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.
Download the geometry here or use Onshape to access the geometry used for this analysis:
- Part 1:
- Inner radius of vessel (R) = 75mm
- Height (h)= 5mm
- Thickness (t) = 15mm
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.
- 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
OnScale Solve automatically generates a 3D second-order tetrahedral mesh. The meshing statistics are:
Mesh Quality: Very Fine
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||Analytical Method||OnScale Solve|
|Radial displacement (ΔR) [um]||0.367||0.368|
|Longitudinal displacement (Δy) [um]||-7.22||-7.0|
 Roark’s Formulas for Stress and Strain, Eighth Edition, p 608, Table 13.1, Row 1
 Ibrahim, Ahmed,; Ryu, Yeong; Siadpour, Mir; “Stress Analysis of Thin-Walled Pressure Vessels,” Modern Mechanical Engineering, 2015, 5, 1-9.