| Title |
A Study on the Analytical Solution using Homotopy Perturbation Method of Shell-like Shallow Trusses |
| Authors |
Shon, Su-Deok ; Lee, Seung-Jae |
| DOI |
http://dx.doi.org/10.5659/JAIK_SC.2015.31.9.27 |
| Keywords |
Homotopy perturbation method ; Analytical solution ; Shell-like shallow truss ; Dynamic instability ; Runge-Kutta method |
| Abstract |
In this study, an analytical solution using the homotopy perturbation method of shell-like shallow trusses was investigated. The dynamic unstable phenomenon that appears in shallow space trusses is sensitive to initial conditions, and its characteristics are analyzed and its instability is examined by obtaining the exact solution or through numerical analysis. In this process, obtaining a more precise solution plays a very important role, and obtaining an analytical solution expressed in infinite terms is one way to get a more accurate result. A homotopy equation, in this study, was derived by formulating a governing equation for a shell-like shallow truss, and a semi-analytical solution was obtained by homotopy perturbation method. Besides, sensitive unstable phenomena were examined and their solutions were compared according to various dynamic behaviors and initial conditions, and the shapes of attractors in the phase space were observed. In conclusion, the analytical solution of the simple nonlinear model using the homotopy method proposed in this study was excellent when compared with the numerical analysis result, and reflected the nonlinear unstable phenomenon of the shell-like shallow truss which was the target model of analysis. |