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http://dx.doi.org/10.12989/sem.2012.42.3.353

Elastodynamic infinite elements based on modified Bessel shape functions, applicable in the finite element method  

Kazakov, K.S. (Department of Structural Mechanics, VSU)
Publication Information
Structural Engineering and Mechanics / v.42, no.3, 2012 , pp. 353-362 More about this Journal
Abstract
In this paper decay and mapped elastodynamic infinite elements, based on modified Bessel shape functions and appropriate for Soil-Structure Interaction problems are described and discussed. These elements can be treated as a new form of the recently proposed Elastodynamic Infinite Elements with United Shape Functions (EIEUSF) infinite elements. The formulation of 2D horizontal type infinite elements (HIE) is demonstrated, but by similar techniques 2D vertical (VIE) and 2D corner (CIE) infinite elements can also be formulated. It is demonstrated that the application of the elastodynamical infinite elements is the easier and appropriate way to achieve an adequate simulation including basic aspects of Soil-Structure Interaction. Continuity along the artificial boundary (the line between finite and infinite elements) is discussed as well and the application of the proposed elastodynamical infinite elements in the Finite Element Method is explained in brief. Finally, a numerical example shows the computational efficiency of the proposed infinite elements.
Keywords
soil-structure interaction; wave propagation; infinite elements; finite element method; Bessel functions;
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1 Aubry, D., Clouteau, D. and D'Azemar, P. (2003), "A dynamic substructure approach to soil-structure interaction", Computat. Mech. Publ., 3, Springer Verlag.
2 Bagheripour, M.H., Rahgozar, R. and Malekinejad, M. (2010), "Efficient analysis of SSI problems using infinite elements and wavelet theory", Geothech. Eng., 2(4), 229-252.
3 Bagheripour, M.H. and Marandi, S.M. (2005), "A numerical model for unbounded soil domain in earthquake SSI analysis using periodic infinite elements", Int. J. Civil Eng., 3(2), 96-111.
4 Basu, U. and Chopra A.K. (2002), "Numerical evaluation of the damping-solvent extraction method in the frequency domain", Earthq. Eng. Struct. Dyn., 31(6), 1231-1250.   DOI   ScienceOn
5 Bathe, K.J. (1982), Finite Element Procedures in Engineering Analysis, New Jersey, Prentice-Hill.
6 Bettess, P. (1978), "Infinite elements", Int. J. Numer. Meth. Eng., 11, 54-64.
7 Fang, K. and Brown, R. (1995), "Numerical simulation of wave propagation in anisotropic media", CREWES Research Report, 7, 101-122.
8 Genes, M.C. and Kocak, S. (2002), "A combined finite element based soil-structure interaction model for largescale system and applications on parallel platforms", Eng. Struct., 10, 154-172.
9 Kausel, E. (2010), "Early history of soil-structure interaction", J. Soil Dyn. Earthq. Eng., 30, 822-832.   DOI   ScienceOn
10 Kazakov, K.S. (2008), "Mapping functions for 2D elastodynamic infinite element with united shape function", Slovak Journal of Civil Engineering, Bratislava, XVI(4), 17-25.
11 Kazakov, K.S. (2009), The Finite Element Method for Structural Modeling, Bulgarian Academy of Science (BAS) Publishing House "Prof. Marin Drinov", Second Edition.
12 Kazakov, K.S. (2010), Infinite Elements in the Finite Element Method, VSU Publishing House, Third Edition.
13 Kazakov, K. (2005), "On an elastodynamic infinite element, appropriate for an soil-structure interaction models", Proceedings of 10th Jubilee National Congress on Theoretical and Applied Mechanics, BAS, Varna, September.
14 Kazakov, K. (2009), "Stiffness and mass matrices of FEM-applicable dynamic infinite element with unified shape basis", American Institute of Physics, Current Themes in Engineering Science 2008, Selected Papers at the World Congress on Engineering, England, London.
15 Kazakov, K. (2010), "Elastodynamic infinite elements with united shape function for soil-structure interaction", Finite Elem. Analy. Des., 46, 936-942.   DOI   ScienceOn
16 Luco, J.E. and Westmann, R.A. (1972), "Dynamic response of a rigid footing bonded to an elastic half space", J. Appl. Mech.-ASME, 18, 92-108.
17 Madabhushi, S.P.G. (1996), Modeling of Deformations in Dynamic Soil-Structure Interaction Problems, VELACS, Technical Report TR277, Cambridge University, England.
18 Oh, H.S. and Jou, Y. Ch. (2001), The Weighted Riesz-Galerkin Method for Elliptic Boundary Value Problems on Unbounded Domain, NC 28223-0001.
19 Patil, V.A., Sawant, V.A. and Kousik, D. (2010), "Use of finite and infinite elements in static analysis of pavement", Interact. Multis. Mech., 3(1), 95-110.   DOI
20 Pradhan, P.K., Baidya, D.K. and Ghosh, D.P. (2003), "Impedance functions of circular foundation resting on soil using cone model", EJGE, 6, 67-80.
21 Todorovski, L.I., Andersen, G.R. and Likos, W.J. (2000), A New Approach to the Physical Modeling of Dynamic Soil-Structure Interaction, www.ce.jhu.edu.
22 Tzong, T.J. and Penzien, J. (1986), "Hybrid-modeling of a single layer half-space system in soil-structure interaction", Earthq. Eng. Struct. D., 14, 92-108.
23 Ungless, R.F. (1973), "Infinite elements", M.A. Sc. Dissertation, University of British Columbia.
24 Wang, J. (2005), "Influence of different boundary conditions on analysis of SSI", Proceedings of 18th International Conference on Structural Mechanics in Reactor Technology (SMIRT 18), Beijing, August.
25 Wolf, J.P. and Song, C. (1996), Finite-element Modeling of Unbounded Media, England, Wiley.
26 Wolf, J.P. (1988), Soil-Structure Interaction Analysis in a Time Domain, Englewood Cliffs, Prentice-Hill, N.J.
27 Yan, Ch.B., Kim, D.K. and Kim, J.N. (2000), "Analytical frequency-dependent infinite elements for soil-structure interaction analysis in a two-dimensional medium", Eng. Struct., 22, 258-271.   DOI   ScienceOn
28 Zhao, Ch. and Valliappan, S. (1993), "A dynamic infinite element for three-dimensional infinite domain wave problems", Int. J. Numer. Meth. Eng., 36, 2567-2580.   DOI   ScienceOn
29 Zienkiewicz, O.C., Bando, K., Bettess, P., Emson, C. and Chiam, T.C. (1985), "Mapped infinite elements for exterior wave problems", Int. J. Numer. Meth. Eng., 21, 1229-1251.   DOI   ScienceOn