Implementation of non-probabilistic methods for stability analysis of nonlocal beam with structural uncertainties

Abstract

In this study, a non-probabilistic approach-based Navier’s method (NM) and Galerkin weighted residual method (GWRM) in terms of double parametric form have been proposed to investigate the buckling behavior of Euler–Bernoulli nonlocal beam under the framework of Eringen’s nonlocal elasticity theory, considering the structural parameters as imprecise or uncertain. The uncertainties in Young’s modulus and diameter of the beam are modeled in terms of triangular fuzzy numbers. The critical buckling loads are calculated for hinged–hinged, clamped–hinged, and clamped–clamped boundary conditions, and these results are compared with the deterministic model in special cases, demonstrating robust agreement. Further, a random sampling technique-based method, namely Monte Carlo simulation technique (MCST), has been implemented to compute the critical buckling loads of uncertain systems. Also, the critical buckling loads obtained from the uncertain model in terms of lower bound and upper bound by the non-probabilistic methods, viz. NM and GWRM, are again verified with the MCST with their time periods, demonstrating the efficacy, accuracy, and effectiveness of the proposed uncertain model. A comparative study is also carried out among the non-probabilistic methods and MCST to demonstrate the effectiveness of methods with respect to time. Additionally, a parametric study has been performed to display the propagation of uncertainties into the nonlocal system in the form of critical buckling loads.