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On new buckling solutions of moderately thick rectangular plates by the symplectic superposition method within the Hamiltonian-system framework

机译：汉密尔顿系统框架中辛叠加法中适度厚矩形板的新屈曲解

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摘要

This paper presents a first attempt to explore the symplectic superposition method for analytic buckling solutions of non-Levy-type moderately thick rectangular plates, which were hard to tackle by classical semi-inverse methods. In contrast with the conventional Lagrangian-system-based expression that is solved in the Euclidean space, this study describes the issue in the Hamiltonian system for treatment in the symplectic space. The follow-up solution procedure involves the conversion of an original problem into sub-problems with symplectic solutions and superposition for final analytic buckling solutions, where the constitution of symplectic eigenvalue problem and symplectic eigen expansion are crucial. Comprehensive buckling load and mode shape results for representative plates are tabulated or plotted, which are all well validated by satisfactory agreement with other solution methods. With the present solutions, parametric analysis has been investigated. Due to the advantages on strictness and accuracy, the developed method provides a solid approach for exploring new analytic solutions of similar problems.
机译：本文提出了第一次尝试探索非征用式中厚矩形板的分析屈曲溶液的辛叠加方法，这很难通过经典半逆方法解决。与欧几里德空间中解决的传统拉格朗日系统的表达相比，该研究描述了汉密尔顿系统在辛杂交空间中治疗的问题。后续解决方案程序涉及将原始问题转换为具有辛溶液的子问题和最终分析屈曲溶液的叠加，其中辛意识值问题和辛酸均征膨胀是至关重要的。制表或绘制代表板的综合屈曲负荷和模式形状结果，这些结果与其他解决方案方法令人满意的协议均得到良好的验证。利用目前的解决方案，研究了参数分析。由于对严格和准确性的优点，开发方法提供了探索类似问题的新分析解决方案的坚实方法。

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  • 来源
    《Applied Mathematical Modelling》 |2021年第6期|226-241|共16页
  • 作者

    Chao Zhou; Dongqi An; Jianyu Zhou; Zixuan Wang; Rui Li;

  • 作者单位

    State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering Mechanics and International Research Center for Computational Mechanics Dalian University of Technology Dalian 116024 China;

    State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering Mechanics and International Research Center for Computational Mechanics Dalian University of Technology Dalian 116024 China;

    Department of Modern Mechanics University of Science and Technology of China Hefei 230027 China;

    State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering Mechanics and International Research Center for Computational Mechanics Dalian University of Technology Dalian 116024 China;

    State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering Mechanics and International Research Center for Computational Mechanics Dalian University of Technology Dalian 116024 China;

  • 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

    Symplectic superposition; Analytic solution; Moderately thick plate; Buckling;

    机译：辛叠加;分析解决方案;适度厚板;屈曲;

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