On the Total Dynamic Response of Soil-Structure Interaction System in Time Domain Using Elastodynamic Infinite Elements with Scaling Modified Bessel Shape Functions
- 1 Structural Mechanic Department, VSU “L. Karavelov”, Sofia, Bulgaria
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.
- 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.
- K. J. Bathe, “Finite Element Procedures in Engineeringanalysis,” Prentice-Hill, Upper Saddle River, 1982.
- 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
- P. Bettess, “Infinite Elements,” International Journal for Numerical Methods in Engineering, Vol. 11, No. 1, 1978, pp. 54-64.
- K. Fang and R. Brown, “Numerical Simulation of Wave Propagation in Anisotropic Media,” CREWES Research Report, Vol. 7, 1995.
- 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
- 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
- S. P. G. Madabhushi, “Modeling of Deformations in Dynamic Soil-Structure Interaction Problems,” VELACS, Technical Report TR277, Cambridge University, Cambridge, 1996.
- H. S. Oh and Y. Ch. Jou, “The Weighted Riesz-Galerkin Method for Elliptic Boundary Value Problems on Unbounded Domain,” NC 28223-0001.
- K. S. Kazakov, “Infinite Elements in the Finite Element Method,” 3rd Edition, VSU Publishing House, Sofia, 2010.
- R. F. Ungless, “Infinite Elements,” M.Sc. Dissertation, University of British Columbia, Vancouver, 1973.
- J. P. Wolf and C. Song, “Finite-Element Modeling of Unbounded Media,” Wiley, London, 1996.
- 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
- K. S. Kazakov, “The Finite Element Method for Structural Modelling,” 2nd Edition, Bulgarian Academy of Science (BAS) Publishing House, Sofia, 2009.
- J. P. Wolf, “Soil-Structure Interaction Analysis in a Time Domain,” Prentice-Hill, Englewood Cliffs, 1988.