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基于小波Galerkin法的矩形薄板二次屈曲分析

张磊 张文明 王林 李世斌

张磊,张文明,王林,李世斌. 基于小波Galerkin法的矩形薄板二次屈曲分析 [J]. 应用数学和力学,2023,44(1):25-35 doi: 10.21656/1000-0887.430097
引用本文: 张磊,张文明,王林,李世斌. 基于小波Galerkin法的矩形薄板二次屈曲分析 [J]. 应用数学和力学,2023,44(1):25-35 doi: 10.21656/1000-0887.430097
ZHANG Lei, ZHANG Wenming, WANG Lin, LI Shibin. Secondary Buckling Analysis of Thin Rectangular Plates Based on the Wavelet Galerkin Method[J]. Applied Mathematics and Mechanics, 2023, 44(1): 25-35. doi: 10.21656/1000-0887.430097
Citation: ZHANG Lei, ZHANG Wenming, WANG Lin, LI Shibin. Secondary Buckling Analysis of Thin Rectangular Plates Based on the Wavelet Galerkin Method[J]. Applied Mathematics and Mechanics, 2023, 44(1): 25-35. doi: 10.21656/1000-0887.430097

基于小波Galerkin法的矩形薄板二次屈曲分析

doi: 10.21656/1000-0887.430097
基金项目: 湖南省自然科学基金(2019JJ50735)
详细信息
    作者简介:

    张磊(1989—),男,讲师,博士(通讯作者. E-mail:leizhg2016@163.com

  • 中图分类号: O343

Secondary Buckling Analysis of Thin Rectangular Plates Based on the Wavelet Galerkin Method

  • 摘要:

    通过经典的弹性矩形薄板,研究了小波Galerkin法(WGM)在非线性屈曲问题数值求解方面的应用。首先,介绍了基于小波Galerkin法的von Kármán方程离散格式,然后提出了离散方程Jacobi矩阵和Hesse矩阵的一个简便计算方法,并讨论了基于小波离散格式的特征方程法、扩展方程法和伪弧长法等非线性屈曲分析方法。其次,较为详细地分析了弹性矩形薄板的二次屈曲平衡路径以及长宽比、边界条件和双向压缩对波形跳跃的影响。数值结果表明,小波Galerkin法在求解矩形板屈曲临界载荷时仍然有良好的收敛性,所获结果与稳定性实验、二次摄动法和非线性有限单元法的结果也非常一致,而结合不同分岔计算方法的可行性,更使其可为典型板壳的复杂非线性稳定性问题提供一种高效的空间离散方法。

  • 图  1  四边简支板屈曲载荷的收敛阶数

    Figure  1.  Convergence orders of buckling loads for 4-edge simply supported plates

    图  2  方形薄板单向压缩的后屈曲路径:(a) 四边简支;(b) 四边固支

    Figure  2.  Post-buckling paths of square plates under uniaxial compression: (a) 4-edge simply supported; (b) 4-edge fixed

    图  3  四边固支方形薄板的二次屈曲系数

    Figure  3.  Secondary buckling coefficients of 4-edge fixed square plates

    图  4  四边简支薄板二次屈曲平衡路径:(a) β=1.0;(b) β=2.0

    Figure  4.  Secondary buckling paths of 4-edge simply supported plates: (a) β=1.0; (b) β=2.0

    图  5  四边固支薄板二次屈曲平衡路径:(a) β=1.0;(b) β=2.0

    Figure  5.  Secondary buckling paths of 4-edge fixed plates: (a) β=1.0; (b) β=2.0

    图  6  方形薄板(β=1.0)后屈曲平衡曲面:(a) λ=110;(b) λ=159.991

    Figure  6.  Equilibrium surfaces of square plates (β=1.0) on postbuckling paths: (a) λ=110; (b) λ=159.991

    图  7  矩形薄板(β=2.0)后屈曲平衡曲面:(a) λ=350;(b) λ=1811.765

    Figure  7.  Equilibrium surfaces of rectangular plates (β=2.0) on postbuckling paths: (a) λ=350; (b) λ=1811.765

    图  8  加载比例k=0.2四边固支方板双向压缩的二次屈曲路径

    Figure  8.  Secondary buckling paths of a 4-edge fixed square plate with load ratio k=0.2

    表  1  单向受压弹性矩形薄板的二次屈曲系数

    Table  1.   Secondary buckling coefficients of rectangular plates under uniaxial compression

    β4-edge simply supported4-edge fixed
    k12k22k12k22
    1.0174.5187.71516.21012.767
    1.521.6935.29224.25913.066
    2.011.1395.35145.89313.297
    2.557.0234.30210.3158.099
    3.055.0594.69452.9479.087
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-03-23
  • 修回日期:  2022-12-29
  • 网络出版日期:  2023-01-09
  • 刊出日期:  2023-01-01

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