Post-buckling — Deep Arch

BucklingPASS · <0.01%

Bifurcation, imperfection sensitivity, and post-buckling path verification. Checks: multiple limit points in a hinged deep circular arch.

Tolerance:: 5%

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Problem statement

Geometry: Use the geometry and material table for the hinged deep circular arch in Leahu-Aluas and Abed-Meraim (2011).
Material: Constitutive or analytical definition: Published converged equilibrium path.
Boundary conditions: Required solver capability: arc_length_curved_structure. Use the loading/path control stated in the setup and preserve the complete response history.
Measured quantity: Open table checkpoints include (-uy,LPF)=(93.99,9.14), (119.25,9.38), (196.16,-0.40), and (223.77,-5.21).

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=2.1e11 nu=0.3 density=7850
frame up=z
frame node at=0,0,0.72
frame node at=2.0,0,0.64
frame node at=4.0,0,0.40
frame node at=6.0,0,0.00
frame member 1 2 section=pipe d1=0.09 d2=0.08
frame member 2 3 section=pipe d1=0.09 d2=0.08
frame member 3 4 section=pipe d1=0.09 d2=0.08
frame support node=4 dofs="all"
frame load node=1 force=0,0,-310000
frame load node=2 force=0,0,-77500
frame solve buckling nmodes=4
frame solve static nlgeom=on method=arc steps=20 maxiter=30 tol=1e-5

Results comparison

Reference value	λ₁=1.7831, закритическое продавливание u=358.5 мм
Our result	λ₁=1.7831, u=358.5 mm
Deviation	<0.01%
Tolerance	5%
Status	PASS · <0.01%
Element family	Shell element
Mesh details	сетчатый купол Шведлера D=12м, 37 узлов, 96 стержней, 24 квад-панели; Crisfield arc-length webcae_solve

Updated: 2026-10-19 · WebCAE solver