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

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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

机译：哈尔小波，高阶哈尔小波和差分正交方法对嵌入弹性介质中应变梯度非局部梁屈曲响应的差分正交方法

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摘要

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, H0HWM, 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.

机译：本研究专注于嵌入在闪光弹性基础中的应变梯度非局部梁的屈曲行为。一阶应变梯度模型与Euler-Bernoulli光束理论结合使用，以使用Hamilton原则制定所提出的模型。三种数值有效的方法，即HAAR小波法（HWM），高阶HAAR小波法（HOHWM）和差分正交方法（DQM）分析应变梯度非局部束的屈曲特性。有效地研究了若干参数，如非本种参数，应变梯度参数和Winkler模量参数的影响。数字方法的基本思路，viz。全面提出了HWM，H0HWM和DQM。此外，已经进行了比较研究以探讨所有三种数值方法在收敛研究方面的有效性和适用性。最后，通过此调查获得的结果与早些时候发布的其他作品合理地验证。

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来源
《Engineering with Computers》 |2021年第2期|1251-1264|共14页
作者
Subrat Kumar Jena; S.Chakraverty; Mohammad Malikan;
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作者单位

Department of Mathematics National Institute of Technology Rourkela Rourkela 769008 India;

Department of Mathematics National Institute of Technology Rourkela Rourkela 769008 India;

Department of Mechanics of Materials and Structures Faculty of Civil and Environmental Engineering Gdansk University of Technology Gdansk Poland Department of Mechanical Engineering Faculty of Engineering Islamic Azad University Mashhad Branch Mashhad Iran;

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正文语种 eng
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关键词
Buckling behavior; Strain gradient model; Nonlocal beam; HWM; HOHWM; DQM;

机译：屈曲行为;应变梯度模型;非本体梁;HWM;HOHWM;DQM.;

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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