Benchmarking by FEA: Best Practices & Key Quality Checks to Verify Results Accuracy

This guest contribution on the Altair blog is written by the ESRD team, a member of the Altair Partner Alliance

With the increased usage of finite element analysis (FEA) software tools for virtual prototyping of new and/or modified engineering designs, and the growing practice of benchmarking FEA results against available experimental data or engineering handbook solutions (i.e. “benchmarking-by-FEA”), it’s important to revisit what steps we must consider before performing an engineering simulation by numerical methods. After all, if we don’t plan ahead, we may find ourselves in a “garbage in, garbage out” situation!

Engineering Simulation Considerations: What Questions Should WE Ask And Why?

Typically, engineering analysts are fully aware of the following considerations when defining a mathematical model for a structural simulation that will be used for comparison with experimental test data or engineering handbook approximations:

  • Is the CAD geometry an accurate representation of our actual part/assembly?
  • Do we have all needed material properties?
  • Are the loads and constraints fully understood and can they be properly defined in the engineering simulation?
  • Is a linear elastic analysis adequate for the goal of the analysis, or do we need a nonlinear analysis and if so, which type?

We know that if any of the above are not clearly understood then the outcome of the effort may result in an ill-defined simulation that will not help the engineering decision process. Or worse, provide false or misleading feedback about the engineering simulation.

That said, the following aspects may not always be considered by engineering analysts in production environments but are critical for establishing confidence in the solution:

  • Are we solving the right set of engineering equations?
    • In other words, are we idealizing the model correctly?
  • To what accuracy is our solution converged?
    • In other words, are we solving the engineering equations, right?
  • Does our FEA software provide simple means to show convergence, or is it a time consuming and difficult process?
    • Do we require multiple mesh refinements to show that the answers don’t depend on the number of elements or degrees of freedom? And these additional refinements are not done automatically by the FEA software tool?
  • Does our FEA software automatically average the results across element boundaries, such as stresses or strains?
    • And, do discontinuities in stresses or strains appear if we disable nodal averaging?
  • Are our FEA results highly sensitive to element types?
    • Do the results change if we modify the element integration scheme or hourglass control?

When was the last time you heard all of the above questions asked in a design review? And, why are these topics even important? Clearly knowing if the engineering simulation was performed using the appropriate modeling assumptions (problem idealization) and verifying that the simulation results have converged (solution verification) are essential aspects of the calculations.

Therefore, we need a clear set of “quality checks” for verifying the accuracy of engineering simulations so that engineering analysts can trust the information produced by the mathematical model and confidently perform “benchmarking-by-FEA” workflows.

Key Quality Checks for Verifying the Accuracy of Engineering Simulations

In a recent Altair webinar, we asked a simple but powerful question: if you routinely perform Numerical Simulation via finite element analysis (FEA), how do you verify the accuracy of your engineering simulations? During this webinar, we reviewed ‘The Four Key Quality Checks’ that should be performed for any detailed stress analysis as part of the solution verification process:

  • Global Error: how small and at what rate is the estimated relative error in the energy norm reduced as the degrees of freedom (DOF) are increased? And, is the associated convergence rate indicative of a smooth solution?
  • Deformed Shape: based on the boundary conditions and material properties, does the overall model deformation at a reasonable scale make sense? Are there any unreasonable displacements and/or rotations?
  • Stress Fringes Continuity: are the unaveraged, unblended stress fringes smooth or are there noticeable “jumps” across element boundaries? Note: stress averaging should ALWAYS be off when performing detailed stress analysis. Significant stress jumps across element boundaries is an indication that the error of approximation is still high.
  • Peak Stress Convergence: is the peak (most tensile or compressive) stress in your region of interest converging to a limit as the DOF are increased? OR is the peak stress diverging?

When the stress gradients are also of interest, there is an additional Key Quality Check that should be performed:

  • Stress Gradient Overlays: when stress distributions are extracted across or through a feature containing the peak stress, are these gradients relatively unchanged with increasing DOF? Or are the stress distribution overlays dissimilar in shape?

All these Key Quality Checks are incorporated and simple to use in ESRD’s StressCheck Professional, available via the Altair Partner Alliance here. The following 6-minute video demonstrates how to use StressCheck Professional to perform “benchmarking-by-FEA” for a practical case study: Watch the video here

In the video, a benchmarking-by-FEA case study is performed for a tension bar of circular cross section with a semi-circular groove. The goal was to compute the 3D stress concentration factor by classical approximation (Walter D. Pilkey’s ‘Peterson’s Stress Concentration Factors’, Section 2.5.2) and Numerical Simulation (StressCheck FEA) for several Poisson’s ratio values and demonstrate the effect of Poisson’s ratio on the 3D stress concentration factors.

Interested in learning more? Watch the ESRD/Altair on-demand webinar “How Do you Verify the Accuracy of Engineering Simulations?” now!

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