APPLICATIONS OF SINGULARITY THEORY IN BUCKLING-BENDING PROBLEM FOR ROTATIONALLY SYMMETRICAL PLATES

The paper deals with the combined buckling - bending problem for a thi n elastic circular plate of constant thickness clamped at its edge whi ch is subjected to force along its edge and under the action of extern al normal force. The forces in the plane of the plate is proportional to a real parameter lambda. The equilibrium state of this problem can be found by solving: the nonlinear von Karman equations. Let lambda(1) and lambda(2) be two smallest eigenvalues of the linearized problem. Then for lambda less than or equal to lambda(1) the problem has unique solution, for lambda is an element of (lambda(1), lambda(c)), where l ambda(1) < lambda(c) < lambda(2) the problem has one or three solution s depending on the external normal force.