LARGE DEFORMATIONS AT THIN PLANE DISKS BENDING UNDER UNIFORM DISTRIBUTED LOADS, CONSIDERING THE MEMBRANE STRESSES PART I – GENERAL THEORETICAL CONSIDERATIONS ON LARGE DEFORMATIONS

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.