Complete solution of the stability problem for elastica of Euler's column

被引：46
|
作者：
Kuznetsov, VV [1 ]
Levyakov, SV
机构：
[1] Novosibirsk State Tech Univ, Dept Theoret Mech, Novosibirsk 630092, Russia
[2] Siberian Aeronaut Res Inst, Novosibirsk 630051, Russia
来源：
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS | 2002年 / 37卷 / 06期
关键词：
elastica; stability; bifurcation point; eigensolution;
D O I：
10.1016/S0020-7462(00)00114-1
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
The stability of postcritical equilibrium forms of a simply supported column loaded with an axial force is analyzed. Investigating the sign of the second variation of the column's total energy, we obtain the Sturm-Liouville boundary-value problem, which is solved numerically. The stability conditions are formulated in terms of eigenvalues of the problem. The complete solution to the column plane elastica is given. The ranges of the compressive force corresponding to stable equilibrium configurations of the column are established. (C), 2002 Elsevier Science Ltd. All rights reserved.
引用
收藏
页码：1003 / 1009
页数：7
相关论文
共 50 条
  • [41] From Euler's elastica to the mKdV hierarchy, through the Faber polynomials
    Matsutani, Shigeki
    Previato, Emma
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2016, 57 (08)
  • [42] Proximal ADMM for Euler's Elastica Based Image Decomposition Model
    Liu, Zhifang
    Wali, Samad
    Duan, Yuping
    Chang, Huibin
    Wu, Chunlin
    Tai, Xue-Cheng
    [J]. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2019, 12 (02) : 370 - 402
  • [43] Image Multiplicative Denoising Using Adaptive Euler’s Elastica as the Regularization
    Yu Zhang
    Songsong Li
    Zhichang Guo
    Boying Wu
    Shan Du
    [J]. Journal of Scientific Computing, 2022, 90
  • [44] On Euler's problem
    Egorov, Yu. V.
    [J]. SBORNIK MATHEMATICS, 2013, 204 (04) : 539 - 562
  • [45] Approximate Analytical Solution for a Unilateral Contact Problem with Heavy Elastica
    Solyaev, Yu.
    Ustenko, A.
    Lykosova, E.
    [J]. LOBACHEVSKII JOURNAL OF MATHEMATICS, 2019, 40 (07) : 1010 - 1015
  • [46] A Restricted Linearised Augmented Lagrangian Method for Euler's Elastica Model
    Zhang, Yinghui
    Deng, Xiaojuan
    Zhao, Xing
    Li, Hongwei
    [J]. EAST ASIAN JOURNAL ON APPLIED MATHEMATICS, 2021, 11 (02) : 276 - 300
  • [47] Analytical solution of spatial elastica and its application to kinking problem
    Miyazaki, Y
    Kondo, K
    [J]. INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 1997, 34 (27) : 3619 - 3636
  • [48] A complete solution of P. Samuel's problem
    Dajczer, Marcos
    Tojeiro, Ruy
    [J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2016, 719 : 75 - 100
  • [49] Approximate Analytical Solution for a Unilateral Contact Problem with Heavy Elastica
    Yu. Solyaev
    A. Ustenko
    E. Lykosova
    [J]. Lobachevskii Journal of Mathematics, 2019, 40 : 1010 - 1015
  • [50] COMPLETE REDUCTION OF THE EULER-POINSOT PROBLEM
    DEPRIT, A
    ELIPE, A
    [J]. JOURNAL OF THE ASTRONAUTICAL SCIENCES, 1993, 41 (04): : 603 - 628
12345