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# Validation Case: Cylindrical Pressure Vessel

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: 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 0
• Symmetry 2
• Part 1 – Face 1
• Symmetry 3
• Part 1 – Face 5 • Pressure Load 1 – 60MPa
• Part 1 – Face 2 ## Meshing:

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

Mesh Quality: Very Fine

## 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:

 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.