Application of the homotopy analysis method to determine the analytical limit state functions and reliability index for large deflection of a cantilever beam subjected to static co-planar loading

A. Kimiaeifar, E. Lund, O.T. Thomsen, J.D. Sørensen

Research output: Contribution to journalArticle (Academic Journal)

Abstract

In this paper, the Homotopy Analysis Method (HAM) is applied to obtain the limit state function, probability of failure and reliability index based on all stochastic and deterministic variables for a cantilever beam subjected to co-planar loading for the first time. First, it is established that a few iterations in the series expansion are sufficient to obtain highly accurate results and a substantial convergence region. After showing the effectiveness of HAM, two limit state functions are introduced as the maximum deflection in the y direction and maximum allowable stress, respectively. Then the first order reliability method (FORM) is employed to obtain reliability index, and omission sensitivity factor analytically. It is shown that HAM is a promising tool to obtain limit state function, probability of failure and reliability index analytically for nonlinear problems. Finally, a sensitivity analysis is done to show that which parameters could be considered deterministic or stochastic variables.
Original languageEnglish
Pages (from-to)4646-4655
Number of pages10
JournalComputers and Mathematics with Applications
Volume62
Issue number12
Publication statusPublished - 1 Dec 2011

Keywords

  • reliability index, omission sensitivity factor, failure function, homotopy analysis method, geometrical nonlinearity

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