Comparison of Variational, Differential Quadrature, and Approximate Closed-Form Solution Methods for Buckling of Highly Flexurally Anisotropic Laminates
Comparison of Variational, Differential Quadrature, and Approximate Closed-Form Solution Methods for Buckling of Highly Flexurally Anisotropic Laminates
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高弯曲各向异性层合板屈曲的变分法、微分求积法和近似闭式求解方法的比较
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
P. Weaver
中科院分区：
文献类型：
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作者：
Zhangming Wu;G. Raju;P. Weaver
本文采用不同的方法研究了具有强弯扭耦合的对称层合板的屈曲响应。由于振型中存在局部梯度，这种板很难分析。首先，能量法（瑞利-里兹）使用勒让德多项式，并讨论了一些极端情况下实现可靠的解决方案的困难。为了克服收敛性问题，拉格朗日乘子的概念被引入到瑞利-里兹公式。拉格朗日乘数法能够提供临界屈曲载荷结果的上界和下界。此外，混合变分原理被用来获得更好的理解背后的力学强弯扭各向异性效应的屈曲解决方案。具体而言，Hellinger-Reissner变分原理被用来研究屈曲的弯扭耦合的影响，并探讨开发这些封闭形式的解决方案的潜力…
AbstractThe buckling response of symmetric laminates that possess strong flexural-twist coupling is studied using different methodologies. Such plates are difficult to analyze because of localized gradients in the mode shape. Initially, the energy method (Rayleigh-Ritz) using Legendre polynomials is employed, and the difficulty of achieving reliable solutions for some extreme cases is discussed. To overcome the convergence problems, the concept of Lagrangian multiplier is introduced into the Rayleigh-Ritz formulation. The Lagrangian multiplier approach is able to provide the upper and lower bounds of critical buckling load results. In addition, mixed variational principles are used to gain a better understanding of the mechanics behind the strong flexural-twist anisotropy effect on buckling solutions. Specifically, the Hellinger-Reissner variational principle is used to study the effect of flexural-twist coupling on buckling and also to explore the potential for developing closed-form solutions for these ...