ABSTRACT

The paper is devoted to the study of the unsymmetric equilibrium states of inhomogeneous circular plates subjected to uniform surface load.

For the first time, unsymmetrical buckling of thin clamped circular isotropic plates under normal pressure was analyzed by Panov and Feodosev in 1948 (Panov and Feodos’ev 1948). The authors assumed that under sufficiently large load an unsymmetric state branchs from the axisymmetric one, and waves develop near the edge of the plates. Nonaxisymmetric displacement was represented in the form W = (1 − r2)2(A + Br4 cos nθ) and the bending problem was studied by Galerkin method (Panov and Feodos’ev 1948). In this approach the pre-buckling axisymmetric state was approximated by function with only one unknown parameter. Later, in 1963, Feodos’ev showed that under large deformations the elastic surfaces of plates or shells are exposed to strong changes, and the stress-strain state of these structures can not be described by one or two unknown parameters in approximating functions (Feodos’ev 1963).