The effects of gradient index, aspect ratio, porosity, and boundary conditions on the buckling behavior of functionally graded porous beams: A k-out-of-n system reliability analysis

•HSDT is used to simulate functionally graded porous beams with uniform and non-uniform porosity distributions.•The system’s dependability was evaluated using k-out-of-n system reliability analysis.•Changing gradient index and boundary conditions significantly impact the buckling characteristics of FGPB.•Clamped -clamped beams provide improved stability and support.•Governing equations are solved using KT conditions for different boundary conditions. Functionally graded materials are a class of multifunctional materials that exhibit spatial variation in composition and microstructure. This deliberate variation is designed to effectively manage and manipulate changes in thermal, structural, or functional qualities within the material. The current study explores the system reliability of functionally graded porous beams (FGPB) subjected to buckling, focusing on the interplay of gradient index (0, 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10), aspect ratio (5, 10, 15, 20, 25, 30 and 35), porosity index (0, 0.1 and 0.2) and boundary conditions (simply supported, clamped–clamped and clamped-free), with a particular emphasis on the k-out-of-n system reliability assessment, employing three distinct methods such as Evolutionary, GRG Non-linear, and Lagrangian. The results show the system's sensitivity to changes in distribution parameters, with the Lagrangian method being the most robust and stable. The 10-out-of-12 system reliability analysis demonstrates that aspect ratio and even porosity distribution are reliable, while uneven porosity is not. This study enhances structural reliability analysis in FGPBs, enhancing system reliability considerations and paving the way for further advancements in structural reliability analysis.