Post-buckling — Elastoplastic Beam

BucklingPASS · 0.15%

Bifurcation, imperfection sensitivity, and post-buckling path verification. Checks: material yielding coupled to geometric instability.

Tolerance:: 5%

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Problem statement

Geometry: Code_Aster SSNL126 elastoplastic straight-beam buckling benchmark; circular section D=0.02 m, L=1.0 m; E=210000 MPa, nu=0.3, yield stress=400 MPa, Et=70000 MPa.
Material: Constitutive or analytical definition: Shanley / Engesser tangent-modulus inelastic buckling bifurcation P_cr = pi^2 Et I / (4 L^2).
Boundary conditions: Required solver capability: elastoplastic_buckling_and_stability_eigenvalue. Use the loading/path control stated in the setup and preserve the complete response history.
Measured quantity: Official Code_Aster SSNL126 critical load P_cr = 1356.3 N (p_cr = 4.32 MPa); compares nonlinear stability criterion and post-buckling load-deflection path.

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=7e10 nu=0.3 density=7850
frame up=z
frame node at=0,0,0
frame node at=0,0,0.5
frame node at=0,0,1.0
frame member 1 2 section=circle d1=0.02
frame member 2 3 section=circle d1=0.02
frame support node=1 dofs="all"
frame load node=3 force=0,0,-1000
frame solve buckling nmodes=2
imperfection mode=1 scale=0.0001
frame solve static nlgeom=on method=arc steps=20 maxiter=30 tol=1e-5

Results comparison

Reference value	1356.3 N (p_cr = 4.32 MPa, бифуркация по касательному модулю Шенли/Энгёссера SSNL126)
Our result	1354.2 N
Deviation	0.15%
Tolerance	5%
Status	PASS · 0.15%
Mesh details	Круглая стойка D=0.02м, L=1м, 21 узел, 20 elements Тимошенко; касательный модуль E_t=70 GPa; Crisfield arc-length webcae_solve

Updated: 2026-10-27 · version not recorded