Implementation of Non-Probabilistic Methods for Stability Analysis of Nonlocal Beam with Structural Uncertainties

Subrat Kumar Subrat; S. Chakraverty; Mohammad Malikan

doi:10.1007/s00366-020-00987-z

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 term of double parametric form has been proposed to investigate the buckling behavior of Euler-Bernoulli nonlocal beam under the framework of the 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 (TFN). The critical buckling loads are calculated for Hinged-Hinged (HH), Clamped-Hinged (CH), and Clamped-Clamped (CC) 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 (LB) and Upper Bound (UB) by the non-probabilistic methods, viz. Navier’s Method (NM) and Galerkin Weighted Residual Method (GWRM), are again verified with the Monte Carlo Simulation Technique (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 Monte Carlo Simulation Technique (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.

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Authors (3)

Subrat Kumar Subrat PhD
- National Institute of Technology Rourkela, 769008, India Department of Mathematics
S. Chakraverty Pofessor
- National Institute of Technology Rourkela, 769008, India Department of Mathematics
Mohammad Malikan dr inż.

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Category:: Articles
Type:: artykuły w czasopismach
Published in:: ENGINEERING WITH COMPUTERS no. 37, pages 2957 - 2969,
ISSN: 0177-0667
Language:: English
Publication year:: 2021
Bibliographic description:: Kumar Subrat S., Chakraverty S., Malikan M.: Implementation of Non-Probabilistic Methods for Stability Analysis of Nonlocal Beam with Structural Uncertainties// ENGINEERING WITH COMPUTERS -Vol. 37, (2021), s.2957-2969
DOI:: Digital Object Identifier (open in new tab) 10.1007/s00366-020-00987-z
Verified by:: Gdańsk University of Technology