Buckling‐Bending Problem for Circular Plate

We consider radially symmetric deformation of a thin flat elastic circular plate of constant thickness clamped at its edge. The plate is under the action of a uniform compressive thrust along its edge in the midplane of the plate. The thrust is proportional to a real parameter λ. The plate is also subjected to a radially symmetric load, normal to its midplane. The equilibrium states of the given buckling‐bending problem are the solutions of von Kármán equations. Let λ 1 < λ 2 be the first and the second eigenvalue of the linearized problem. If λ ≤ λ 1 the buckling‐bending problem has unique solution for any normal load. If λ ∈ (λ 1 , λ c ), where λ 1 < λ c < λ 2 the buckling‐bending problem has one or three solutions depending on the normal load. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)