Geometric nonlinearity — Elastica Tip Force

Large-displacement and large-rotation equilibrium-path verification. Checks: dead-load direction large-deflection elastica.

Tolerance:

5%

Problem statement

Geometry

Slender inextensible cantilever with a constant-direction transverse tip force; use load parameter lambda=P L^2/(E I).

Material

Constitutive or analytical definition: Integrate d2(phi)/ds2=-(P/EI) cos(phi) with clamp phi(0)=0 and free-end curvature phi'(L)=0.

Boundary conditions

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

Measured quantity

Tip x(lambda), y(lambda), and end rotation from the Bisshopp-Drucker elliptic-integral solution; no hard-coded target is claimed until the elliptic oracle is implemented.

WebCAE Terminal

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 force=0,350,0
frame solve static nlgeom=on steps=10 maxiter=30 tol=1e-6

Results comparison

Updated: 2026-10-19 · WebCAE solver