Total deformation of the vessel under uniform internal pressure (FEA result).
Executive summary
- Load case: uniform internal pressure, 5 MPa
- Model: 3D solid FEA with refined shell-region mesh
- Outputs: deformation, hoop stress, axial stress, von Mises stress
- Validation: agreement with thin-wall closed-form theory
Key results (reported)
- Max deformation: ~0.41 mm (radial expansion, mid-span)
- Hoop stress: ~132–140 MPa (uniform membrane region)
- Axial stress: ~65–70 MPa (closed-end behavior)
- Max von Mises: ~164 MPa near end/transition regions
- Min safety factor: ~1.52 (localized), ~2.2–2.3 along body
Overview
Tetra Elements performed a structural assessment of a cylindrical pressure vessel subjected to internal pressure. The objective was to verify membrane stress levels, compare finite element results against classical thin-walled theory, and confirm that deformation and equivalent stress remain within acceptable limits under operating pressure.
Why this matters: For thin-walled vessels, internal pressure produces dominant membrane stresses (hoop and axial). A validated FEA model helps confirm stress uniformity, identifies localized effects near constraints/end regions, and supports reliable safety-factor evaluation.
Geometry and dimensions
The vessel geometry and wall thickness were defined per the design specification. The baseline wall thickness is 15 mm for the initial evaluation.
Geometry and key dimensions (initial wall thickness: 15 mm).
FEA setup and boundary conditions
A full 3D finite element model was used to capture deformation and stress fields under uniform internal pressure. Mesh density was increased near the inner surface and around boundary regions to resolve stress gradients while preserving smooth membrane behavior across the cylindrical body.
- Loading: uniform internal pressure of 5 MPa applied to all internal surfaces.
- Constraints: one end axially constrained to represent a realistic closed-end condition while allowing radial expansion.
- Mesh strategy: refined elements through the wall to accurately capture membrane stress distribution.
Results and validation
The vessel was evaluated for total deformation, hoop (circumferential) stress, longitudinal (axial) stress, and equivalent (von Mises) stress. Results show smooth membrane behavior along the cylindrical section and localized, expected increases near boundary/transition regions. Reported stress values closely match thin-wall theory within approximately 3%.
Total deformation
The vessel exhibits smooth radial expansion with a maximum deformation of approximately 0.41 mm concentrated near mid-span, consistent with elastic thin-wall response under internal pressure.
Hoop (circumferential) stress
Hoop stress remains uniform along the cylinder body with peak values around 132–140 MPa, aligning with the theoretical thin-wall prediction (~133.3 MPa) for the specified geometry and pressure.
Longitudinal (axial) stress
Axial stress distribution is consistent with closed-end vessel behavior, with typical membrane values around 65–70 MPa, matching the analytical estimate (~66.7 MPa).
Equivalent (von Mises) stress
von Mises stress remains below the critical yield threshold for the evaluated material model, with maximum values around 164 MPa occurring near geometric transitions and constrained end regions. The cylindrical body maintains a uniform membrane stress field without unexpected hot spots.
Von Mises stress distribution (FEA result).
Safety factor assessment
A safety factor contour was generated based on the selected material yield strength. The analysis reports a minimum safety factor of approximately 1.52 in localized regions and approximately 2.2–2.3 along the cylindrical body, confirming acceptable operating margins under the 5 MPa load case.
Safety factor distribution (FEA result).
Engineering takeaways
- Deformation remains small (sub-millimeter) and consistent with elastic thin-wall behavior.
- Hoop and axial membrane stresses match analytical theory within ~3% (validation of setup and boundary conditions).
- von Mises stress stays below critical limits, with predictable localized increases near end/transition regions.
- Safety factor remains above ~1.5 in the worst localized regions and >2 along the main shell.
Need pressure vessel verification or code-aligned analysis?
For structural FEA, sensitivity studies (thickness, material, pressure), or validation support, contact us at info@tetraelements.com .
Note: Results shown are simulation-based. Final allowables and compliance requirements depend on the applicable design code, material certification, weld/joint details, load combinations, and inspection/testing plans.