How to Decide Whether an Analysis Needs to Be Nonlinear
Running a nonlinear analysis when a linear one would suffice wastes time. Running a linear analysis when nonlinearity is significant produces wrong answers. This guide explains how to decide.
1. The Engineering Task
Determine whether the structural response involves any nonlinear behaviour — material yielding, large deformation, contact opening/closing or follower forces — that would make a linear analysis invalid.
2. When to Use This Method
This decision is made at the analysis planning stage. If nonlinearity is expected, the model construction, solver settings and verification approach all change. It is much easier to build a nonlinear model from the start than to retrofit nonlinearity later.
3. What You Need Before Starting
- The expected stress level relative to material yield — if stress may exceed yield, material nonlinearity is needed
- The expected displacement magnitude relative to the structural dimensions — if displacements are large, geometric nonlinearity is needed
- Whether joints, gaps or interfaces may open, close or slip — if so, contact nonlinearity is needed
- Whether the load direction changes with deformation (follower forces, pressure on a deforming surface)
4. Step-by-Step Method
- Estimate the peak stress from a linear analysis or hand calculation. If it exceeds the material yield strength, material nonlinearity is required
- Estimate the peak displacement. If it exceeds approximately 1/1000 of a characteristic length, geometric nonlinearity (NLGEOM) should be considered. If it exceeds 1/100, it is required
- List all interfaces in the model. If any interface may open, close or slip under the applied load, contact nonlinearity is required
- Check for follower-force effects: pressure on a deforming surface, or aerodynamic load on a deflecting wing. If the load direction changes with deformation, geometric nonlinearity is required
- If none of the above apply, a linear analysis is sufficient
- If any one applies, run a nonlinear analysis. If multiple sources of nonlinearity are present, they must all be included — partial nonlinearity is not valid
5. What to Check
After running the nonlinear analysis, verify that the nonlinearity was actually significant. Compare the nonlinear result with the linear result. If they differ by less than 5%, the nonlinearity was minor and a linear analysis would have been acceptable — but the nonlinear result is still the correct one to report.
| Nonlinearity Type | Trigger | Solver Feature |
|---|---|---|
| Material | Stress exceeds yield | Plasticity model (Mises, Johnson-Cook) |
| Geometric | Displacement > L/1000 | NLGEOM / large deformation |
| Contact | Gap may open or close | Contact interaction |
| Follower force | Load direction changes | Load stiffness contribution |
| Buckling | Load approaches critical | Imperfection-based nonlinear buckling |
6. How to Interpret the Result
A nonlinear analysis produces results that account for the changing stiffness of the structure. The load-displacement response may show softening (yielding, buckling) or stiffening (membrane action, contact widening). The result is valid over the full load range, not just at the linearised operating point.
7. Common Mistakes
- Assuming "it is only a static analysis" means linear is adequate — material yield and contact make it nonlinear
- Including geometric nonlinearity but not material nonlinearity when stress exceeds yield
- Running a nonlinear analysis without checking convergence of the equilibrium iterations
- Using a single load step when the nonlinearity requires gradual loading to converge
- Assuming a linear buckling eigenvalue is accurate when post-buckling behaviour is relevant
8. Further Reading
See the Non-Linear & Transient Analysis Knowledge category for nonlinear solution theory. See How to Interpret an Eigenvalue Buckling Analysis for buckling-specific guidance.