Geometric nonlinearity — Pure Moment Quarter Circle

Static (geometric NL)PASS · 0.05%

Large-displacement and large-rotation equilibrium-path verification. Checks: finite rotation kinematics and moment control.

Tolerance:: 5%

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Problem statement

Geometry: Straight cantilever: L=1000 mm, E=210000 MPa, rectangular 20x10 mm, I=1666.66666667 mm^4; apply end moment 549778.714378 N-mm with self-contact disabled.
Material: Constitutive or analytical definition: theta=M L/(E I); kappa=theta/L; x=sin(theta)/kappa; y=(1-cos(theta))/kappa.
Boundary conditions: Required solver capability: large_rotation_beam_or_shell. Use the loading/path control stated in the setup and preserve the complete response history.
Measured quantity: Circular arc with theta=pi/2: tip (x,y)=(636.619772368, 636.619772368) mm, displacement (ux,uy)=(-363.380227632, 636.619772368) mm, rotation=1.57079632679 rad.

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 mm
frame up=z
material E=210000 nu=0.3
frame node at=0,0,0
frame node at=250,0,0
frame node at=500,0,0
frame node at=750,0,0
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 support node=1 dofs="all"
frame load node=5 moment=0,0,549778.714378
frame solve static nlgeom=on steps=10 maxiter=30 tol=1e-6

Results comparison

Reference value	ux=-363.380 mm, uy=636.620 mm, θ=1.5708 rad (четверть круга)
Our result	ux=-363.212 mm, uy=636.781 mm, θ=1.5708 rad
Deviation	0.05%
Tolerance	5%
Status	PASS · 0.05%
Element family	Beam element
Mesh details	20 эл., чистый изгиб M=πEI/(2L); нативный сайдкар webcae_solve

Updated: 2026-10-19 · WebCAE solver