Verifying Your Finite Element Analysis Results
Engineering VISION Grant posted on January 25, 2016 |

By Nicholas M. Veikos, president of CAE Associates Inc.

Is your analysis predicting a continuous stress distribution? Plot showing contours of un-averaged nodal stress using a coarse mesh. Note the 10 percent variation (2355 vs. 2122) at the peak stress location. Is a 10 percent mesh discretization error within your high stress region acceptable?

Is your analysis predicting a continuous stress distribution? Plot showing contours of un-averaged nodal stress using a coarse mesh. Note the 10 percent variation (2355 vs. 2122) at the peak stress location. Is a 10 percent mesh discretization error within your high stress region acceptable?

Integration of simulation into multiple stages of a product development process can yield big benefits in terms of cost reduction and process efficiency. However, it is key that engineering firms perform this integration in an organized manner with strict accountability.

A critical piece of this integration is verification and validation, sometimes referred to in quality circles as “V&V.” Verification and validation form the backbone of any good quality assurance plan related to simulation.

Without proper focus on these V&V items, it is unlikely that a simulation plan will succeed. Ignoring V&V can create instances where simulation will do more harm than good by leading the design process in the wrong direction.

Yes, simulation can actually lead you astray—if you don’t have the right checks and balances in place. Let’s first clarify what is meant by V&V using structural analysis and FEA procedures as a specific example. The overall concepts are easily extended to CFD analysis or other CAE analysis types.

Verification is the process by which we check that the FEA was conducted properly. Validation is the process to check whether the simulation results reflect real world results. I came across the following definition a long time ago, which helps clarify the difference:

  • Verification is how we see if we have solved the problem correctly.
  • Validation is how we see if we solved the correct problem.

Verification – Why Is It important?

Two things that engineers know about finite element analysis: It is approximate, and it is not robust. Small errors in modeling, data input and boundary conditions can lead to very large errors in the results. Even worse, these errors can be relatively small and difficult to identify, but have significant impact on performance or service life.

For example, using the incorrect reference temperature for thermal strain in a structural model may only affect the stresses by a few percent. This error will not be large enough to raise a flag when comparing FEA results to a hand calculation. However, the error may be more than large enough to change fatigue life significantly. These types of mistakes are hard to catch unless someone is reviewing the analysis very thoroughly.

Errors are inevitable in finite element models—the more complex the model, the higher the probability that they will occur. The important thing is to put a process in place to catch them before they do any damage—the verification process.

Verification – Steps in the Process

All locked up and no place to go? Discontinuous pattern hydrostatic stress indicates volumetric locking.

All locked up and no place to go? Discontinuous pattern hydrostatic stress indicates volumetric locking.

The verification process can take many different forms depending on:

  • The type of analysis being conducted
  • The parts being analyzed
  • The accuracy required
  • The level of risk involved

The analysis must begin with clearly defined goals, accuracy requirements and key assumptions.

For ease-of-use, repeatability and ultimate success, it is helpful to create a verification template. Verification should also be a gated process that is used by everyone in the organization who performs FEA.

For example, some typical items to check as part of the verification process for a static structural analysis might include:

  • Geometry—do key model dimensions agree with the actual part dimensions?
  • Does the FE model mass and CG compare well with the actual part?
  • Are the material properties correct and are they properly associated to model regions?
  • Are element properties like shell thickness or beam properties correct and properly associated to model regions?
  • Is the mesh sufficiently refined to produce the required accuracy? What is the plan to check this?
  • Are there cracks in the mesh?
  • Do the elements pass shape distortion testing criteria?
  • Are the element formulations consistent with the application?
  • Are the applied loads and constraints correct—location, magnitude and direction?
  • Are assemblies properly connected?
  • Does the model pass free thermal expansion and rigid body motion checks?
  • Does a 1G static load produce the expected reaction forces?
  • Have FE code errors and warning messages been reviewed and reconciled?
  • Do the reaction forces balance the applied loads in each direction?
  • Are the deformations and stresses believable—magnitude and direction? Do they compare well with hand calculations?
  • Are the results consistent with the assumptions, e.g. small deformation or small strain?
  • Is shear or volumetric locking a problem? Is your numerical integration scheme too low?
  • Are stresses continuous across elements?

The above list is not complete. In fact, some important checks have been left out. Would you like to guess what they are? Please suggest them in the comments below. We’d like to look at verification checklists for other types of analysis, too.

About the Author

Nicholas M. Veikos, Eng.Sc.D., is president of CAE Associates Inc. Nick has more than 30 years of experience in engineering analysis across finite element theory, structural dynamics, random vibrations, structural nonlinearities and rotordynamics.

All opinions are those of Nicholas M. Veikos and are not necessarily those of ENGINEERING.com.

Recommended For You