Nonlinear solver — Tangent Finite Difference

Nonlinear solverPASS · 0%

Nonlinear iteration, tangent, path-following, and state-management verification. Checks: residual/Jacobian consistency.

Tolerance:: 5%

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Problem statement

Geometry: For random state x and direction v compare K(x)v with [R(x+h v)-R(x-h v)]/(2h) over h=1e-2..1e-8.
Material: Constitutive or analytical definition: Directional derivative identity K v=dR(x)[v].
Boundary conditions: Required solver capability: consistent_tangent. Use the loading/path control stated in the setup and preserve the complete response history.
Measured quantity: Second-order finite-difference error decreases as h^2, reaches a roundoff floor, and the minimum normalized error is <=1e-6.

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 load node=3 force=0,350,0
frame solve static nlgeom=on tangent=analytic check_fd=on

Results comparison

Reference value	\|\|Ka - K_FD\|\|/\|\|K_FD\|\| <= 1e-6, asymmetry < 1e-12
Our result	diff=8.22e-10, asym=5.01e-17
Deviation	0%
Tolerance	5%
Status	PASS · 0%
Element family	Beam element
Mesh details	аналитическая касательная балок vs центральные разности O(h²); C++ beam_corot_tangent_test

Updated: 2026-10-19 · WebCAE solver