When Nonlinear Analysis Is Required — and When It Is Not

Best-practice guidance on justifying nonlinear analysis: indicators that nonlinearity is physically required and when linear analysis is demonstrably adequate.

Article 07.01Linear versus Nonlinear7 min read

FEAnonlinearlinearplasticitygeometric nonlinearitybest practice

Principle

Nonlinear analysis should be introduced because the physics requires it, not because it appears more sophisticated. Linear analysis should not be rejected where it is demonstrably adequate. The choice should be justified by the expected physical behaviour, not by the availability of nonlinear capability.

Why it matters

Unnecessary nonlinear analysis increases runtime, complicates convergence, reduces transparency and makes verification harder. Insufficient nonlinear analysis misses critical behaviour — plastic redistribution, contact opening, large-displacement effects, buckling. The analyst must judge which nonlinearity is relevant.

Indicators that nonlinearity is required

Stress exceeds yield — material nonlinearity (plasticity) is required for accurate stress and strain
Displacements are large relative to the structure (typically > t/2 or L/100) — geometric nonlinearity (large deformation) is required
Contact status changes during loading — contact nonlinearity is required
The structure shows buckling, snap-through or post-buckling behaviour — nonlinear collapse analysis is required
Follower loads (pressure that remains normal to the deformed surface) are significant — geometric nonlinearity with follower loads
Material properties change with temperature or strain rate — nonlinear material model is required

When linear analysis is adequate

Stress is well below yield (typically < 80% of Fty) — no plasticity
Displacements are small (typically < t/2 or < L/200) — no geometric nonlinearity
Contact status does not change (always bonded or always open) — no contact nonlinearity
The structure is statically determinate with a clear load path — simple behaviour
The analysis is a screening or sizing study where ±10% accuracy is sufficient

Warning signs

Nonlinear analysis is used "to be safe" without identifying which nonlinearity is relevant
Linear analysis is used when stress exceeds yield — the reported stress is not the real stress
Geometric nonlinearity is activated but displacements are tiny — unnecessary cost
The analyst cannot explain why nonlinear analysis was or was not used

Verification checks

Compare linear and nonlinear results — if they differ by < 5%, linear is adequate for this load case
Check that the nonlinear analysis converges to a physically meaningful equilibrium path
For plasticity: verify that the plastic strain is in the expected range and location
For geometric nonlinearity: verify that the load-displacement curve is smooth (no spurious snaps)