Geometric nonlinearity — Euler Column Bifurcation

Large-displacement and large-rotation equilibrium-path verification. Checks: initial-stress stiffness and bifurcation load.

Tolerance:

5%

Problem statement

Geometry

Pinned-pinned column with E=210000 MPa, I=1666.66666667 mm4, L=1000 mm; introduce a tiny first-mode imperfection for nonlinear tracing.

Material

Constitutive or analytical definition: Pcr=pi^2 E I/L^2.

Boundary conditions

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

Measured quantity

Euler bifurcation load Pcr=pi^2 E I/L^2=3454.36154038 N.

WebCAE Terminal

units mm
frame up=z
material E=210000 nu=0.3
frame node at=0,0,0
frame node at=200,0,0
frame node at=400,0,0
frame node at=600,0,0
frame node at=800,0,0
frame node at=1000,0,0
frame member 1 2 section=rect w=20 h=10
frame member 2 3 section=rect w=20 h=10
frame member 3 4 section=rect w=20 h=10
frame member 4 5 section=rect w=20 h=10
frame member 5 6 section=rect w=20 h=10
frame support node=1 dofs="ux,uy,uz,rx"
frame support node=6 dofs="uy,uz,rx"
frame load node=6 force=-1,0,0
frame solve buckling nmodes=2

Results comparison

Updated: 2026-10-19 · WebCAE solver