Citation: | ZHAO Yan-ping, LI Lin, JIN Ming. Some Stable and Unstable Critical States of a Compression Rod With a Flexible Support[J]. Applied Mathematics and Mechanics, 2017, 38(8): 877-887. doi: 10.21656/1000-0887.370299 |
[1] |
车小玉, 段梦兰, 曾霞光, 等. 双层管道整体屈曲实验研究及数值模拟[J]. 应用数学和力学, 2014,35(2): 188-201.(CHE Xiao-yu, DUAN Meng-lan, ZENG Xia-guang, et al. Experiments study and numerical simulation of global buckling of pipe-in-pipe systems[J]. Applied Mathematics and Mechanics,2014,35(2): 188-201.(in Chinese))
|
[2] |
Ziegler H. Principle of Structure Stability [M]. 2nd ed. Birkhuser Verlag Basel und Stuttgart, 1977.
|
[3] |
van der Heijden A M A. W. T. Koiter’s Elastic Stability of Solids and Structures [M]. New York: Cambridge University Press, 2009.
|
[4] |
Hoffman K A, Manning R S. An extended conjugate point theory with application to the stability of planar buckling of an elastic rod subject to a repulsive self-potential[J].SIAM Journal on Mathematical Analysis,2009,41(2): 465-494.
|
[5] |
Manning R S, Rogers K A, Maddocks J H. Isoperimetric conjugate points with application to the stability of DNA minicircles[J]. Proceedings: Mathematical, Physical and Engineering Sciences,1998,454(1980): 3047-3074.
|
[6] |
Manning R S. Conjugate points revisited and Neumann-Neumann problems[J]. SIAM Review,2009,51(1): 193-212.
|
[7] |
Jin M, Bao Z B. An improved proof of instability of some Euler elasticas[J]. Journal of Elasticity,2015,121(2): 303-308.
|
[8] |
Jin M, Bao Z B. Extensibility effects on Euler elastica’s stability[J]. Journal of Elasticity,2013,112(2): 217-232.
|
[9] |
Jin M, Bao Z B. Sufficient conditions for stability of Euler elasticas[J]. Mechanics Research Communications,2008,35(3): 193-200.
|
[10] |
Jin M, Bao Z B. A proof of instability of some Euler elasticas[J]. Mechanics Research Communications,2014,59: 37-41.
|
[11] |
Levyakov S V. Stability analysis of curvilinear configurations of an inextensible elastic rod with clamped ends[J]. Mechanics Research Communications,2009,36(5): 612-617.
|
[12] |
Levyakov S V, Kuznetsov V V. Stability analysis of planar equilibrium configurations of elastic rods subjected to end loads[J]. Acta Mechanica,2010,211(1):73-87.
|
[13] |
Manning R S. A catalogue of stable equilibria of planar extensible or inextensible elastic rods for all possible Dirichlet boundary conditions[J]. Journal of Elasticity,2014,115(2): 105-130.
|
[14] |
Sachkov Y L. Maxwell strata in the Euler elastic problem[J]. Journal of Dynamical and Control Systems,2008,14(2): 169-234.
|
[15] |
Sachkov Y L. Conjugate points in the Euler elastic problem[J]. Journal of Dynamical and Control Systems,2008,14(3): 409-439.
|
[16] |
Sachkov Y L, Levyakov S V. Stability of inflectional elasticae centered at vertices or inflection points[J]. Proceedings of the Steklov Institute of Mathematics,2010,271(1): 177-192.
|
[17] |
Batista M. On stability of columns at the first bifurcation point[J]. Mechanics Research Communications,2016,75: 89-90
|
[18] |
Jin M, Bao Z B. ‘Stability in the large’ of columns just at the first bifurcation point[J]. Mechanics Research Communications,2015,67: 31-33.
|
[19] |
武际可, 苏先樾. 弹性系统的稳定性[M]. 北京: 科学出版社, 1994.(WU Ji-ke, SU Xian-yue.The Stability of Elastic System [M]. Beijing: Science Press, 1994.(in Chinese))
|
[20] |
Zygmund A. Trigonometric Series [M]. American: Cambridge University Press, 1959.
|