Post-buckling — Plate Imperfection Sweep

Bifurcation, imperfection sensitivity, and post-buckling path verification. Checks: imperfection sensitivity and branch selection.

Tolerance:

5%

Problem statement

Geometry

Use the square plate and seed the first buckling mode with amplitudes t/100, t/50, t/20, and t/10; displacement control beyond Ncrit.

Material

Constitutive or analytical definition: Imperfection sweep anchored by the exact perfect-plate bifurcation.

Boundary conditions

Required solver capability: postbuckling_path_following. Use the loading/path control stated in the setup and preserve the complete response history.

Measured quantity

As imperfection tends to zero, initial tangent bifurcation approaches the analytic Ncrit; larger imperfections smooth the transition without changing equilibrium/energy balance.

WebCAE Terminal

units mm
material E=210000 nu=0.3 density=7850
sketch points=0,0,0,1000,0,0,1000,1000,0,0,1000,0 as=face
section shell t=10
mesh shell size=83.3 element=quad pattern=structured
fix edge number 2 uz=0
fix edge number 3 uz=0
fix edge number 4 uz=0
fix edge number 5 uz=0
fix edge number 5 ux=0
fix edge number 2 uy=0
load edge number 3 fx=-1
solve buckling nmodes=2
imperfection mode=1 scale=0.1
solve static nlgeom=on method=arc steps=20 maxiter=30 tol=1e-5

Results comparison

Updated: 2026-10-27 · version not recorded