Kimiaeifar, A., Lund, E., Thomsen, O.T. and Sørensen, J.D.
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
Computers & Mathematics with Applications, 62, (12), . (doi:10.1016/j.camwa.2011.10.050).
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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.
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