On the theory of coupled loss of stability in stiffened thin-walled structures.

*(English. Russian original)*Zbl 0574.73059
J. Appl. Math. Mech. 46, 261-267 (1983); translation from Prikl. Mat. Mekh. 46, No. 2, 337-345 (1982).

A system of the principal nonlinear approximation equations is obtained for the problem of loss of stability in stiffened thin-walled structures in the presence of finite displacements, taking into account the presence of a set of local modes with critical loads differing little from each other. A concept of ”modified” local modes is proposed, allowing an estimation of the mode interaction already in the first nonlinear approximation. The possibility of simplification of the final system of equations, taking into account the fact that the local mode length is short compared with that of the overall mode, is shown. It is established that within the framework of the principal nonlinear approximation every local mode in the stiffened plates and shells interacts with the overall mode, but here is no explicit interaction between the local modes themselves. A theorem is proved establishing the correlation between the system with one, and with many local modes. The problem of stability of a compressed stiffened plate, i.e. of a wide strut, is solved as an example. The proposed theory can be applied to structures almost equally stable when no local waves form up to the moment of coupled buckling.

##### Keywords:

system of the principal nonlinear approximation equations; loss of stability; stiffened thin-walled structures; finite displacements; set of local modes; critical loads; concept of ”modified” local modes; estimation of the mode interaction; correlation between the system with one, and with many local modes; compressed stiffened plate; wide strut
PDF
BibTeX
XML
Cite

\textit{A. I. Manevich}, J. Appl. Math. Mech. 46, 261--267 (1983; Zbl 0574.73059); translation from Prikl. Mat. Mekh. 46, No. 2, 337--345 (1982)

Full Text:
DOI

##### References:

[1] | Tvergaard, V., Buckling behavior of plate and shell structures, () · Zbl 0367.73057 |

[2] | Manevich, A.I., Stability and optimal design of stiffened shells, (1979), Vishcha shkola Kiev-Donetsk |

[3] | Manevich, A.I., Coupled modes of the loss of stability in a thin-walled panel, (), Vyp. 20 · Zbl 0574.73059 |

[4] | Manevich, A.I., Coupled loss of stability in a longitudinally stiffened cylindrical shell, () · Zbl 0574.73059 |

[5] | Koiter, W.T., General theory of mode interaction in stiffened plate and shell structures, WTHD report, no.590, (1976) · Zbl 0405.73044 |

[6] | Koiter, W.T., Stability and postcritical behavior of elastic systems mekhanika, (1960), (Russian translation), No. 5 · Zbl 0109.43002 |

[7] | Budiansky, B.; Hutchinson, J.W., Dynamic buckling of imperfection-sensitive structures, () · Zbl 0427.73022 |

[8] | Byskov, E.; Hutchinson, J.W., Mode interaction in axially stiffened cylindrical shells, AIAA journal, Vol. 15, No. 7, (1977) |

[9] | Hutchinson, J.W., Imperfection-sensitivity of externally pressurized spherical shells, Trans. ASME. ser. E. J. appl. mech., Vol. 34, No. 1, (1967) · Zbl 0159.27006 |

[10] | Tvergaard, V., Imperfection-sensitivity of a wide integrally stiffened panel under compression, Internat. J. solids and struct., Vol. 9, No. 1, (1973) · Zbl 0264.73064 |

[11] | Manevich, A.I., Mode interaction in the loss of stability in stiffened panel, Stroitel’naia mekhanika i raschot sooruzhenii, No. 5, (1981) |

[12] | Supple, W.J., Initial post-buckling behavior of a class of elastic structural systems, Internat. J. nonlinear mech., Vol.4, No.1, (1969) · Zbl 0167.53403 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.