English
Log in
English
Documentation
Help > Solve > OnScale Solve Validation Cases > Validation Case: Cylindrical Pressure Vessel

Validation Case: Cylindrical Pressure Vessel

This article is part of the series of FEA validation cases performed using OnScale Solve. 

In this case, A 1/8th-symmetry model is built with three orthogonal symmetry planes, a uniform radial pressure is applied to the inner surface of the cylindrical vessel. This example demonstrates the calculation of membrane stresses in a simple thin-walled cylindrical pressure vessel.

Results are verified against hand calculations per Roark’s Formulas for Stress and Strain, Eighth Edition, p 608, Table 13.1, Row 1. A derivation of these equations can be found in Ibrahim, Ahmed,; Ryu, Yeong; Siadpour, Mir; “Stress Analysis of Thin-Walled Pressure Vessels,” Modern Mechanical Engineering, 2015, 5, 1-9.

Geometry:

Download the geometry here or use Onshape to access the geometry used for this analysis:

Geometry Dimensions

  • Part 1:
    • Inner radius of vessel (R) = 75mm
    • Height (h)= 5mm
    • Thickness (t) = 15mm

Material:

These materials are taken directly from the OnScale library of materials.

Part 1 – Structural Steel:

  • Young’s Modulus (E) = 190 GPa
  • Density (ρ) = 7750 kg/m³
  • Poisson’s Ratio (v) = 0.305

Note: All other material properties can be left as their default values.

Physics:

Mechanical Physics:

  • Symmetry 1
    • Part 1 – Face 1
  • Symmetry 2
    • Part 1 – Face 5
  • Symmetry 3
    • Part 1 – Face 3

  • Pressure Load 1 – 60MPa
    • Part 1 – Face 0

Meshing:

OnScale Solve automatically generates a 3D second-order tetrahedral mesh. The meshing statistics are:

Mesh Quality: Very Fine

Elements: 2029

Vertices: 642

Analytical Solution:

The circumferential stresses σhoop acting in the wall of the vessel can be calculated:

Because the top surface of the cylindrical vessel is unrestrained:

The radial displacement (ΔR) can be calculated using the following equation:

The longitudinal displacement (Δy) can be calculated using the following equation:

Results Comparison:

Results Analytical Method OnScale Solve
σhoop (GPa) 0.9 0.9
σaxial (GPa) 0.0 0.0
Radial displacement (ΔR) [um] 0.367 0.368
Longitudinal displacement (Δy) [um] -7.22 -7.0

References:

[1] Roark’s Formulas for Stress and Strain, Eighth Edition, p 608, Table 13.1, Row 1

[2] Ibrahim, Ahmed,; Ryu, Yeong; Siadpour, Mir; “Stress Analysis of Thin-Walled Pressure Vessels,” Modern Mechanical Engineering, 2015, 5, 1-9.