computers and Geotechnics, 62 (2014) 100-109. [14] J. Sladek, V. Sladek, M. Schanz, The MLPG applied to porous materials with variable stiffness and permeability, Meccanica, 49(10) (2014) 2359-2373. [15] S.M. Hosseini, F. Shahabian, Stochastic assessment of thermo-elastic wave propagation in functionally graded materials (FGMs) with Gaussian uncertainty in constitutive mechanical properties, Journal of Thermal Stresses, 34(10) (2011) 1071-1099. [16] S.M. Hosseini, F. Shahabian, Transient analysis of thermo-elastic waves in thick hollow cylinders using a stochastic hybrid numerical method, considering Gaussian mechanical properties, Applied Mathematical Modelling, 35(10) (2011) 4697-4714. [17] F. Shahabian, S.M. Hosseini, Stochastic dynamic analysis of a functionally graded thick hollow cylinder with uncertain material properties subjected to shock loading, Materials & Design, 31(2) (2010) 894-901. [18] S.M. Hosseini, F. Shahabian, Reliability of stress field in Al–Al2O3 functionally graded thick hollow cylinder subjected to sudden unloading, considering uncertain mechanical properties, Materials & Design, 31(8) (2010) 3748-3760. [19] O. Coussy, Poromechanics, John Wiley & Sons, 2004. [20] G. Liu, 1013 Mesh Free Methods: Moving beyond the Finite Element Method, CRC Press, 2003(16) (2003) 937-938. [21] E. Detournay, A. Cheng, Fundamentals of Poroelasticity, volume 2 of Comprehensive Rock Engineering: Principles, Practice & Projects. Pergamon Press, (1993). | ||
| کلیدواژهها | ||
| Porous materials؛ Stress wave propagation؛ Displacement wave propagation؛ MLPG method؛ Radial basis functions | ||
| موضوعات | ||
| تحلیل خطی و غیر خطی؛ دینامیک سازه؛ مصالح مختلف ساختمانی؛ مواد و مصالح | ||
| مراجع | ||
|
[1] K. Terzaghi, Erdbaumechanik auf bodenphysikalischer Grundlage, (1925).
[2] M.A. Biot, General theory of three.dimensional consolidation, Journal of applied physics, 12(2) (1941) 155-164.
[3] A.P. Selvadurai, Mechanics of poroelastic media, Springer Science & Business Media, 2013.
[4] M. Schanz, Poroelastodynamics: linear models, analytical solutions, and numerical methods, Applied mechanics reviews, 62(3) (2009) 030803.
[5] M. Schanz, A.-D. Cheng, Transient wave propagation in a one-dimensional poroelastic column, Acta Mechanica, 145(1-4) (2000) 1-18.
[6] M.H.G. Rad, F. Shahabian, S.M. Hosseini, A meshless local Petrov–Galerkin method for nonlinear dynamic analyses of hyper-elastic FG thick hollow cylinder with Rayleigh damping, Acta Mechanica, 226(5) (2015) 1497-1513.
[7] X. Lai, M. Cai, F. Ren, M. Xie, T. Esaki, Assessment of rock mass characteristics and the excavation disturbed zone in the Lingxin Coal Mine beneath the Xitian river, China, International Journal of Rock Mechanics and Mining Sciences, 43(4) (2006) 572-581.
[8] S. Kwon, C. Lee, S. Cho, S. Jeon, W. Cho, An investigation of the excavation damaged zone at the KAERI underground research tunnel, Tunnelling and underground space technology, 24(1) (2009) 1-13.
[9] W. Kaewjuea, Poroelastic solutions for borehole and cylinder, Chulalongkorn University, 2010.
[10] J. Sladek, V. Sladek, C. Zhang, M. Schanz, Meshless local Petrov-Galerkin method for continuously nonhomogeneous linear viscoelastic solids, Computational Mechanics, 37(3) (2006) 279-289.
[11] S. Moussavinezhad, F. Shahabian, S.M. Hosseini, Two-dimensional stress-wave propagation in finite-length FG cylinders with two-directional nonlinear grading patterns using the MLPG method, Journal of Engineering Mechanics, 140(3) (2013) 575-592.
[12] S. Chen, C. Xu, G. Tong, A meshless local natural neighbour interpolation method to modeling of functionally graded viscoelastic materials, Engineering Analysis with Boundary Elements, 52 (2015) 92-98.
[13] J. Sladek, V. Sladek, M. Schanz, A meshless method for axisymmetric problems in continuously nonhomogeneous saturated porous media, Computers and Geotechnics, 62 (2014) 100-109.
[14] J. Sladek, V. Sladek, M. Schanz, The MLPG applied to porous materials with variable stiffness and permeability, Meccanica, 49(10) (2014) 2359-2373.
[15] S.M. Hosseini, F. Shahabian, Stochastic assessment of thermo-elastic wave propagation in functionally graded materials (FGMs) with Gaussian uncertainty in constitutive mechanical properties, Journal of Thermal Stresses, 34(10) (2011) 1071-1099.
[16] S.M. Hosseini, F. Shahabian, Transient analysis of thermo-elastic waves in thick hollow cylinders using a stochastic hybrid numerical method, considering Gaussian mechanical properties, Applied Mathematical Modelling, 35(10) (2011) 4697-4714.
[17] F. Shahabian, S.M. Hosseini, Stochastic dynamic analysis of a functionally graded thick hollow cylinder with uncertain material properties subjected to shock loading, Materials & Design, 31(2) (2010) 894-901.
[18] S.M. Hosseini, F. Shahabian, Reliability of stress field in Al–Al2O3 functionally graded thick hollow cylinder subjected to sudden unloading, considering uncertain mechanical properties, Materials & Design, 31(8) (2010) 3748-3760. [19] O. Coussy, Poromechanics, John Wiley & Sons, 2004.
[20] G. Liu, 1013 Mesh Free Methods: Moving beyond the Finite Element Method, CRC Press, 2003(16) (2003) 937-938.
[21] E. Detournay, A. Cheng, Fundamentals of Poroelasticity, volume 2 of Comprehensive Rock Engineering: Principles, Practice & Projects. Pergamon Press, (1993). | ||
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