Abstract
A 1D finite element method in time domain is developed in this paper and applied to calculate in-plane wave motions of free field exited by SV or P wave oblique incidence in an elastic layered half-space. First, the layered half-space is discretized on the basis of the propagation characteristic of elastic wave according to the Snell law. Then, the finite element method with lumped mass and the central difference method are incorporated to establish 2D wave motion equations, which can be transformed into 1D equations by discretization principle and explicit finite element method. By solving the 1D equations, the displacements of nodes in any vertical line can be obtained, and the wave motions in layered half-space are finally determined based on the characteristic of traveling wave. Both the theoretical analysis and the numerical results demonstrate that the proposed method has high accuracy and good stability.
Similar content being viewed by others
References
Hu Y.X. and Zhou X.Y. (1999). The inter-century development trend of earthquake engineering (in Chinese). Earthq. Resist. Eng. 1: 3–9
Shen J.M., Zhou X.Y., Gao X.W. and Liu J.B. (2000). Aseismic Engineering (in Chinese). China Architecture and Building Press, Beijing
Liao Z.P. and Zheng T.Y. (1997). Development of engineering seismology in China (in Chinese). Acta Geophys. Sin. 40: 177–191
Wolf J.P. and Obernhuber P. (1979). Effects of horizontally traveling waves in soil–structure interaction. Nucl. Eng. Des. 57(2): 221–244
Zhang C.H. (1993). Theory and application of soil–structure interaction (in Chinese). HoHai University Press, Nanjing
Haskel N.A. (1953). The dispersion of surface waves in multi-layered media. Bull. Seism. Soc. Am. 43: 17–34
Brekhovshikh L.M. (1980). Waves in Layered Media. Academic, New York
Li S.Y., Wang X.L. and Zhou Z.H. (2003). The time-step numerical simulation of free field motion of layered half-space for inclined seismic waves (in Chinese). J. JiLin Univ. (Earth edition) 33(3): 372–376
Liu J.B. and Wang Y. (2006). 1D time-domain method for 2D wave motion in elastic half-space by antiplane wave oblique incidence (in Chinese). Chin. J. Appl. Mech. 23(2): 263–266
Liu J.B. and Wang Y. (2006). A 1D time-domain method for 2D wave motion in elastic layered half-space by antiplane wave oblique incidence (in Chinese). Chin. J. Theor. Appl. Mech. 38(2): 219–225
Aki K. and Richards P.G. (1980). Quantitative Seismology: Theory and Methods. W.H. Freeman and Company, New York
Liao Z.P. (1984). The finite element solution of near-field wave motion problem (in Chinese). Earthq. Eng. Eng. Vib. 4(2): 1–14
Liao Z.P. (1997). Numerical simulation of near-field wave motion (in Chinese). Adv. Mech. 27(2): 193–212
Lysmer J. and Kulemeyer R.L. (1969). Finite dynamic model for infinite media. J. Eng. Mech. 95: 759–877
Liao Z.P., Huang K.L. and Yang B.P. (1984). A transmitting boundary for transient wave analysis. Sci. China (Ser. A) 27(10): 1063–1076
Liao Z.P. (2001). Transmitting boundary and radiation conditions at infinity. Sci. China (Ser. E) 44(2): 177–186
Guan H.M. and Liao Z.P. (1996). An accuracy analysis of the multi-transmitting boundary in the simulation of transient waves in layered media (in Chinese). Earthq. Eng. Eng. Vib. 16(1): 60–69
Liu J.B. and Lv Y.D. (1998). A direct method for analysis of dynamic soil-structure interaction (in Chinese). China Civ. Eng. J. 31(3): 55–64
Liu J.B. and Liao Z.P. (1992). In-plane wave motion in finite element model. Acta Mech. Sin. 8(1): 80–87
Fu S.F. and Liu B.C. (1991). Seismology Tutorial (in Chinese). Seismic Press, Beijing
Author information
Authors and Affiliations
Corresponding author
Additional information
The project supported by the National Natural Science Foundation of China (50478014), the National 973 Program (2007CB714200) and the Beijing Natural Science Foundation (8061003).
The English text was polished by Yunming Chen.
Rights and permissions
About this article
Cite this article
Liu, J., Wang, Y. A 1D time-domain method for in-plane wave motions in a layered half-space. Acta Mech. Sin. 23, 673–680 (2007). https://doi.org/10.1007/s10409-007-0114-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10409-007-0114-1