Influence of transverse loading on the stability of a clamped rectangular plate

Abstract

Shapes of a square Kirchhoff plate with a clamped edge are obtained and analyzed, before and after losing stability in the case of a compound bending (uniform transverse loading in combination with edge compressive loading), as well as equilibrium forms and critical loadings only with clamping in the plate’s surface. Hyperbolic trigonometric series are used for solving. It was established that transverse loading causing small deformations does not affect the plate’s stability. The range of the critical state corresponds with an unlimited increase in bends of interior points of a plate. As critical loading, we suggest taking the one at which the bends at the plate’s center tend to infinity the most rapidly. As balanced loading, we suggest taking the one at which the plate acquires a new stable equilibrium form. A range of critical and balanced loadings of a square plate with a clamped edge was presented. The corresponding 3D forms of supercritical equilibrium of the given plate were obtained. A comparison with the results of other authors is given.