A characteristic type of instability in the large deflexions of elastic plates. I. Curved rectangular plates bent about one axis II. Flat square plates bent about all edges

Abstract

Part I . From a general equation governing the bending of thin elastic plates into certain types of surfaces of revolution are derived expressions for the behaviour of rectangular plates with initial curvatures, subjected to pure bending about one axis. It is found that such plates exhibit the type of instability characteristic of thin-walled structures which depend for their stiffness on curvature. Curves are drawn showing the deformation suffered by such plates, and an expression for the critical bending moment at which instability occurs is obtained. Experimental results show satisfactory agreement. Part II . The analysis of part I is extended to deal with the case of flat square or rectangular plates loaded by distributed bending moments applied to all four edges. Curves are drawn to describe their behaviour, and they are found to exhibit the characteristic instability displayed by thin-walled curved structures. Experimental verification is satisfactory.