Reliability Analysis of Composite-Nanofluid Tube Using Finite-Based Armijo Method

The reliable performance of composite tubes conveying nanofluid is an essential issue for robust design under dynamic loads. Further, the frequency failure mode of these structures is a considerable performance function to provide a balance between mass and stiffness of the structure. The ability of the first-order reliability method (FORM)-based finite-step adaptive length (FAL) is discussed for reliability analysis of composite tubes under frequency failure mode. The performances for efficiency and robustness to evaluate the failure probability FORM formulas are discussed. Therefore, the capability of FAL using the steepest descent sensitivity vector is compared with three FORM formulations that are extended by the steepest descent search direction for nanocomposite tubes conveying nanofluid. In this current work, the Navier scheme is employed for calculating the frequency failure mode. Furthermore, the robustness and efficiency related to the steepest descent FORM formulas of HL-RF, directional stability transformation method (DSTM), and finite-step length (FSL) are compared with FAL. Based on this discussion, FAL contains efficient formula in comparison with other FORM formulas. Moreover, it is found that FSL formulas as well as FAL formulas are more robust than HL-RF and DSTM. This structure's failure probability rises as the fluid velocity and pipe diameter increase.