Ship Hull Deck Panel Buckling and Eccentric Stiffener Strip Bending
Buckling & Statics (beam-shell)PASS · 1.36%Elastic bifurcation buckling of an isolated ship deck panel (3.0 × 1.167 m, t = 18 mm) bounded by transverse web frames and longitudinal stiffeners under uniaxial compression verified against Bryan's classical plate formula, along with composite bending of an eccentric tee bottom longitudinal strip verified against Steiner parallel axis theorem.Elastic bifurcation buckling of an isolated ship deck panel (3.0 × 1.167 m, t = 18 mm) bounded by transverse web frames and longitudinal stiffeners under uniaxial compression verified against Bryan's classical plate formula, along with composite bending of an… show full text
- Tolerance:
- 5%
Problem statement
- Geometry
- 1) Deck panel: a = 3.0 m (transverse frame spacing), b = 1.167 m (longitudinal stiffener spacing), thickness t = 18 mm. Mesh: 24 × 10 quad shells (240 elements). 2) Bottom strip: L = 6.0 m, b = 1.167 m, sheet t = 22 mm with eccentric tee longitudinal stiffener (tee 300 × 120 × 12 × 16 mm, flush=inner).
- Material
- Shipbuilding structural steel: E = 206 GPa, ν = 0.30, ρ = 7850 kg/m³.
- Boundary conditions
- 1) Deck panel: simply supported (uz = 0) on all four edges, in-plane constraint at corners, uniform compressive edge force σ = 1.0 MPa along transverse edges. 2) Bottom strip: simply supported ends, transverse pressure p = 20 kPa.
- Measured quantity
Deck panel critical compressive stress: Bryan analytical reference σ_cr = k·π²E / [12(1-ν²)] · (t/b)² = 181.52 MPa (aspect ratio a/b = 2.57, m = 3 half-waves, k = 4.096), computed eigenvalue σ_cr = 183.99 MPa (1.40% deviation). Eccentric bottom rib mid-span deflection: Steiner composite beam analytical reference 20.97… show full text
Deck panel critical compressive stress: Bryan analytical reference σ_cr = k·π²E / [12(1-ν²)] · (t/b)² = 181.52 MPa (aspect ratio a/b = 2.57, m = 3 half-waves, k = 4.096), computed eigenvalue σ_cr = 183.99 MPa (1.40% deviation). Eccentric bottom rib mid-span deflection: Steiner composite beam analytical reference 20.97 mm, computed 20.93 mm (0.23% deviation).
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=206e9 nu=0.3 density=7850
frame up=z
frame patch geom=quad p00=0,0,0 p10=3,0,0 p11=3,1.166667,0 p01=0,1.166667,0 nu=24 nv=10 t=0.018
frame support patch=1 side=i0 dofs="uz"
frame support patch=1 side=j0 dofs="uz"
frame support patch=1 side=j1 dofs="uz"
frame support patch=1 side=i1 dofs="ux,uz"
frame support at=3,0,0 dofs="ux,uy,uz"
frame load patch=1 edge=i0 fx=21000
frame solve buckling nmodes=3
frame probe frequency mode=1 id="lambda1"Results comparison
| Reference value | 181.52 MPa (Bryan deck buckling), 20.97 mm (Steiner rib w) |
| Our result | 183.99 MPa (Bryan, 1.36%), 20.93 mm (Steiner, 0.19%) |
| Deviation | 1.36% |
| Tolerance | 5% |
| Status | PASS · 1.36% |
| Element family | Beam + Shell |
| Mesh details | 240 shell quad + beam stiffeners (frame patch + frame stiffen); webcae_solve buckling & static |
Updated: 2026-10-19 · WebCAE solver