Abstract
An experimental method is described whereby symmetrically loaded cylinders of nonuniform thickness are analyzed using two-dimensional photoelastic models mounted on elastic foundations. The technique is most conveniently applied to ring-stiffened or notched cylinders. The particular model studied simulated a notched cylindrical pressure vessel which had been previously studied with three-dimensional photoelasticity. The stress-concentration factors at the base of the notch, found using both methods, showed excellent agreement. An analysis was also performed which allows estimation of the error involved when a beam-on-elastic-foundation model does not rigorously simulate a cylinder.
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Abbreviations
- b :
-
width of beam (in.)
- C 1,C 2....:
-
constant coefficients
- E :
-
modulus of elasticity (lb/in.2)
- E b :
-
modulus of elasticity of beam (lb/in.2)
- E c :
-
modulus of elasticity of cylinder (lb/in.2)
- f :
-
fringe constant (lb/in.-fringe)
- k :
-
foundation modulus (lb/in.2)
- K :
-
stress-concentration factor
- n :
-
fringe order (fringes)
- P :
-
applied load (lb)
- q :
-
pressure (lb/in.2) or distributed load (lb/in.)
- r,θ,x :
-
cylindrical coordinates
- r c :
-
radius of cylinder (in.)
- t :
-
thickness (in.)
- t b :
-
thickness of beam (in.)
- t c :
-
thickness of cylinder (in.)
- y,z,x :
-
Cartesian coordinates
- β:
-
root of “characteristics” equation (l/in.)
- β b :
-
root of beam equation (l/in.)
- β c :
-
root of cylinder equation (l/in.)
- δ:
-
deflection (in.)
- ν:
-
Poisson's ratio of cylinder
- σ:
-
stress (lb/in.2)
- \(\mathop \sigma \nolimits_x \) :
-
axial surface stress (lb/in.2)
- σθ :
-
circumferential stress (lb/in.2)
References
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Jenkins, W.C. Analysis of cylindrical shells of nonuniform thickness using two-dimensional photoelastic models. Experimental Mechanics 10, 39–45 (1970). https://doi.org/10.1007/BF02320084
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DOI: https://doi.org/10.1007/BF02320084