On the Total Dynamic Response of Soil-Structure Interaction System in Time Domain Using Elastodynamic Infinite Elements with Scaling Modified Bessel Shape Functions

Konstantin Kazakov

Structural Mechanic Department, VSU “L. Karavelov”, Sofia, Bulgaria.

DOI: 10.4236/ajcm.2013.32017                

Abstract

This paper is devoted to a new approach—the dynamic response of Soil-Structure System (SSS), the far field of which is discretized by decay or mapped elastodynamic infinite elements, based on scaling modified Bessel shape functions are to be calculated. These elements are appropriate for Soil-Structure Interaction problems, solved in time or frequency domain and can be treated as a new form of the recently proposed elastodynamic infinite elements with united shape functions (EIEUSF) infinite elements. Here the time domain form of the equations of motion is demonstrated and used in the numerical example. In the paper only the formulation of 2D horizontal type infinite elements (HIE) is used, but by similar techniques 2D vertical (VIE) and 2D corner (CIE) infinite elements can also be added. 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. A numerical example shows the computational efficiency and accuracy of the proposed infinite elements, based on scaling Bessel shape functions.

Keywords

Soil-Structure Interaction; Wave Propagation; Infinite Elements; Finite Element Method; Bessel Functions; Duhamel Integral

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	D. Aubry, D. Clouteau and P. D’Azemar, “A Dynamic Substructure Approach to Soil-Structure Interaction,” Computational Mechanics Publications, Vol. 3, Springer Verlag, Berlin, 2002.
[2]	K. J. Bathe, “Finite Element Procedures in Engineeringanalysis,” Prentice-Hill, Upper Saddle River, 1982.
[3]	U. Basu and A. K. Chopra, “Numerical Evaluation of the Damping-Solvent Extraction Method in the Frequency Domain,” Earthquake Engineering and Structural Dynamics, Vol. 31, No. 6, 2002, pp. 1231-1250. doi:10.1002/eqe.156
[4]	P. Bettess, “Infinite Elements,” International Journal for Numerical Methods in Engineering, Vol. 11, No. 1, 1978, pp. 54-64.
[5]	K. Fang and R. Brown, “Numerical Simulation of Wave Propagation in Anisotropic Media,” CREWES Research Report, Vol. 7, 1995.
[6]	K. S. Kazakov, “Elastodynamic Infinite Elements with United Shape Function for Soil-Structure Interaction,” Finite Elements in Analysis and Design, Vol. 46, No. 10, 2010, pp. 936-942. doi:10.1016/j.finel.2010.06.008
[7]	J. E. Luco and R. A. Westmann, “Dynamic Response of a Rigid Footing Bonded to an Elastic Half Space,” Journal of Applied Mechanics, Vol. 39, No. 2, 1972, pp. 93-99. doi:10.1115/1.3422711
[8]	S. P. G. Madabhushi, “Modeling of Deformations in Dynamic Soil-Structure Interaction Problems,” VELACS, Technical Report TR277, Cambridge University, Cambridge, 1996.
[9]	H. S. Oh and Y. Ch. Jou, “The Weighted Riesz-Galerkin Method for Elliptic Boundary Value Problems on Unbounded Domain,” NC 28223-0001.
[10]	K. S. Kazakov, “Infinite Elements in the Finite Element Method,” 3rd Edition, VSU Publishing House, Sofia, 2010.
[11]	R. F. Ungless, “Infinite Elements,” M.Sc. Dissertation, University of British Columbia, Vancouver, 1973.
[12]	J. P. Wolf and C. Song, “Finite-Element Modeling of Unbounded Media,” Wiley, London, 1996.
[13]	M. C. Genes and S. Kocak, “A Combined Finite Element Based Soil-Structure Interaction Model for Large-Scale System and Applications on Parallel Platforms,” Engineering Structures, Vol. 24, No. 9, 2002, pp. 1119-1131. doi:10.1016/S0141-0296(02)00042-1
[14]	K. S. Kazakov, “The Finite Element Method for Structural Modelling,” 2nd Edition, Bulgarian Academy of Science (BAS) Publishing House, Sofia, 2009.
[15]	J. P. Wolf, “Soil-Structure Interaction Analysis in a Time Domain,” Prentice-Hill, Englewood Cliffs, 1988.
[16]	Ch. B. Yan, D. K. Kim and J. N. Kim, “Analytical Frequency-Dependent Infinite Elements for Soil-Structure Interaction Analysis in a Two-Dimensional Medium,” Engineering Structures, Vol. 22, No. 3, 2000, pp. 258-271. doi:10.1016/S0141-0296(98)00070-4
[17]	Ch. Zhao and S. Valliappan, “A Dynamic Infinite Element for Three-Dimensional Infinite Domain Wave Problems,” International Journal for Numerical Methods in Engineering, Vol. 36, No. 15, 1993, pp. 2567-2580. doi:10.1002/nme.1620361505
[18]	K. S. Kazakov, “Formulation of Elastodynamic Infinite Elements for Dynamic Soil-Structure Interaction,” WSEAS Transactions on Applied and Theoretical Mechanics, Vol. 6, No. 1, 2011, pp. 91-96.
[19]	K. S. Kazakov, “Mapping Functions for 2D Elastodynamic Infinite Element with United Shape Function,” Slovak Journal of Civil Engineering, Vol. 16, 2008, pp. 17-25.
[20]	K. S. Kazakov, “On an Elastodynamic Infinite Element, Appropriate for an Soil-Structure Interaction Models,” Proceedings of 10th Jubilee National Congress on Theoretical and Applied Mechanics, Varna, Vol. 1, 2005, pp. 230-236.
[21]	K. S. Kazakov, “Stiffness and Mass Matrices of FEM-Applicable Dynamic Infinite Element with Unified Shape Basis,” AIP Conference Proceedings, Vol. 1138, No. 1, 2009, p. 95. doi:10.1063/1.3155133
[22]	P. K. Pradhan, D. K. Baidya and D. P. Ghosh, “Impedance Functions of Circular Foundation Resting on Soil Using Cone Model,” ASME Report 12, 2003.
[23]	F. E. Relton, “Applied Bessel Functions,” Blackie and Son, London, 1946.