Abstract
The anticipated use of a hollow linearly elastic annular membrane for designing elastic shells has provided an impetus for this paper to investigate the large deflection geometrically nonlinear phenomena of such a hollow linearly elastic annular membrane under transverse uniform loads. The so-called hollow annular membranes differ from the traditional annular membranes available in the literature only in that the former has the inner edge attached to a movable but weightless rigid concentric circular ring while the latter has the inner edge attached to a movable but weightless rigid concentric circular plate. The hollow annular membranes remove the transverse uniform loads distributed on “circular plate” due to the use of “circular ring” and result in a reduction in elastic response. In this paper, the large deflection geometrically nonlinear problem of an initially flat, peripherally fixed, linearly elastic, transversely uniformly loaded hollow annular membrane is formulated, the problem formulated is solved by using power series method, and its closed-form solution is presented for the first time. The convergence and effectiveness of the closed-form solution presented are investigated numerically. A comparison between closed-form solutions for hollow and traditional annular membranes under the same conditions is conducted, to reveal the difference in elastic response, as well as the influence of different closed-form solutions on the anticipated use for designing elastic shells.
Highlights
The so-called circular or annular membrane problem is well known, that is, the problem of axisymmetric deformation and deflection of an initially flat circular or annular membrane subjected to uniform transverse or normal loading
Hencky was the first scholar to deal with analytically the circular membrane problem, who used the power series method to solve the system of equations of large deflection of thin plates with vanishing bending stiffness [1]
Lian et al [28] dealt with analytically the problem of axisymmetric deformation and deflection of the classic Alekseev’s annular membrane structure subjected to uniform transverse loading, where both the entire annular membrane and the movable rigid concentric circular thin plate are subjected to uniformly distributed transverse loads
Summary
The so-called circular or annular membrane problem is well known, that is, the problem of axisymmetric deformation and deflection of an initially flat circular or annular membrane subjected to uniform transverse (lateral) or normal loading. Lian et al [28] dealt with analytically the problem of axisymmetric deformation and deflection of the classic Alekseev’s annular membrane structure subjected to uniform transverse loading, where both the entire annular membrane and the movable rigid concentric circular thin plate are subjected to uniformly distributed transverse loads. Attention is focused on the problem of axisymmetric deformation and deflection of a hollow annular membrane structure subjected to uniform transverse loading, an initially flat, linearly elastic, transversely uniformly loaded annular membrane with an immovable and indeformable outer edge and a movable but indeformable inner edge attached to a movable but weightless rigid concentric ring. Which are tween the closed-form solutions presented in this paper and in Lian et al [28] which are both suitable suitable for for uniform uniform transverse transverse loading
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