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SLS 04: Thin cylinder under uniform radial pressure

Description


Material Modulus of elasticity E =210 000N/mm^2
Poisson’s ratio \nu= 0.3
Geometry Cross-section Thickness e=20 mm
Boundary conditions At bottom edge R_y fixed
In point A R_x fixed
In point B R_z fixed
Loads On all plates 10.0kN/m^2
Mesh Maximum element size 0.05m
Minimum element size 0.00m

Results

Handcalculation

    \[\Delta R=\frac{q \cdot R^2}{E \cdot e}=\frac{10kN/m^2 \cdot (1m)^2}{210 000N/mm^2 \cdot 0,02m}=0.002381mm\]

    \[\Delta y=\frac{q \cdot R \cdot \nu \cdot L}{E \cdot e}=\frac{10kN/m^2 \cdot 1m \cdot 0.03 \cdot 4m}{210 000N/mm^2 \cdot 0,02m} = 0.002857mm\]

Deformation \delta_y in Diamonds

Point Which result Independent reference Diamonds Difference
Y=4m Longitudinal deformation \delta_y 0,002857mm 0,002846mm -0,71%
Y=2m Radial deformation \delta_x and \delta_z 0,002381mm 0,002364mm -0,39%

References

  • Mécaniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SSLS 06: cylindre mince sous pression radiale uniforme
  • Roark, R. J., & Young, W. C. (2002). Roark’s Formulas for Stress and Strain (7th edition, Table 13.1 case 1b). McGraw-Hill Companies.
  • Tested in Diamonds 2023r01.

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