The elastic stability of annular thin plates having one free edge and subjected to axisymmetric radial edge loads at the other edge is investigated. The supported edge is allowed to be either simply supported or clamped against axial (transverse) deflection. Both compression buckling and tension buckling (wrinkling) are investigated. To insure accuracy, two methods of solving the appropriate eigenvalue problems are used and found to yield essentially identical results. A selection of these results for both compression and tension buckling is presented graphically and used to illustrate interesting aspects of the solutions.

This paper deals with the elastic stability of an annular thin plate subjected to axisymmetric in-plane edge loads. The case of equal compressive loads applied at both boundaries was dealt with definitively by Yamaki [

The present paper reports an investigation of the elastic stability of an annular thin plate having one load-free edge. The other edge is subjected to uniform radial tension or compression and is either simply supported or clamped against axial deflection. This investigation both overlaps some findings of the papers referenced above (as discussed subsequently) and adds significant new information.

The remainder of the paper is organized as follows. First, the pertinent governing equations are reviewed. Next, a selection of results for both compression and tension buckling is presented and discussed. Finally, a summary of the work and a recapitulation of important conclusions are given.

In this section the governing equations are reviewed for the bending of thin, elastic, homogeneous, isotropic annular plates of uniform thickness undergoing small deflections and subjected to axisymmetric in-plane loads (see, for instance, Timoshenko and Gere [

For the purpose of numerical analysis it is convenient to convert the equations to dimensionless forms. Towards this end it is helpful to define dimensionless quantities (denoted by superposed asterisks) through the equations

Substituting

Equation (

Majumdar [

In the present notation a radial loading involving a free inner edge and uniform tension or compression at the outer edge corresponds to

Predictions relevant to compression buckling are reported in Figures

Buckling load versus inner radius (free/clamped,

Buckling load versus inner radius (free/clamped,

Buckling load versus inner radius (free/clamped,

Buckling load versus inner radius (free/clamped,

The curves corresponding to

As stated earlier, the composite curve formed by combining the lowest portions of curves for each circumferential buckling mode (value of

It is often asserted in the literature that compression buckling loads are insensitive to the value of Poisson’s ratio. It is of interest to use the results presented herein to test this assertion. Figures

Figure

Results for compression buckling of the free/simply supported configuration are reported in Figures

Buckling load versus inner radius (free/simply supported,

Buckling load versus inner radius (free/simply supported,

Buckling load versus inner radius (free/simply supported,

To be consistent with the results presented in [

Yu and Zhang [

In the present notation a radial loading involving a free outer edge and uniform tension or compression at the inner edge corresponds to

Figures

Buckling load versus inner radius (simply supported/free,

Buckling load versus inner radius (simply supported/free,

Buckling load versus inner radius (simply supported/free,

Figure

Figures

Results for tension buckling of the clamped/free configuration are reported in Figures

Buckling load versus inner radius (clamped/free,

Buckling load versus inner radius (clamped/free,

Buckling load versus inner radius (clamped/free,

As discussed in detail by Jillella and Peddieson [

Results for compression buckling of the simply supported/free configuration are reported in Figure

Buckling load versus inner radius (simply supported/free,

Results for compression buckling of the clamped/free configuration are reported in Figure

Buckling load versus inner radius (clamped/free,

The foregoing discussed the elastic stability of thin, elastic, homogeneous, isotropic annular plates of uniform thickness. Two independent numerical approaches were used to solve the eigenvalue problem associated with buckling analysis. Predictions were obtained for several configurations involving a load-free inner or outer edge with axisymmetric radial loading at the opposite edge exhibiting either compression or tension buckling. Two of these were used to verify the numerical approach by comparison with previous published results and several involved new results. Some important conclusions are as follows.

First, some of the results reported herein exhibit significant sensitivities of thin plate buckling loads to Poisson’s ratio. Of the configurations investigated, the largest sensitivity was observed for simply supported/free tension buckling while the smallest was observed for clamped/free compression buckling; however no definite pattern is obvious.

Second, standard elastic stability methodology provides a unified approach to both tension and compression buckling of thin plates. In particular, when applied to tension buckling (wrinkling) this approach can make certain quantitative predictions of which tension field theories are incapable. The most important of these are the wrinkle pattern (buckling mode shape) and the effect of axial support conditions. The present work provides examples of such predictions. The papers by Jillella and Peddieson [

Third, the plate thickness enters the dimensionless equations employed herein only through the dimensionless buckling load