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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

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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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Acknowledgements

The first two authors are very much thankful to the Defence Research and Development Organization(DRDO), New Delhi, India (Sanction Code: DG/TM/ERIPR/GIA/17-18/0129/020) for the funding to carry out the present research work.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Rourkela, Rourkela, 769008, India

    Subrat Kumar Jena & S. Chakraverty

  2. Department of Mechanics of Materials and Structures, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Gdansk, Poland

    Mohammad Malikan

  3. Department of Mechanical Engineering, Faculty of Engineering, Islamic Azad University, Mashhad Branch, Mashhad, Iran

    Mohammad Malikan

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  1. Subrat Kumar Jena
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  2. S. Chakraverty
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  3. Mohammad Malikan
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Correspondence to S. Chakraverty.

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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 37, 1251–1264 (2021). https://doi.org/10.1007/s00366-019-00883-1

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