On Membrane and Plate Problems for Which the Linear Theories are Not Admissible

Abstract

A horizontal clamped plate is subjected to the weight of a liquid above it. When the free surface of the liquid coalesces with the plane of the undeformed upper surface of the plate, according to the classical theory of plates (which results in an eigen-value problem), nonzero deflections will exist only for discrete values of the ratio γ/D; where γ is the specific weight of the liquid and D is the flexural stiffness of the plate. The purpose of this paper is to clarify this apparently unreasonble result. It is shown, using a nonlinear analysis, that problems of this type exhibit a bifurcation point from the undeformed state and that the eigenvalues of the linear analysis determine merely the bifurcation points. Thus, for problems of this type, a linear formulation is not suitable. Because of its analytical simplicity, at first, the membrane strip is analyzed in detail. This is followed by the analysis of the plate.