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On the application of the Ritz method to free vibration and buckling analysis of highly anisotropic plates

机译：Ritz方法在高各向异性板自由振动和屈曲分析中的应用

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摘要

In this paper insights are provided into the implementation and use of the Ritz method for free vibration and buckling analysis of composite plates. Focus is given on the choice of the trial functions in relation to the degree and the kind of anisotropy exhibited by the plates. The Ritz approximation is applied to models based both on the classical lamination theory and a more advanced variable-kinematic formulation, capable of dealing with several higher order plate theories within an unified framework. A very efficient computation of the Ritz integrals is proposed, which allows to handle hundreds of admissible functions. In this way, accurate upper bound solutions can be obtained even for problems where the convergence rate of the Ritz method is low due to extreme levels of anisotropy. The effect of different forms of elastic couplings, boundary conditions and amount of material anisotropy on the convergence and accuracy of the solution is investigated when different sets of admissible functions - Legendre and Chebyshev polynomials, as well as of trigonometric type - are adopted. Important remarks about the completeness and numerical efficiency of the selected basis are also provided.
机译：在本文中，我们将深入了解Ritz方法的实现和对复合板的自由振动和屈曲分析的使用。将重点放在与平板显示的各向异性程度和种类有关的试验函数的选择上。 Ritz逼近应用于基于经典层合理论和更高级的可变运动学公式的模型，能够在统一的框架内处理几种更高阶的板理论。提出了一种非常有效的Ritz积分计算，它可以处理数百个允许的函数。以此方式，即使对于由于极端水平的各向异性而导致的丽兹方法的收敛速度较低的问题，也可以获得准确的上限解。当采用不同的允许函数集-Legendre和Chebyshev多项式以及三角函数类型时，研究了不同形式的弹性联轴器，边界条件和材料各向异性的量对解的收敛性和准确性的影响。还提供了有关所选基准的完整性和数值效率的重要说明。

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  • 来源
    《Composite Structures》 |2018年第5期|460-474|共15页
  • 作者

    Vescovini R.; Dozio L.; DOttavio M.; Polit O.;

  • 作者单位

    Politecn Milan, Dipartimento Sci & Tecnol Aerosp, Via La Masa 34, I-20156 Milan, Italy;

    Politecn Milan, Dipartimento Sci & Tecnol Aerosp, Via La Masa 34, I-20156 Milan, Italy;

    Univ Paris Nanterre, UPL, LEME, 50 Rue Sevres, F-92410 Ville Davray, France;

    Univ Paris Nanterre, UPL, LEME, 50 Rue Sevres, F-92410 Ville Davray, France;

  • 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

    Ritz method; Anisotropic plates; Variable-kinematic; Free-vibrations; Buckling;

    机译：里兹法;各向异性板;运动学;自由振动;屈曲;

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