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Buckling and postcritical behaviour of the elastic infinite plate strip resting on linear elastic foundation. (English) Zbl 1069.74019

Summary: We study von Kármán model for thin elastic infinite plate strip resting on a linear elastic foundation of Winkler type. The infinite plate strip is simply supported and subjected to evenly distributed compressive loads. The critical values of bifurcation parameters and buckling modes for given frequency of longitudinal waves are found on the basis of investigation of linearized problem. The mathematical nonlinear model is reduced to operator equation with Fredholm-type operator of index 0 depending on parameters defined in corresponding Hölder spaces. The Lyapunov-Schmidt reduction and Crandall-Rabinowitz bifurcation theorem (gradient case) are used to examine the postcritical behaviour of the plate. It is proved that there exists maximal frequency of longitudinal waves depending on the compressive load and on the stiffness modulus of foundation.

MSC:

74G60 Bifurcation and buckling
74K20 Plates
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