Fuselage Barrel Internal Pressurization with 96 Smeared Stringers

Statics (beam-shell)PASS · 0.01%

Internal pressurization (dp = 0.06 MPa) of a cylindrical aircraft fuselage section (D = 3.9 m, L = 7.0 m, t = 1.8 mm) reinforced by 96 tee stringers: axial stress, radial expansion, and hoop stress verified against Lamé-Barlow shell theory with smeared stringe… show full text

Tolerance:: 5%

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Problem statement

Geometry: Cylindrical fuselage barrel radius R = 1.95 m, length L = 7.0 m, skin thickness t = 1.8 mm. 96 tee stringers (tee 36 × 1.6 mm flange, h = 24 mm, tw = 1.6 mm, A_s = 93.4 mm²) on common mesh nodes at 128 mm arc spacing.
Material: Aviation aluminum: E = 72 GPa, ν = 0.33, ρ = 2780 kg/m³.
Boundary conditions: Closed ends: internal pressure dp = 0.06 MPa (60 kPa) on shell surface plus axial tension p·πR² distributed over end rings. Isostatic 3-2-1 constraint at root to eliminate rigid body modes.
Measured quantity: Mid-bay membrane stresses and radial displacement: axial stress σ_x = 29.306 MPa vs analytical smeared stringer 29.305 MPa (0.00%), radial expansion u_r = 1498.49 μm vs analytical 1498.50 μm (0.00%), and hoop stress σ_θ = 64.991 MPa vs 65.000 MPa (0.01%).

WebCAE Terminal

Paste these commands into the Terminal panel inside WebCAE. They use the same text DSL as the application; run one command per line:

units m
material E=72e9 nu=0.33 density=2780
frame up=z
frame patch geom=cyl o=0,0,0 axis=1,0,0 ref=0,0,1 r=1.95 a0=0 a1=360 len=7 nu=192 nv=56 t=0.0018
frame stiffen patch=1 i="0:191:2" section=tee d1=0.024 d2=0.036 d3=0.0016 d4=0.0016 flush=inner
frame load patch=1 p=60000
frame support node=1 dofs="ux,uy,uz"
frame support node=49 dofs="ux,uz"
frame support node=97 dofs="ux"
frame solve static
frame probe shell patch=1 comp=vm stat=mean id="vm"

Results comparison

Reference value	29.305 MPa (axial), 1498.50 um (ur), 65.000 MPa (hoop)
Our result	29.306 MPa (axial, 0.00%), 1498.49 um (ur, 0.00%), 64.991 MPa (hoop, 0.01%)
Deviation	0.01%
Tolerance	5%
Status	PASS · 0.01%
Element family	Beam + Shell
Mesh details	16240 shell quad + beam stiffeners (frame patch + frame stiffen), 16353 nodes, 8861 beams, 98118 DOFs; webcae_solve

Updated: 2026-10-19 · WebCAE solver