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Effect of sequence of combined loading on buckling of stiffened shells

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Abstract

The vibration-correlation technique, VCT for definition of real boundary conditions, and the method of repeated buckling were employed for nondestructive generation of improved interaction curves for buckling of stringer-stiffened circular-cylindrical shells subjected to a combined axial compression and external-pressure state of loading. Thirteen shells were tested, five on clamped boundary conditions and eight on norminal simple supports. The study also included an assessment of the influence of the order of loading on the behavior of the shells before and at buckling as a result of the nonlinear interaction. It has been shown that the VCT and repeated buckling approach are feasible for closely stiffened shells and are adequate tools for the derivation of more realistic buckling interaction curves. It appears that the sequence of loading, constant axial compression first and then increasing the external pressure until buckling occurs, or the reverse order of loading, does not influence the buckling loads.

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Abbreviations

A 11 :

cross-sectional area of stringer

b 1 :

distance between centers of stringers

c 1 :

width of stringer

d 1 :

height of stringer

E :

Young's modulus of shell and stringer

e 1 :

stringer eccentricity (distance from middle surface to centroid of stringer)

f :

frequency

h :

thickness of shell

I 11 :

moment of inertia of stringer cross section about its centroidal axis

L :

length of shell

m :

number of longitudinal half waves

n :

circumferential wave number

P cr, Pcr :

theoretical buckling load, axial compression, and pressure, respectively

P const, pconst :

constant axial load and pressure, respectively

P exp, pexp :

experimental buckling load, axial compression and pressure, respectively

P sp, psp :

calculated buckling load, axial compression and pressure, respectively, for shell with axial or rotational restraint

P ssx, pssx :

theoretical buckling load, axial compression and pressure respectively, for SS type BCs

P c4, pc4 :

theoretical buckling load, axial compression and pressure, respectively, for C-4 type BCs

R :

radius of middle surface of cylindrical shell

Z :

[1-v 2]1/2(L2/Rh), Batdorf shell parameter

ϱ sp :

P exp/Psp orp exp/psp

ϱ th :

P ss3 imp/Pss3

ϱ ssx :

P exp/Pssx, orp exp/pssx

ϱ c4 :

P exp/Pc4, orp c4/pc4

ϱ ecc :

‘knock-down’ factor including load eccentricity

SS-1w :

M x=Nx=NxΦ=0

SS-2w :

M x=u=NxΦ=0

SS-3w :

M x=Nx=ν=0

SS-4w :

M x=u=ν=0

C-1w :

W ,x=Nx=NxΦ=0

C-2w :

W ,x=u=NxΦ=0

C-3w :

W ,x=Nx=ν=0

C-4w :

W ,x=u=ν=0

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Authors and Affiliations

  1. Department of Aeronautical Engineering, Technion-Israel Institute of Technology, 32000, Haifa, Israel

    H. Abramovich (Research Fellow), T. Weller (Associate Professor) & J. Singer (Professor of Aircraft Structures)

Authors
  1. H. Abramovich
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  2. T. Weller
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  3. J. Singer
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Abramovich, H., Weller, T. & Singer, J. Effect of sequence of combined loading on buckling of stiffened shells. Experimental Mechanics 28, 1–13 (1988). https://doi.org/10.1007/BF02328988

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