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Experimental studies on buckling of ring-stiffened conical shells under axial compression

Main purpose of test program is to make a close study of the influence of stiffener geometry and spacing on the applicability of the linear theory

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Abstract

The buckling of integrally external ringstiffened conical shells under axial compression was investigated experimentally. Experimental results were compared with theory to find the effect of the stiffener parameters (e 2 /h), (A 2 /a 0 h) and (I 22 /a 0 h 3) as well as of shell geometry. Agreement between classical linear theory and experiments was found to be governed primarily by the area parameter (A 2 /a 0 h), and correlation with theory was significantly affected in the range 0.1<(A 2 /a 0 h)<0.5 of that parameter. Beyond this region there is practically no improvement with increase in ring area, whereas the weight of the shell continues to increase linearly.

An approximate formula is proposed for calculation of critical loads and found to yield results very close to the more exact critical values calculated by linear theory.

A modified “Southwell plot” method was applied and both the intercept method and slope method were used. Critical loads computed from the strain records were found to be below the classical linear-theory predictions and closer to experimental ones.

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Abbreviations

A 0 :

out of roundness

A 2 :

cross-sectional area of rings

e 2 :

eccentricity of rings (see Fig. 1)

h :

thickness of shell

J :

torsional constant of ring cross section

I 02 :

moment of inertia of a ring cross section about the middle line of the sheet respecitively

I 22 :

moment of inertia of stiffener cross section about its centroidal axis

L :

length of shell between bulkheads

n :

number of half longitudinal waves in conical shell

P :

axial force

P cl :

classical buckling load for isotropic cylinder for “classical” simple supports (SS3)

P cr :

defined by eq (2)

P cr unst :

linear-theory buckling load for unstiffened conical shells

P th :

linear-theory general instability for stiffened conical shell with “smeared” stiffeners and “classical” simple supports

P exp :

empirical buckling load for ring-stiffened conical shell

(P th ) app :

approximate linear-theory general instability of ring-stiffened conical shell defined by eq (3)

P South. ,P Inter. :

critical loads obtained by the slope and intercept methods, respectively

R :

radius of cylinder

t :

number of circumferential waves

t exp :

experimental number of circumferential waves

u, v, w :

nondimensional displacements,u=(u */a),v=(v */a),w=(w * /a) (see Fig. 1)

\(\tilde u,\tilde u\) :

average nondimensional displacements

x *,z *, ϕ:

axial coordinate along a generator, radial and circumferential coordinates

x :

nondimensional axial coordinatex=(x * /a)

Z :

(1 - ν2) 1/2(L/R)2(R/H) Batdorf shell parameter

ν:

Poisson's ratio

ξ:

defined by eq (7)

ρ:

“linearity” =P exp /P th

ρ1:

small radius of curvature = (R 1/cos α)

ρ1:

large radius of curvature = (R 2/cos α)

ρav :

average radius of curvature of conical shell = [(R 1+R 2)/2 cos α]

\(\rho _{av} \) :

average radius of curvature of conical sub-shell

σy.p. :

yield stress

(σcr ss :

critical stress of a simply supported plate defined by eq (4)

(σcr)clamped :

critical stress of a clamped plate defined by eq (5)

ψ:

taper ratio = [1−(R 1/R 2)]

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Authors and Affiliations

  1. Department of Aeronautical Engineering, Technion-Israel Institute of Technology, Technion City, Haifa, Israel

    T. Weller (Graduate Student) & J. Singer (Professor)

Authors
  1. T. Weller
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  2. J. Singer
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The research reported in this paper was sponsored in part by the Air Force Office of Scientific Research, OAR, through the European Office of Aerospace Research, United States Air Force under Contract AF 61(052)-905. The paper is part of the master's thesis of T. Weller submitted to the Senate of the Technion, Israel Institute of Technology.

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Weller, T., Singer, J. Experimental studies on buckling of ring-stiffened conical shells under axial compression. Experimental Mechanics 10, 449–457 (1970). https://doi.org/10.1007/BF02327672

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