Conjugate and Directional Chaos Control Methods for Reliability Analysis of CNT–Reinforced Nanocomposite Beams under Buckling Forces; A Comparative Study

The efficiency and robustness of reliability methods are two important factors in the first-order reliability method (FORM). The conjugate choice control (CCC) and directional chaos control method (DCC) are developed to improve the robustness and efficiency of the FORM formula using the stability transformation method. In this paper, the CCC and DCC methods are applied for the reliability analysis of a nanocomposite beam as a complex engineering problem, which is reinforced by carbon nanotubes (CNTs) under buckling force. The probabilistic model for nanocomposite beam is developed through the buckling failure mode which is computed by using the Euler-Bernoulli beam model. The robustness and efficiency CCC and DCC are compared using the stable solution and a number of call limit state functions. The results demonstrate that the CCC method is more robust than the DCC in this case, while the DCC method is simpler than the CCC.