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International Journal of Steel Structures

, Volume 15, Issue 2, pp 335–346 | Cite as

Application of multistage homotopy perturbation method to the nonlinear space truss model

  • Sudeok Shon
  • Junhong Ha
  • Seungjae Lee
  • Jae-Jun Kim
Article

Abstract

The purpose of this study is to investigate the applicability of multistage homotopy perturbation method (MHPM) to space truss structures composed of discrete members in order to obtain an analytical solution. For this research purpose, a nonlinear dynamic governing equation of the space truss structures was formulated in consideration of geometrical nonlinearity, and homotopy equations were derived using a formulated differential equation. The result of carrying out a dynamic analysis on a single-free-node model and a double-free-nodes model were compared with the classical homotopy perturbation method and the 4th order Runge-Kutta method (RK4), and it was found that the dynamic response by MHPM concurred with the numerical results. Additionally, the pattern of the response and attractor in the phase space could delineate the dynamic snapping properties of the space truss structures under excitations, and the attraction of the model in consideration of damping reflected well the convergence and asymptotic stable.

Keywords

multistage homotopy perturbation method (MHPM) analytical solution space truss nonlinear dynamic system geometric nonlinearity 

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Copyright information

© Korean Society of Steel Construction and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Sudeok Shon
    • 1
  • Junhong Ha
    • 2
  • Seungjae Lee
    • 1
  • Jae-Jun Kim
    • 3
  1. 1.School of Architectural EngineeringKorea University of Technology and EducationCheonanKorea
  2. 2.School of Liberal ArtsKorea University of Technology and EducationCheonanKorea
  3. 3.Department of Architectural EngineeringHanyang UniversitySeoulKorea

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