LARGE DEFORMATIONS AT THIN PLANE CIRCULAR PLATES BENDING UNDER CONSTANT LOADING, TAKING INTO ACCOUNT THE MEMBRANE STRESSES PART II – BENDING UNDER INITIAL LOADING OF THE PLATES MEAN PLANE

Abstract

The present paper deals with the state of stress and deformation at thin circular plates subjected to symmetrical axial loading. The loading is a bending owing to the uniform distributed loads which act perpendicular to the mean surface of the plate, simultaneous with a membrane load (loads acting in the mean plane of the plate). This type of problem is solved by help of equations which result from the equilibrium of a plate’s element and from the boundary and continuity conditions of the mean surface of the plate. One considers the following two cases: the membrane stresses are small comparatively to the bending stresses; in this case the calculus is precise enough if we take into account only the mean plane extensions which will be superposed over the effects given by the transversal bending stress q; the membrane stresses are considerable and can not be neglected; in this case, second order calculus is required.