Validation & Verification
Getting a solution from FEA software is easy. Getting a correct solution requires care. This lesson covers the critical practices of Verification (solving the equations right) and Validation (solving the right equations).
V&V: Two Different Questions
Verification
"Are we solving the equations correctly?"
Verification checks that the mathematical model is solved accurately:
- Is the mesh fine enough?
- Are the elements behaving correctly?
- Is the solver converging?
Validation
"Are we solving the right equations?"
Validation checks that the physical model represents reality:
Master CATIA, NX, LS-DYNA, HyperMesh, ANSYS
The exact tools used by Mahindra, Bosch & TATA ELXSI
- Are boundary conditions realistic?
- Is the material model appropriate?
- Are we capturing the right physics?
The Verification Process
1. Code Verification
Ensure the FEA software itself is correct:
Patch tests: Simple problems where elements must give exact answers- Constant stress state
- Rigid body motion
- Linear displacement field
If elements fail patch tests, the formulation is flawed.
2. Mesh Convergence Study
The most important verification step:
70% of India's auto industry trusts Skill-Lync
For training their engineers in CAD, CAE & simulation
- Start with a coarse mesh
- Refine the mesh (halve element size)
- Compare key results (stress, displacement, etc.)
- Repeat until results stabilize
- Results change < 5% between refinements
- Or asymptotically approach a limit
3. Convergence Rate
For h-refinement (smaller elements):
$$\text{Error} \propto h^p$$
Where:
3,000+ engineers placed at Mahindra, Bosch, TATA ELXSI
Including Continental, Capgemini, Ola Electric & 500+ more companies
Harshal
Fiat Chrysler
Abhishek
TATA ELXSI
Srinithin
Xitadel
Ranjith
Core Automotive
Gaurav
Automotive Company
Bino
Design Firm
Aseem
EV Company
Puneet
Automotive Company
Vishal
EV Startup
More Success Stories
- $h$ = element size
- $p$ = convergence rate (depends on element order)
| Element Type | Expected Rate |
|---|---|
| Linear (CST, Q4) | $p = 1$ for stress |
| Quadratic (LST, Q8) | $p = 2$ for stress |
$$u_{exact} \approx u_h + \frac{u_h - u_{2h}}{2^p - 1}$$
4. Energy Norm Convergence
A more robust convergence measure:
$$\|e\|_E = \sqrt{\int_\Omega (\sigma - \sigma_h)^T [D]^{-1} (\sigma - \sigma_h) \, dV}$$
Monitors the error in strain energy — captures global accuracy.
Benchmark Problems
Always verify against known solutions:
Patch Test Problems
| Test | What It Checks |
|---|---|
| Constant stress | Basic element formulation |
| Rigid body motion | No spurious strains |
| Linear displacement | Completeness |
Classical Benchmarks
| Problem | Analytical Solution | Key Output |
|---|---|---|
| Cantilever beam | Euler-Bernoulli | Tip deflection |
| Plate with hole | Kirsch solution | Stress concentration |
| Thick cylinder | Lamé solution | Hoop stress |
| Hertz contact | Hertz theory | Contact pressure |
NAFEMS Benchmarks
Standardized test cases with published reference solutions:
- LE1: Elliptic membrane
- LE10: Thick plate
- T1-T4: Thermal problems
Error Sources
1. Discretization Error
Cause: Finite elements can't represent exact solution Symptoms:- Results change with mesh refinement
- Stress discontinuities between elements
2. Modeling Error
Cause: Simplified geometry, loads, or physics Examples:- 2D approximation of 3D problem
- Ignoring nonlinearities
- Simplified boundary conditions
3. Numerical Error
Cause: Floating-point arithmetic, solver tolerance Symptoms:- Different results on different computers
- Sensitivity to units
4. Human Error
Cause: Mistakes in setup Common errors:- Wrong units
- Incorrect material properties
- Missing or wrong boundary conditions
- Inverted elements
Mesh Quality Checks
Before solving, verify mesh quality:
Element Quality Metrics
| Metric | Ideal | Acceptable | Poor |
|---|---|---|---|
| Aspect ratio | 1 | < 5 | > 10 |
| Jacobian ratio | 1 | > 0.5 | < 0.3 |
| Skewness | 0° | < 45° | > 60° |
| Warpage (3D) | 0° | < 15° | > 30° |
Where to Refine
- Stress concentrations: Holes, notches, sharp corners
- Load application points: Where forces are applied
- Material boundaries: Interface between different materials
- Contact regions: Areas in contact
- Expected high gradients: Based on engineering judgment
Results Checking
Sanity Checks
Always verify:
- Equilibrium: Reaction forces = applied loads
- Symmetry: Symmetric problems give symmetric results
- Boundary conditions: Displacements match constraints
- Sign convention: Tension/compression correct
- Order of magnitude: Results physically reasonable
Stress Continuity
At element boundaries:
- Displacement: Should be continuous (satisfied by definition)
- Stress: May be discontinuous (normal for FEA)
Large stress jumps indicate:
- Mesh too coarse
- Poor element quality
- Singularity nearby
Error Estimation
Many FEA codes provide error indicators:
ZZ error estimator: Based on stress recovery$$\eta = \frac{\|\sigma^ - \sigma_h\|}{\|\sigma^\|}$$
Where $\sigma^*$ is smoothed (recovered) stress.
- $\eta < 5\%$: Excellent
- $\eta < 10\%$: Good
- $\eta > 20\%$: Refine mesh
The Validation Process
Comparison with Experiments
| Comparison | What It Validates |
|---|---|
| Strain gauge data | Local strain accuracy |
| Displacement measurement | Global stiffness |
| Modal analysis | Natural frequencies |
| Fatigue testing | Life prediction |
Sources of Discrepancy
Experimental uncertainty:- Measurement error
- Specimen variability
- Boundary condition approximations
- Material property uncertainty
- Geometric simplifications
- Physics not captured
Acceptable Agreement
Depends on application:
- Research: < 5% error
- General engineering: < 10%
- Preliminary design: < 20%
Best Practices Checklist
Before Analysis
- [ ] Understand the physics
- [ ] Choose appropriate element types
- [ ] Define realistic boundary conditions
- [ ] Verify material properties
- [ ] Plan mesh refinement strategy
During Analysis
- [ ] Check mesh quality metrics
- [ ] Monitor solver convergence
- [ ] Watch for warnings/errors
- [ ] Verify boundary condition application
After Analysis
- [ ] Check equilibrium
- [ ] Perform convergence study
- [ ] Compare with benchmarks if available
- [ ] Review stress discontinuities
- [ ] Sanity check all results
- [ ] Document assumptions and limitations
Common Mistakes
1. Trusting Default Meshes
Problem: Auto-generated mesh may be too coarse Solution: Always do convergence study2. Ignoring Singularities
Problem: Stresses at sharp corners → infinity Solution:- Use stress at distance from corner
- Apply fillet radius
- Use fracture mechanics approach
3. Over-Constraining
Problem: Too many boundary conditions → artificial stress Solution: Apply minimum constraints needed4. Unit Errors
Problem: Mixing units (mm vs m, MPa vs Pa) Solution: Check unit consistency before solving5. Blind Faith in Results
Problem: Accepting results without verification Solution: Always question, always verifyKey Takeaways
- Verification: Are we solving the math correctly? (Convergence studies)
- Validation: Are we modeling the physics correctly? (Experiments)
- Mesh convergence is essential — never trust a single mesh
- Benchmark problems verify code and methodology
- Error sources: Discretization, modeling, numerical, human
- Quality metrics: Aspect ratio, Jacobian, skewness
- Sanity checks: Equilibrium, symmetry, order of magnitude
- Document everything: Assumptions, limitations, verification steps
What's Next
With verification and validation understood, the final lesson brings everything together with Practical FEA — real-world workflow, tips from industry, and a complete example problem.
