Nonlinear solver — Energy Balance

Nonlinear iteration, tangent, path-following, and state-management verification. Checks: external work internal energy and contact work accounting.

Tolerance:

5%

Problem statement

Geometry

Ramp the pure-moment quarter-circle beam monotonically from zero moment; no contact or dissipation.

Material

Constitutive or analytical definition: U=M^2 L/(2EI)=integral_0^theta M(theta) dtheta for linear elastic pure bending.

Boundary conditions

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

Measured quantity

Final strain energy and external work both equal 431795.192548 N-mm; imbalance is zero.

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 moment=0,0,549778.714378
frame solve static nlgeom=on steps=20 energy_output=on

Results comparison

Updated: 2026-10-19 · WebCAE solver