Implementation of Haar wavelet, higher order Haar wavelet, and differential quadrature methods on buckling response of strain gradient nonlocal beam embedded in an elastic medium

Subrat Kumar Jena; S. Chakraverty; Mohammad Malikan

doi:10.1007/s00366-019-00883-1

Implementation of Haar wavelet, higher order Haar wavelet, and differential quadrature methods on buckling response of strain gradient nonlocal beam embedded in an elastic medium

Abstract

The present investigation is focused on the buckling behavior of strain gradient nonlocal beam embedded in Winkler elastic foundation. The first-order strain gradient model has been combined with the Euler–Bernoulli beam theory to formulate the proposed model using Hamilton’s principle. Three numerically efficient methods, namely Haar wavelet method (HWM), higher order Haar wavelet method (HOHWM), and differential quadrature method (DQM) are employed to analyze the buckling characteristics of the strain gradient nonlocal beam. The impacts of several parameters such as nonlocal parameter, strain gradient parameter, and Winkler modulus parameter on critical buckling loads are studied effectively. The basic ideas of the numerical methods, viz. HWM, HOHWM, and DQM are presented comprehensively. Also, a comparative study has been conducted to explore the effectiveness and applicability of all the three numerical methods in terms of convergence study. Finally, the results, obtained by this investigation, are validated properly with other works published earlier.

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Publication version: Accepted or Published Version
License: Copyright (Springer-Verlag London Ltd., part of Springer Nature 2019)

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Category:: Articles
Type:: artykuły w czasopismach
Published in:: ENGINEERING WITH COMPUTERS no. 37, pages 1251 - 1264,
ISSN: 0177-0667
Language:: English
Publication year:: 2021
Bibliographic description:: Jena S. K., Chakraverty S., Malikan M.: Implementation of Haar wavelet, higher order Haar wavelet, and differential quadrature methods on buckling response of strain gradient nonlocal beam embedded in an elastic medium// ENGINEERING WITH COMPUTERS -Vol. 37, (2021), s.1251-1264
DOI:: Digital Object Identifier (open in new tab) 10.1007/s00366-019-00883-1
Verified by:: Gdańsk University of Technology