SLS 06: Thin cylinder under hydrostatic pressure


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 Triangular load varying from 0kN/m^2 at the bottom to 20.0kN/m^2 at the top.
Mesh Maximum element size 0.05m
Minimum element size 0.00m



    \[\sigma_1(y)=\sigma_{xx}= \frac{q_0 \cdot R \cdot y}{L \cdot e}\]

    \[\sigma_{xx}(2m)=\frac{20kN/m^2 \cdot 1m \cdot 2m}{4m \cdot 0,02m}=0.5N/mm^2\]

    \[\Delta R(y)=\delta_x(y)=\delta_z(y)=\frac{q_0 \cdot R^2 \cdot y}{E \cdot L \cdot e}\]

    \[\delta_x(2m)=\frac{20kN/m^2 \cdot (1m)^2 \cdot 2m}{210000N/mm^2 \cdot 4m \cdot 0,02m}=0.002381mm\]

    \[\Delta y(y)=\delta_y(y)=\frac{q_0 \cdot R \cdot \nu \cdot y^2}{2 \cdot E \cdot L \cdot e}\]

    \[\delta_y(4m)=\frac{20kN/m^2 \cdot 1m\cdot 0.3 \cdot (4m)^2}{2 \cdot 210000N/mm^2 \cdot 4m \cdot 0,02m}=0.002857mm\]

Deformation \delta_y in Diamonds

Point Which result Independent
Diamonds Difference
Y=2m Stress \sigma_xx 0.5N/mm^2 0.514 N/mm^2 (1) 2,80%
Y=4m Longitudinal deformation \delta_y 0,002857mm 0,002847mm -0,36%
Y=2m Radial deformation \delta_x and \delta_z 0,002381mm 0,002363mm -0,75%
(1) The stress in Diamonds is determined using a cutline over which the average stress is calculated.


  • Mécaniciens, S. F. D. (1990). Guide de validation des progiciels de calcul des structures: SSLS 08: cylindre mince sous pression hydrostatique
  • 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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