Muhammed Shehzad Hassan

Wall forces per unit length of a closed cylinder (R = 150 mm), sized at the burst pressure p_b = 2.25 × 70 = 157.5 MPa:

Netting theory (fibres carry everything, resin nothing), fibre strength X = 2,231 MPa, helical angle α = 15°:

Rounded up to 0.25 mm plies: 24 helical (6.0 mm) + 41 hoop (10.25 mm) = 16.25 mm. Laminate theory at the working pressure of 70 MPa then gives the strains and ply stresses:

Stress across the fibres, which decides matrix cracking (strength 29 MPa). A ±15° layer is pulled across its fibres almost in the hoop direction, where the strain is largest:

Fibre check: 950/2,231 ≈ 0.43, so fibre failure is expected at about 70/0.43 ≈ 163 MPa.

• A quarter of the cylinder (R 150 mm, 300 mm long) as layered shells. The 0° reference runs along the axis and the layer normals point outward, so layer 1 sits against the liner.
• Symmetry built by hand on the three cut edges: on each, the movement through the mirror plane and the two tilts out of it are fixed. The closed dome is replaced by its axial pull, 70 × π × 150² / 4 = 1.24 MN, on the free end.
• Every result in the middle of the tank agrees with laminate theory within 1 %: the wall works as a membrane there, which is what the hand calculation assumes.
• Where the model corrected me: my first check looked at the hoop layers (IRF 2.5). Ansys showed that the helical layers crack first. Redoing the hand check for the helical layers gave 81 MPa and IRF 2.8, matching Ansys. The innermost layer is worst because the same growth over a smaller radius means more strain.
• Error caught by the hand check: the first run gave 64 mm of radial growth instead of 1.15 mm. Checking the edge centroids showed two symmetry supports on swapped edges, which stopped the ring from expanding and forced it to bend. After the fix the result matched the prediction.
• Near the loaded end the stresses rise: the dome is missing and the end force acts 8 mm off the middle of the wall. The disturbance fades within about √(R·t) ≈ 50 mm, so all values are read in the middle.
• Engineering meaning: the resin cracks at working pressure while the fibres use only 43 % of their strength. This is why a type 4 tank needs its gas-tight liner, and why the fibres, not the resin, set the burst pressure.
• Limits: coarse mesh (about 30 mm elements), no dome, linear first-failure estimate of burst. The cylinder–dome junction, a known hotspot in real tanks, is not captured by this model.

Stress intensity at the crack tip, with the finite-width correction for a centre crack (W = 100 mm, a = 10 mm):

The panel is thin: plane strain would need a thickness of 2.5(K_Ic/σ_ys)² = 27.4 mm, so plane stress applies and

The crack becomes critical when K reaches the fracture toughness K_Ic = 34 MPa√m. Since Y grows with a, this was solved by bracketing:

Fatigue life from the Paris law (C = 10⁻¹¹, m = 3, Δσ = 100 MPa, R = 0), integrated from 10 to 25.6 mm:

• A quarter of the panel (50 × 100 mm) in 2D plane stress, 5 mm thick. The left edge may only move up and down, the uncracked part of the crack line may only slide sideways, and the crack face carries no support so the crack can open.
• The crack is defined as a pre-meshed crack with symmetry on, so Ansys accounts for the mirrored half. J is evaluated on six rings of elements around the tip, with quadratic 0.1 mm elements near the tip.
• The first ring is 0.8 % low because it runs through the elements at the singular tip. Rings 2 to 6 agree to four digits: J is path independent, which shows the tip mesh is fine enough.
• The panel stretches 3 % more than an uncracked bar of the same size. The crack makes the panel slightly softer, which the bar formula does not include.
• Fatigue: the crack grows from 10 to 25.6 mm in about 109,000 cycles. Treating the panel as infinitely wide (Y = 1) predicts 23 % more life, an error on the unsafe side. The Python integration converged from 106,602 cycles with 3 steps to 109,219 with 1,000, the same idea as a mesh study.
• K_Ic is a plane-strain value; a thin 5 mm panel is tougher in reality, so the critical crack length is on the safe side.
• Limits: linear elastic, no plastic zone or crack closure, textbook Paris constants instead of test data for this alloy and stress ratio.

Ply stiffness from the material data (E₁ = 121 GPa, E₂ = 8.6 GPa, ν₁₂ = 0.27, G₁₂ = 4.7 GPa):

Averaging the rotated ply stiffness over the stack (two plies at 0°, four at ±45°, two at 90°):

Peak strain at the hole, then the stress across the fibres in a 90° ply, including the Poisson narrowing:

Against a transverse tensile strength of 29 MPa, the 90° plies are at 90 % of their limit at 10 kN, so first ply failure is predicted at about 11 kN.

• Surface geometry meshed with layered shell elements; eight 0.25 mm plies defined in ACP with the 0° direction along the load.
• Ansys is about 9 % more critical than the hand estimate because Tsai-Wu combines all ply stresses, while the hand check uses only the stress across the fibres.
• First ply failure is matrix cracking, not rupture: the 0° fibres are at roughly 18 % of their strength at the same load.
• Error caught by the hand check: the first run showed 88 mm of deflection where 0.33 mm was expected. The plies were stacked on one side of the reference surface, so the load acted 1 mm off-centre and bent the plate. A beam estimate of this bending gave 86 mm, confirming the cause before it was corrected.

• All meshes fall within ±2.5 % of theory. The small scatter comes from reading the peak at a single node, whose position on the hole edge shifts with each mesh.
• The 2 mm mesh gives the same accuracy as 0.5 mm with 70 % fewer nodes, so it is the efficient choice for design work.
• Elongation is 3 % above the bar formula because the hole softens the plate, which the formula ignores.

• Bed ridge modelled in FreeCAD; domain meshed with blockMesh and snappyHexMesh, refined where the lab showed strong turbulence; run in parallel on four cores.
• Constant inflow of 0.152 m³/s at 0.335 m depth, as in the experiment.
• The main mismatch is the position of the water-level dip. Likely causes are the coarse base mesh and turbulence modelling near the jump, plus reading errors in a highly turbulent lab flow. No mesh study was done at the time; this is now standard in my work.