Buckling and post-buckling of annular plates in shearing. I: Buckling. (English) Zbl 0743.73013
Summary: Using the generalized and modified Von Kármán theory for perforated thin plates having large deflections, the elastic buckling of annular plates under in-plane shear forces is studied in this paper. The mathematical problem is formulated rationally. The generalized eigenvalues of the linearized problem are discussed and the existence of bifurcation solutions near eigenvalues is analysed.
MSC:
| 74G60 | Bifurcation and buckling |
| 35B27 | Homogenization in context of PDEs; PDEs in media with periodic structure |
| 74B20 | Nonlinear elasticity |
| 74K20 | Plates |
| 35D05 | Existence of generalized solutions of PDE (MSC2000) |
Keywords:
Lyusternik-Schnirelmann theorem; Von Kármán theory; perforated thin plates; large deflections; elastic buckling; annular plates; in-plane shear forces; generalized eigenvalues; linearized problem; existence of bifurcation solutionsReferences:
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