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Nonlinear analysis for extreme large bending deflection of a rectangular plate on non-uniform elastic foundations

机译：非均匀弹性地基上矩形板极大弯曲挠度的非线性分析

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摘要

An analysis is presented for different bearing loadings of a plate resting on various linear and nonlinear foundations subjected to different boundary conditions such as the circled clamped, simply supported, and mixed boundary conditions. The highly accurate solutions of the plate deflection and the stress under different work conditions are obtained by the novel wavelet-homotopy technique, which are in full agreement with previous ones in literature. Different from previous studies, our solutions are also valid for the extra large plate bending cases, which are rarely considered before. Particularly, we consider the important case that the connection coefficients of various foundations are variational, which seems to be overlooked in previous studies owing to their extreme difficulties in mathematical treatments and programming. Besides, to overcome the limitation of existing wavelet technique of poor capability on handling complex boundary conditions, we reconstruct the boundary wavelet by the Coiflets so that it can be used to handle the governing partial differential equations subjected to nonhomogeneous boundary conditions. Moreover, we introduce the homotopy iteration technique so that the computational efficiency improves to a large extent as compared with the traditional Homotopy Analysis Method (HAM) technique. It is expected the proposed wavelet-homotopy method can be as a new generation of analytical tool for solving strong nonlinear problems subjected to complicated boundary conditions, especially for those with variable coefficients.
机译：针对在各种线性和非线性基础上承受不同边界条件（例如圆形夹紧，简单支撑和混合边界条件）的板的不同轴承载荷进行了分析。通过新颖的小波同伦方法获得了在不同工作条件下板变形和应力的高精度解决方案，与文献中的方法完全吻合。与以前的研究不同，我们的解决方案也适用于以前很少考虑的特大板弯曲情况。特别是，我们考虑了各种基础的连接系数是变化的重要情况，由于它们在数学处理和编程方面的极端困难，因此在以前的研究中似乎忽略了这一点。此外，为克服现有小波技术处理复杂边界条件的局限性，我们通过Coiflets重构边界小波，使其可用于处理非均匀边界条件下的控制偏微分方程。此外，我们引入了同伦迭代技术，从而与传统的同伦分析方法（HAM）技术相比，在很大程度上提高了计算效率。期望所提出的小波同态方法可以作为解决复杂边界条件（特别是对于那些具有可变系数的条件）的强非线性问题的新一代分析工具。

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  • 来源
    《Applied Mathematical Modelling》 |2018年第9期|316-340|共25页
  • 作者

    Qiang Yu; Hang Xu; Shijun Liao;

  • 作者单位

    Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration (CISSE), State Key Laboratory of Ocean Engineering, School of Naval Architecture Ocean and Civil Engineering, Shanghai Jiao Tong University;

    Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration (CISSE), State Key Laboratory of Ocean Engineering, School of Naval Architecture Ocean and Civil Engineering, Shanghai Jiao Tong University;

    Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration (CISSE), State Key Laboratory of Ocean Engineering, School of Naval Architecture Ocean and Civil Engineering, Shanghai Jiao Tong University;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Thin rectangular plates; Elastic foundation; Wavelet-Galerkin method; Closed wavelet method; Wavelet-homotopy;

    机译：矩形薄板;弹性基础;小波-加勒金法;封闭小波法;小波同伦;

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