Geometric nonlinearity — Rigid Rotation Objectivity

Static (geometric NL)PASS · 0%

Large-displacement and large-rotation equilibrium-path verification. Checks: frame indifference under large rigid rotation.

Tolerance:: 5%

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Problem statement

Geometry: Apply the same rigid translation plus rotations of 30, 90, 180, and 359 degrees to every node of one element and a distorted multi-element patch.
Material: Constitutive or analytical definition: For F=R with R^T R=I, C=F^T F=I and E_Green=(C-I)/2=0.
Boundary conditions: Required solver capability: finite_strain_kinematics. Use the loading/path control stated in the setup and preserve the complete response history.
Measured quantity: Green-Lagrange strain, stress, internal force, and strain energy are zero to roundoff; reactions only enforce prescribed motion.

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=500,0,0
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 support node=1 dofs="all"
frame constraint motion="rigid_rotate" angle=90 axis="0,0,1"
frame solve static nlgeom=on steps=5

Results comparison

Reference value	EG=0, σ=0, fint=0, drift < 1e-12 (объективность конечных поворотов)
Our result	fint=1.97e-31, drift=3.69e-17 mm
Deviation	0%
Tolerance	5%
Status	PASS · 0%
Element family	Beam element
Mesh details	жесткое кольцо со связями и конечным поворотом мастера на 90°; C++ nl_constraints_test

Updated: 2026-10-19 · WebCAE solver