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Seismic Ground Response Analysis pp 215–240Cite as

Equation of Motion: Spatial Modeling

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Part of the book series: Geotechnical, Geological and Earthquake Engineering ((GGEE,volume 36))

Abstract

The equation of motion is a partial differential equation with respect to space and time. Therefore, it is to be solved against both variables. Among them, a method to solve with respect to space is shown in this chapter and that with respect to time is explained in the next chapter.

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References

  • Achenbach JD (ed) (1983) Computational methods for transient analysis, vol 1, Mechanics and mathematical methods. Elsevier Science Publications, Amsterdam

    Google Scholar 

  • Association for Disaster Prevention Research (1990) Report on investigation and research on development of two-dimensional liquefaction analysis computer program (in Japanese)

    Google Scholar 

  • Building Research Institute and Japan Society of Construction Engineering (1997) Sectional committee report on risk evaluation of earthquake motion amplification, Building Research Institute Technical Project “Development of earthquake disaster prevention in urban area”, 381 pp (in Japanese)

    Google Scholar 

  • Committee of gas facility standard (2000) Design specification of high pressure gas pipeline. Japan Gas Association (in Japanese)

    Google Scholar 

  • Cook RD, Malkus DS, Plesha ME (1989) Concepts and applications of finite element analysis, 3rd edn. Wiley, New York

    MATH  Google Scholar 

  • Flanagan DP, Belytschko T (1981) A uniform strain hexahedron and quadrilateral with orthogonal hourglass control. Int J Numer Methods Eng 17:679–706

    Article  MATH  Google Scholar 

  • Joyner WB (1975) A method for calculating nonlinear response in two dimensions. Bull Seismol Soc Am 65(5):1337–1357

    Google Scholar 

  • Lysmer J, Drake LA (1971) Chapter 6: A finite element method for seismology. In: Alder B, Fernbach F, Boit BA (eds) Methods in computational physics, vol 11, Seismology. University of California, Berkeley

    Google Scholar 

  • Lysmer J, Kuhlemeyer RL (1969) Finite dynamic model for infinite media. J Eng Mech Div Proc ASCE 95(EM4):859–877

    Google Scholar 

  • Lysmer J, Udaka T, Tsai C-F, Seed HB (1975) FLUSH a computer program for approximate 3-D analysis of soil-structure interaction problems, Report no. EERC75-30. University of California, Berkeley

    Google Scholar 

  • Miura F, Okinaka H (1989) Dynamic analysis method for 3-D soil-structure interaction systems with the viscous boundary based on the principle of virtual work. J Geotech Eng Proc JSCE 404(I–11):395–404 (in Japanese)

    Google Scholar 

  • Ohya Y (2009) A study on numerical analysis of liquefaction and liquefaction-induced flow for practical use, theses submitted to Tohoku Gakuin University, 180 pp (in Japanese)

    Google Scholar 

  • Ohya Y, Yoshida N (2008) FE formulation of effective stress analysis free from volume locking and hourglass instability. J Struct Eng 54B:45–50 (in Japanese)

    Google Scholar 

  • Sakai H, Sawada S, Toki K (2000) Non-linear analyses of dynamic behavior of embankment structures considering tensile failure. In: Proceedings of the 12th WCEE, New Zealand, No. 678/5/A

    Google Scholar 

  • Schnabel PB, Lysmer J, Seed HB (1972) SHAKE a computer program for earthquake response analysis of horizontally layered sites, Report no. EERC72-12. University of California, Berkeley

    Google Scholar 

  • Sekiba Y, Chiba Y, Yoshida N (2009) Effect of soft layer on earthquake response of irregular ground. In: Proceedings, Meeting of Tohoku Branch of JSCE, Tagajo, pp 319–320 (in Japanese)

    Google Scholar 

  • Smith WD (1974) A non reflecting boundary for wave propagation problems. J Comput Phys 15:492–503

    Article  MATH  Google Scholar 

  • Togawa H (1975) Vibration analysis by finite element method. Science-sha (in Japanese)

    Google Scholar 

  • Yasuda S, Yoshida N, Adachi K, Kiku H, Gose S, Masuda T (1999) A simplified practical method for evaluating liquefaction-induced flow. J Geotech Eng Proc JSCE 638/III-49:71–89 (in Japanese)

    Google Scholar 

  • Yoshida N (1988) Effectiveness of the conventional effective stress analysis to predict liquefaction-induced permanent ground displacement. In: Proceedings, First Japan-US workshop on liquefaction, large ground deformation and their effects on lifeline facilities, Tokyo, pp 57–65

    Google Scholar 

  • Yoshida N (1989) Large deformation analysis of liquefaction-induced ground displacement by reduced integral method. In: Proceedings of the 3rd symposium on computational mechanics, Japan Union of scientists, Tokyo, pp 391–396 (in Japanese)

    Google Scholar 

  • Yoshida N, Abo H, Yasuda S, Higuchi K (1999) Case study on applicability of one-dimensional analysis. In: Proceedings of the 54th annual conference of the Japan Society of Civil Engineering, vol 1(A), Hiroshima, pp 216–217 (in Japanese)

    Google Scholar 

  • Zienkiewicz OC (1971) The finite element method in engineering science. McGraw-Hill, London, 521 pp

    MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Civil and Environment Engineering, Tohoku Gakuin University, Miyagi, Japan

    Nozomu Yoshida

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  1. Nozomu Yoshida
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Yoshida, N. (2015). Equation of Motion: Spatial Modeling. In: Seismic Ground Response Analysis. Geotechnical, Geological and Earthquake Engineering, vol 36. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9460-2_10

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