Elastic Stability of Annular Thin Plates with One Free Edge

Nagarjuna Jillella,John Peddieson

doi:10.1155/2013/389148

Abstract

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.

Highlights

This paper deals with the elastic stability of an annular thin plate subjected to axisymmetric in-plane edge loads
A interesting facet of this class of problems is that radial tensile loads can produce compressive circumferential stress resultants over a portion of the plate that lead to radial wrinkling
The present paper reports an investigation of the elastic stability of an annular thin plate having one load-free edge

Summary

Introduction

This paper deals with the elastic stability of an annular thin plate subjected to axisymmetric in-plane edge loads. If the in-plane boundary loads (either tensile or compressive) are unequal the in-plane stress resultants are variable and unequal, creating a more complicated situation in which numerical work is normally required. Various aspects of this general problem have been investigated by Timoshenko and Gere [2], Mansfield [3], Majumdar [4], Yu and Zhang [5], Machinek and Troger [6], Coman and Haughton [7, 8], Coman and Bassom [9, 10], Noh et al [11], and Jillella and Peddieson [12]. The other edge is subjected to uniform radial tension or compression and is either 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. A summary of the work and a recapitulation of important conclusions are given

Governing Equations

Results for Load-Free Inner Edge

Results for Load-Free Outer Edge

Conclusion