Stiffened Ship Hull Stillwater and Wave Bending

Statics (beam-shell)PASS · 0.37%

Global longitudinal bending of a 180 m cargo ship hull (180 × 28 × 16.5 m, draft T = 10.5 m, displacement 48,099 t) reinforced by longitudinal and transverse stiffeners: midship vertical deflection, deck stress, and bottom stress in stillwater and sagging wave… show full text

Tolerance:: 5%

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Problem statement

Geometry: Ship hull L = 180 m, B = 28 m, D = 16.5 m, draft T = 10.5 m, 53 shell patches, mesh 120 × 24, frame spacing 1.5 m. Skin plates: bottom t = 22 mm, side t = 20 mm, deck t = 18 mm, double bottom t = 18 mm, bulkheads t = 12-14 mm. Stiffened by 34,724 tee beam members (bottom longs 300×120, deck longs 200×80, side frames).… show full text
Ship hull L = 180 m, B = 28 m, D = 16.5 m, draft T = 10.5 m, 53 shell patches, mesh 120 × 24, frame spacing 1.5 m. Skin plates: bottom t = 22 mm, side t = 20 mm, deck t = 18 mm, double bottom t = 18 mm, bulkheads t = 12-14 mm. Stiffened by 34,724 tee beam members (bottom longs 300×120, deck longs 200×80, side frames). Total mass 48,099 t (lightship 6,682 t + cargo/ballast 40,928 t + superstructure 489 t).
Material: Shipbuilding structural steel: E = 206 GPa, ν = 0.30, ρ = 7850 kg/m³.
Boundary conditions: Self-equilibrated free-body floating condition with 3 isostatic supports on the keel line to remove rigid body modes: midship keel (ux,uy,uz), end keel (uy,uz), and off-center bottom (uz). Loads: self-weight + distributed cargo on inner bottom + hydrostatic pressure (stillwater T = 10.5 m or trochoidal sagging wave amp… show full text
Self-equilibrated free-body floating condition with 3 isostatic supports on the keel line to remove rigid body modes: midship keel (ux,uy,uz), end keel (uy,uz), and off-center bottom (uz). Loads: self-weight + distributed cargo on inner bottom + hydrostatic pressure (stillwater T = 10.5 m or trochoidal sagging wave amplitude a = L/40 = 4.5 m).
Measured quantity: Midship bulkhead vertical deflection from chord: wave sagging computed -157.62 mm vs reference -158.21 mm (0.38% deviation); stillwater computed -37.01 mm vs reference -35.99 mm (2.83%). Midship cargo hold longitudinal stress σ_x: deck computed -38.47 MPa vs reference -38.39 MPa (0.20%); bottom computed 21.57 MPa vs re… show full text
Midship bulkhead vertical deflection from chord: wave sagging computed -157.62 mm vs reference -158.21 mm (0.38% deviation); stillwater computed -37.01 mm vs reference -35.99 mm (2.83%). Midship cargo hold longitudinal stress σ_x: deck computed -38.47 MPa vs reference -38.39 MPa (0.20%); bottom computed 21.57 MPa vs reference 21.39 MPa (0.84%).

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,-14,0 p10=180,-14,0 p11=180,14,0 p01=0,14,0 nu=60 nv=12 t=0.022
frame patch geom=quad p00=0,-14,16.5 p10=180,-14,16.5 p11=180,14,16.5 p01=0,14,16.5 nu=60 nv=12 t=0.018
frame stiffen patch=1 j="0:12:1" section=tee d1=0.3 d2=0.12 d3=0.012 d4=0.016 flush=inner
frame stiffen patch=2 j="0:12:1" section=tee d1=0.2 d2=0.08 d3=0.009 d4=0.012 flush=inner
frame support at=90,0,0 dofs="ux,uy,uz"
frame support at=0,0,0 dofs="uy,uz"
frame support at=90,7,0 dofs="uz"
frame gravity on
frame load patch=1 p=-103005
frame solve static
frame probe disp at=90,0,0 comp=uz id="midship_uz"

Results comparison

Reference value	-158.21 mm (wave w), -35.99 mm (stillwater w), -38.39 MPa (deck sigma), 21.39 MPa (bottom sigma)
Our result	-157.62 mm (wave w, 0.37%), -37.01 mm (stillwater, 2.83%), -38.47 MPa (deck, 0.21%), 21.57 MPa (bottom, 0.84%)
Deviation	0.37%
Tolerance	5%
Status	PASS · 0.37%
Element family	Beam + Shell
Mesh details	27216 shell quad + 34724 beam stiffeners (frame patch + frame stiffen), 24211 nodes, 145266 DOFs; webcae_solve

Updated: 2026-10-19 · WebCAE solver