Knockdown factors for buckling of cylindrical and spherical shells subject to reduced biaxial membrane stress

John W Hutchinson

doi:10.1016/j.ijsolstr.2010.02.009

Abstract

Cylindrical shells under uniaxial compression and spherical shells under equi-biaxial compression display the most extreme buckling sensitivity to imperfections. In engineering practice, the reduction of load carrying capacity due to imperfections is usually addressed by use of a knockdown factor to lower the critical buckling stress estimated or computed without accounting for imperfections. For thin elastic cylindrical shells under uniaxial compression and spherical shells under equi-biaxial compression, the knockdown factor is typically as small as 0.2. This paper explores the alleviation of imperfection-sensitivity for loadings with a reduced circumferential (transverse) membrane stress component. The analysis of Koiter (1963) on the effect of an axisymmetric imperfection on the elastic buckling of a cylindrical shell under uniaxial compression is extended to both cylinders and spheres for loadings that produce general combinations of biaxial membrane stresses. Increases in the knockdown factor due to a reduction of the transverse membrane component are remarkably similar for cylindrical and spherical shells.

Highlights

Design of structures comprising thin cylindrical and spherical shells subject to compressive membrane stresses makes use of a knockdown factor, to account for the fact that imperfections can reduce the compressive stress at buckling to a small fraction of the critical stress at which the perfect shell buckles
For all the cases considered in this paper, the relevant compressive stress at buckling of the imperfect shell is given by where C is the critical compressive stress component in the 1-direction of the perfect shell
Due to similarity with the cylindrical shell under axial compression noted above and the data that does exist, it has been common practice to adopt the knockdown factor for cylindrical shells plotted in Fig. 1 for the spherical shells under equi-biaxial compression

Summary

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Knockdown factors for buckling of cylindrical and spherical shells subject to reduced biaxial membrane stress. International Journal of Solids and Structures 47(10): 1443-1448.

Introduction

At sin

The solution in the buckled state is written as