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An Energy Transmitting Boundary for Semi-Infinite Structures

Published online by Cambridge University Press:  05 May 2011

S.-S. Chen  and
W.-C. Hsu
S.-S. Chen*
Affiliation:
Department of Construction Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan 10607, R.O.C.
W.-C. Hsu*
Affiliation:
Department of Construction Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan 10607, R.O.C.
*
*Professor
**Graduate student
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Abstract

A soil-structure system associated with a semi-infinite structure such as tunnel or pavement is usually investigated by finite element analysis. If the boundary of the finite element model selected is not far enough from the excitation source or does not have an appropriate energy-absorption mechanism, it may introduce a significant error induced by reflected waves. This study develops a structural transmitting boundary to absorb the transmitting energy at the boundary of the analytical model. The structure is divided into finite and semi-infinite regions. The stiffness of the semi-infinite region is established by the principle of virtual work and applied at the transmitting boundary. The comparisons of the structural displacements induced by vertical harmonic excitations show that the analytical model size can be significantly reduced, if the proposed transmitting boundary is used to simulate the semi-infinite structural region.

Keywords

Transmitting boundarySemi-infinite structureSoil-structure interaction
Type
Articles
Information
Journal of Mechanics , Volume 23 , Issue 2 , June 2007 , pp. 159 - 172
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2007

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References

1.Lysmer, J. and Kuhlemeyer, R., “Finite Dynamic Model for Infinite Media,” Journal of the Engineering Mechanics Division ASCE; 95(EM4), pp. 859–877 (1969).CrossRefGoogle Scholar
2. ABAQUS Inc., “ABAQUS theory manual - v. 6.5,” Chap. 3, (2005).Google Scholar
3.Lysmer, J., “Lumped Mass Method for Rayleigh Waves,” Bulletin of Seismological Society of America; 60(1), pp. 89–104 (1970).CrossRefGoogle Scholar
4.Waas, G., “Earth Vibration Effects and Abatement for Military Facilities – Analysis Method for Footing Vibration Through Layered Media,” Report S-71-14, U.S. Army Engineer Waterways Experiment Station (1972).Google Scholar
5.Lysmer, J., Udaka, T., Tsai, C. F. and Seed, B., “FLUSH – A Computer Program for Approximate 3-D Analysis of Soil-Structure Interaction Problems,” Report No. EERC 75–30, Engineering Research Center, University of California, Berkeley (1975).Google Scholar
6.Kausel, E., “Forced Vibrations of Circular Foundations on Layered Media,” Ph.D. dissertation, Massachusetts Institute of Technology (1974).Google Scholar
7.Tassoulas, J., “Elements for the Numerical Analysis Wave Motion in Layered Media,” Ph.D. dissertation, Massachusetts Institute of Technology (1981).Google Scholar
8.Schlue, J. W., “Finite Element Matrices for Seismic Surface Waves in Three-Dimensional Structures,” Bulletin of Seismological Society of America; 69(5), pp. 1425–1437 (1979).Google Scholar
9.Kim, J. K., et al., “A Three-Dimensional Transmitting Boundary Formulated in Cartesian Co-Ordinate System for the Dynamics of Non-Axisymmetric Foundations,” Earthquake Engineering and Structural Dynamics, 29, pp. 1527–1546(2000).3.0.CO;2-S>CrossRefGoogle Scholar
10.Bettess, P. and Zienkiewicz, O. C., “Diffraction and Refraction of Surface Waves Using Finite and Infinite Elements,” International Journal for Numerical Methods in Engineering, 11, Issue 8, pp. 1271–1290 (1977).CrossRefGoogle Scholar
11.Park, W.-S., Yun, C.-B. and Pyun, C.-K., “Infinite Elements for 3-Dimensional Wave-Structure Interaction Problems,” Engineering Structures, 14(5), pp. 335–346 (1992).CrossRefGoogle Scholar
12.Shirron, J. J. and Babuska, I., “A Comparison of Approximate Boundary Conditions and Infinite Element Proximate Boundary Condition and Infinite Element Methods for Exterior Helmholtz Problems,” Computer Methods in Applied Mechanics and Engineering, 164, pp. 121–139(1998)CrossRefGoogle Scholar
13.Astley, R. J., “Infinite Elements for Wave Problems: A Review of Current Formulations and an Assessment of Accuracy,” International Journal for Numerical Method in Engineering, 49(7), pp. 951–976 (2000).3.0.CO;2-T>CrossRefGoogle Scholar
14.Angelov, T. A., “Infinite Elements- Theory and Applications,” Computers and Structures, 41(5), pp. 959–962 (1991).CrossRefGoogle Scholar
15.Viladkar, M. N., Godbole, P. N. and Noorzaei, J.“Some New Three-Dimensional Infinite Elements,” Computers and Structures, 34(3), pp. 455–467 (1990).CrossRefGoogle Scholar
16.Zienkiewicz, O. C. and Taylor, R. L., “The Finite Element Method - Fourth Edition,Vol.2,” McGraw-Hill Book Company, Chapter 15 (1991).Google Scholar
17.Cheng, Y. M., “The Use of Infinite Element,” Computers and Geotechnics, 18(1), pp. 65–70 (1996).CrossRefGoogle Scholar
18.Kumar, P., “Infinite Elements for Numerical Analysis of Underground Excavations,” Tunnelling and Underground Space Technology, 15(1), pp. 117–124 (2000).CrossRefGoogle Scholar
19.Brill, D. R. and Parsons, I. D., “Three-Dimensional Finite Element Analysis in Airport Pavement Design,” The International Journal of Geomechanics, 1(3), pp. 273–290 (2001).CrossRefGoogle Scholar
20.Wu, C. Y., Chang, J. S. and Wu, K. C., “Analysis of Wave Propagation in Infinite Piezoelectric Plates,” Journal of Mechanics, 21, pp. 103–108 (2005).CrossRefGoogle Scholar
21.Lysmer, J., “Analytical Procedures in Soil Dynamics,” Report No. EERC 78–29, Earthquake Engineering Research Center, University of California, Berkeley (1978).Google Scholar
22.Tajirian, F., “Impedance Matrices and Interpolation Techniques for 3-D Interaction Analysis by the Flexible Volume Method,” Ph.D. dissertation, University of California, Berkeley (1981).Google Scholar
23.Lysmer, J., Ostadan, F., Tabatabaie, M., Vahdani, S. and Tarjirian, F., “SASSI - A System for Analysis of Soil- Structure Interaction,” University of California, Berkeley (1981).Google Scholar
24.Chin, C. C., “Substructure Subtraction Method and Dynamic Analysis of Pile Foundations,” Ph.D. dissertation, University of California, Berkeley (1998).Google Scholar
25.Kramer, S.Geotechnical earthquake engineering, Prentice-Hall Inc. (1996).Google Scholar
26.Zienkiewicz, O. C. and Taylor, R. L., “The Finite Element Method - Fifth Edition, Vol.1,” Butterworth- Heinemann, Chapter 9 (2000).Google Scholar
27.Wilson, E. L., “Three-Dimensional Static and Dynamic Analysis of Structures - Third Edition,” Computer and structures, Inc. (2002).Google Scholar