Experimental Mechanics

, Volume 9, Issue 3, pp 129–136 | Cite as

Stresses in shallow axisymmetric shells using a casting procedure

Authors describe semiexperimental method of determining bending and membrane stresses in shallow thin shells of revolution experiencing large axisymmetrical deflections. Calculations proceed from radial slope measurements on epoxy castings of the deflected and undeflected shell surfaces
  • W. Soedel
  • R. Cohen
Article

Abstract

Normal and radial displacements of a shallow thin sheil of revolution are related by theoretical considerations. Radial displacements are calculated from slope measurements on the generatrices of the initial shell surface (before loading) and of the final shell surface (after loading). Membrane and bending stresses over the entire shell surface are then computed from the measured slope values and the calculated radial displacements.

A measuring technique is developed which is especially suitable for shallow shells enclosed in small spaces. It consists mainly of making a cast of the initial and final shell surface using an epoxy platic. The disklike cast is cut along its diameter. The slope values are measured optically along the line which is formed by the intersection of the cutting plane with the deflection surface.

The method is applied to a shallow thin shell of revolution in contact with a concentric piston and to a clamped circular plate, both experiencing large axisymmetric deflection.

Keywords

Epoxy Fluid Dynamics Measuring Technique Theoretical Consideration Circular Plate 

List of symbols

σrm, σtm

radial and tangential membrane stress

σrb, σtb

radial and tangential bending stress

rm, ∈tm

radial and tangential membrane strain

rb, ∈tb

radial and tangential bending strain

E

modulus of elasticity

v

Poisson's ratio

ds

element length

r, θ

polar coordinates

dr, dθ

increments

w

normal deflection

Φ

radial slope

u

radial deflection

z

distance from neutral plane

c1,c2

integration constants

ui, uo

radial displacement at inner and outer boundary

Ri, Ro

radius of inner and outer boundary

φu

uncorrected slope data

φH

angle between axis of shell and normal to reference plane

η

tiltage angle

a

boundary radius, reference radius

c

boundary radius

p

uniform pressure

q

nondimensionalized pressure

h

shell thickness

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References

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Copyright information

© Society for Experimental Mechanics, Inc. 1969

Authors and Affiliations

  • W. Soedel
    • 1
  • R. Cohen
    • 1
  1. 1.School of Mechanical Engineering, Ray W. Herrick LaboratoriesPurdue UniversityLafayette

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