Abstract.We consider shallow elastic membrane caps that are rotationally symmetric in their undeformed state, and investigate their deformation under small uniform vertical pressure and a given boundary stress or boundary displacement.To do this we use the small-strain theory developed by Bromberg and Stoker, Reissner, and Dickey We deal with the two-parameter family of membranes whose undeformed configuration is given in cylindrical coordinates aswhich includes the spherical cap as a special case (7 = 2 and C small). We show that if 7 > 4/3 then a circularly symmetric deformation is possible for any positive boundary stress (or any boundary displacement) and any positive pressure, but if 1 < 7 < 4/3 then no circularly symmetric deformation is possible if the stress and pressure are positive and small (or for non-positive boundary displacement and small positive pressure).1. Introduction. This study addresses how an elastic membrane cap deforms under the influence of particular stress and body force. We show, among other things, that under certain conditions a cap that is initially rotationally symmetric will fail to have a symmetric configuration after deformation.To be specific, we consider an elastic membrane cap that is shallow (that is, nearly flat) and rotationally symmetric in its undeformed state (or reference configuration), and then investigate the shape that the cap takes on when radial stress is applied on the boundary and a small uniform vertical pressure P is applied to the membrane. We use the small-strain, small-pressure theory developed by Bromberg and Stoker [2], Reissner [15], and Dickey [5,6] (a generalization to curved membranes of the Foppl theory for plane membranes), which allows for large displacements of the membrane.Dickey [5,6,7] showed that under the assumptions of small strain and small pressure, the radial stress <7r on a membrane whose undeformed profile is given in cylindrical coordinates by

No abstract

No abstract