Pressure Vessel Stress Analysis

FEA Simulation Highlights

• High-resolution 3D solid mesh was used, with refined elements near the inner surface to accurately capture stress gradients resulting from internal pressure.
• Uniform internal pressure of 5 MPa applied across all internal surfaces to replicate operational loading conditions.
• Accurate boundary representation: one end of the vessel was axially constrained to model a realistic closed-end condition while allowing free radial expansion.
• Stress results matched theoretical predictions, with maximum hoop stress from FEA (~135 MPa) deviating less than 3% from classical thin-walled calculations.
• Von Mises stress distribution showed smooth membrane behavior along the cylinder with localized, predictable increases near constrained boundaries.
• Axial stress profile aligned with expectations for a closed-end pressure vessel, confirming correct load transfer and constraint application.
• Deformation analysis revealed small radial expansion concentrated at mid-length; deformation remained fully elastic and within safe operating limits.
• FEA validation: the close agreement between simulation and analytical methods confirms the vessel is structurally sound under the applied pressure.

a) Internal pressure of 5.0 MPa.       b) Mesh and Geometry Representation.

FEA Analysis Results

The pressure vessel was analyzed using a full 3D finite element model to evaluate deformation, membrane stresses (hoop and longitudinal), von Mises stress, and safety factor under an internal pressure of 5 MPa. The mesh was refined near the vessel shell to accurately capture membrane stress behavior.

1. Pressure Loading

The internal surface was uniformly pressurized at 5 MPa, consistent with operating conditions.

2. Total Deformation

The vessel exhibits smooth radial expansion with a maximum deformation of approximately 0.41 mm at mid-span. This is expected for a thin-walled cylinder and confirms purely elastic behavior.

3. Hoop (Circumferential) Stress

The hoop stress field shows uniform membrane stress along the cylindrical section, with peak values around 132–140 MPa, closely matching the theoretical prediction of 133.3 MPa.

4. Longitudinal (Axial) Stress

Axial stress distribution aligns with thin-walled pressure vessel theory, with membrane values around 65–70 MPa, consistent with the analytical value of 66.7 MPa.

5. Equivalent (von Mises) Stress

von Mises stress remains below critical yield strength, with maximum values around 164 MPa occurring near geometric transitions and endcap regions. The cylindrical shell shows uniform membrane stress and no overstressed locations.

Von Mises Stress distribution

a) Hoop (Circumferential) Stress Visualization   b) Longitudinal (Axial) Stress Visualization

6. Safety Factor

A safety factor evaluation based on material yield strength shows a minimum factor of safety of ~1.52 at localized regions, and ~2.2–2.3 along the cylindrical body. This confirms safe operation under the 5 MPa internal pressure.

Stress Safety factor distribution

Summary of Results

• Deformation remains small (0.5 mm) and fully elastic.
• Hoop and longitudinal stresses match analytical theory within 3% accuracy.
• von Mises stress remains below yield strength, even at transitions.
• Safety factor exceeds 1.5, indicating safe operating margins.

Overall, the FEA confirms that the vessel design is structurally sound and performs as expected for a thin-walled pressurized cylinder.