A Semi-analytical Solution of Shallow Sinusoidal Arches by using Multistage Homotopy Perturbation Method

Title & Authors
A Semi-analytical Solution of Shallow Sinusoidal Arches by using Multistage Homotopy Perturbation Method
Shon, Su-Deok; Lee, Seung-Jae;

Abstract
The purpose of this study is to investigate the applicability of multistage homotopy perturbation method (MHPM) to shallow sinusoidal arches in order to obtain a semi-analytical solution. For this research purpose, a nonlinear governing equation of the arches was formulated and a homotopy equation was derived using the formulated differential equation. The result of a dynamic analysis on a symmetric mode and an asymmetric one was compared with the classical homotopy perturbation method and the $\small{4^{th}}$ order Runge-Kutta method. From the comparison results, it was found that the dynamic response by MHPM concurred with the numerical results. Besides, the pattern of the response and the attractor by semi-analytical solution could delineate the dynamic snapping of the arches under excitations, and the attraction of the model in consideration of damping reflected the convergence and asymptotic stability well.
Keywords
Multistage homotopy perturbation method (MHPM);Semi-analytical method;Shallow sinusoidal arch;Dynamic snapping;Runge-Kutta method;
Language
Korean
Cited by
1.
쉘형 얕은 트러스의 호모토피 섭동법을 이용한 해석적 해에 관한 연구,손수덕;이승재;

대한건축학회논문집:구조계, 2015. vol.31. 9, pp.27-34
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