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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.

MSC:
74G60 Bifurcation and buckling
74K20 Plates
74K15 Membranes
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