Practical Finite Element Analysis
for Mechanical Engineers


Practical Finite Element Analysis
for Mechanical Engineers


Practical Finite Element Analysis
for Mechanical Engineers


Practical Finite Element Analysis
for Mechanical Engineers


How to Verify & Validate Your FEA

How to Verify & Validate Your FEA

In FEA, both careless users and experienced engineers who are not careful to systematically validate their models can easily make significant mistakes. Expensive decisions in terms of both time and money can sometimes turn out be based on incorrect answers. FEA is demanding, in the sense that the FEA analyst must be proficient not only in mechanics but also in mathematics, computer science, and especially FEA itself. Therefore, it is important to employ validation and correlation procedures whenever FEA is used to solve a problem.

When there are no test data you can use to validate an FEA during the first design stages, you must employ methods for verifying its quality and ensuring there are no errors. Ultimately, when test data are available, correlation with the FEA must be done to ensure that the modeling abstractions do not hide real physical problems that will occur after the structure has been manufactured.

The Three Steps of Verification & Validation

First, let’s define what we mean by Verify & Validate an FEA. The FEA V&V process can be split into three steps. The first two steps are intended to remove modeling errors early in the FEA development process, while the third step focuses on comparison with experimental data:

  • Step 1: Accuracy Checks
  • Checks that ensure the model properly represents the physical system

  • Step 2: Mathematical Checks
  • Checks that ensure the model is mathematically accurate. These checks are not to confirm that the model accurately represents a physical system but simply that it is mathematically well-conditioned and does not introduce problematic mathematical artefacts.

  • Step 3: Correlation
  • Correlation ensures that the model predicts correct strains, stresses, and behavior, compared to real physical and experimental behaviors

Verification & Validation

Accuracy Checks

This first step ensures that your model represents the physical system you wish to model. You will find below a list of accuracy checks you should perform once your FEA is completed. You should not proceed any further in the use of your model without conducting these checks, which is usually done with pre-processing software.

They should be strictly applied to every new model. Afterward, regular sanity and spot-checking are recommended as the model evolves and incremental changes are introduced.

  • Dimensions
  • Element properties Vs DMU
  • Units
  • Mesh Quality
  • Material properties
  • Material orientation
  • Free edges and free faces
  • Coincident nodes and elements
  • Local coordinate systems
  • Nodal coordinate systems
  • Consistent shell normals
  • 1D released DOF's
  • Mass
  • Proper element use
  • Shrink plot
  • Hidden lines/shaded plots
  • Zipper effect
  • MPCs and rigid body elements
  • Beam element orientation and offset check

The Table 16-1 in the Chapter 16 of my book "Practical Finite Element Analysis for Mechanical Engineers" explains these checks in detail and give you recommendations about what to check in your FEM.

Mathematical Checks

This second step will alleviate risks and ensure that your FEA is mathematically accurate and well-conditioned. Mathematical validity checks can be performed with simple static analyses. They are generally a relatively inexpensive means of checking that your FEM is reliable and sound.

The four mathematical validity checks are:

  • Free-free modal analysis – rigid body and flexible modes check
  • Unit gravity check
  • Unit enforced displacement check
  • Thermal equilibrium check

The results of such mathematical validity checks must be verified prior to running the FEA with any other type of analysis (static, dynamic, thermal, or other).

Mathematical Checks

Basic Concepts

In order to conduct the four mathematical validity checks, you must be familiar with the following concepts to better interpret the results you will obtain during the four mathematical checks:

  • Check for singularities and the presence of mechanisms
  • Weight check
  • Applied loads check
  • Reacted loads check
  • Post-processing software checks
  • Load path

The paragraph 16.3.1 in the Chapter 16 of my book "Practical Finite Element Analysis for Mechanical Engineers" explains these concepts in detail.

The same chapter illustrates the mathematical checks with examples.

Basic Concepts

Correlation

Correlation is an exercise that consists of checking an FEA against existing reference data. The analyses performed to size and validate structures are frequently supported by tests. This experimental data can be used to check the FEA.

The correlation will be used to demonstrate that your FEA is valid and reliable:

  • Valid: the FEA predicts the correct strains and stresses.
  • Reliable: the FEA predicts the correct behavior for ALL critical conditions.
Accuracy

During the correlation process, the FEA can be modified to improve the match with the test results. Correlation is generally done using the FEA results of linear solutions. However, some local nonlinear effects with the test articles could force the run of nonlinear solutions to obtain better correlation (large displacement effects, nonlinear material behavior, etc.).

The paragraph 16.6 of my book "Practical Finite Element Analysis for Mechanical Engineers" explains the tools used to conduct this correlation

  • Strain Gauge Measurements
  • Validation Factors Calculation
  • Correlation Plots

Document the Verification & Validation

A complete documentation of the validation process must be supplied for each FEA used for the product certification. This document, known as the “FEM Validation Report,” must contain the following information:

  • The FEA identification, with the reference to the corresponding model book (the model book is the document that describes the FEM in detail)
  • The accuracy check results
  • The mathematical check results
  • The correlation

To record my checks during the V&V process, I like to use an Excel spreadsheet where I save all the checks. You can download a template of the file below. The green cells should contain a “YES” if the check was successfully performed, a “NO” if the check failed, or an “N/A” if it is not applicable to the FEA. The template permits to record the basic results related to the check.

Download

Finally, the correlation should be documented with the following information:

  • The exact locations and types of all gauges on the test articles used for the correlation (CAD and/or pictures of the test article)
  • The purpose of each gauge
  • The tables showing, for each gauge and test condition, the recorded strain, FEA strain, validation factors, and explanations of non-correlated gauges (see example in template file)
  • The correlation plots (see example in template file)
Documentation
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ABOUT THE AUTHOR
Dominique Madier

Dominique Madier is a senior aerospace consultant with 20 years’ experience and advanced expertise in Finite Element Analysis (FEA) of static and dynamic problems for linear and nonlinear structural behaviors.

He has conducted detailed finite element analyses for aerospace companies in Europe and in North America (e.g., Airbus, Dassault Aviation, Hispano-Suiza [now Safran], Bell Helicopter Textron Canada, Bombardier Aerospace, Pratt & Whitney Canada, and their subcontractors) on metallic and composite structures such as fuselages, wings, nacelles, engine pylons, helicopter airframes, and systems.

He is the author of the book “Practical Finite Element Analysis for Mechanical Engineer”: 650+ pages about the best practical methods and guidelines for the development and validation of finite element models.

He earned a Master’s degree in Mechanical and Aerospace Engineering from Paul Sabatier University, Toulouse, France.
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