*Figure 1: FEA mesh and shear stress results for a reinforced concrete slab
© Glew Engineering Consulting, 2016
*

# Finite Element Analysis Consulting (FEA)

In this series of blogs on FEA, we will first cover some basic elements common to many FEA projects, and then in subsequent blogs in this series, illustrate those methods through examples.

One of the services that Glew Engineering Consulting provides is finite element analysis consulting (FEA). FEA consulting has been a great boon to the engineering profession, allowing mechanical engineers and civil engineers to accurately model the stress and strain behavior of complicated parts and assemblies prior to building physical prototypes. FEA programs are capable of predicting the effects of loads and impacts, variations in temperature, changes in pressure, and more, on an object modeled in a computer-aided design (CAD) program. However, finite element analysis requires a good deal of forethought and careful review to ensure that the meaningful results. Even if the engineer is an FEA expert, complicated models can be very time-consuming. An engineer might leave their FEA stress analysis running overnight, only to check the results in the morning and find that a corner of the model has a stress concentration (or “stress riser”) 10 times higher than should be possible. This is often due to an inadequate mesh at that specific point. In this case, he/she must adjust the model or mesh and then perform another overnight run. Furthermore, as much as FEA software has improved, it still requires a certain level of expertise. The programs sometimes crash or can’t converge after a 99% successful operation, consuming valuable time, and leaving few clues as to how to debug the problem.

With the considerable costs of performing FEA, many organizations lack the resources (skill, time, or money) to take full advantage of the method’s capabilities. As such, many of these groups turn to engineering firms that offer FEA consulting, such as Glew Engineering Consulting, when they need accurate and trustworthy analysis performed on their products.

Those designing products usually rely on others to perform the FEA. The FEA may be performed by an in-house FEA group, or an external consulting group. Sometimes, even with an internal FEA function, it is not uncommon to out-source some of the FEA effort due to exceeding manpower capacity during a design crunch, exceeding licensed seat requirements, or lacking special skills for certain analysis. Alternatively, a company sometimes needs an independent third part to perform the analysis.

# A Brief Intro to FEA Methods

## Why many small finite elements

The stress and strain on a portion of material is the solution to a partial differential equation with certain boundary conditions. These equations can only be solved for certain simple shapes. Thus, real parts, which generally have complex shapes, are broken into many small elements or sections that can be solved. Computers can efficiently solve the partial differential equations numerically for each small section, and then move onto the next section until the entire part is solve in small pieces. In that it is a numerical solution, the computer iteratively solves the equations, applying the boundary conditions, again and again, until the error is minimized to an acceptable level.

As defined by the McGraw-Hill Dictionary of Scientific and Technical Terms, finite element analysis is as follows:

“An approximation method for studying continuous physical systems, used in structural mechanics, electrical field theory, and fluid mechanics; the system is broken into discrete elements interconnected at discrete node points” (5

^{th}ed., pp. 756-757)

## Three steps of FEA

At a high level, there are essentially three steps in performing an FEA on a part or assembly:

- Mesh the model, and apply boundary conditions or loads and constraints.
- Analyze the model.
- Prepare the results in user friendly form.

## Meshing the Model and Boundary Conditions

This system of elements and nodes is call the “mesh”, and the engineer has the option of constructing it manually or letting the computer generate it automatically. It is generally preferable to let the software mesh it automatically, but this requires that the CAD model be intelligently edited beforehand. Sometimes, one must define the mesh by hand, but this has many disadvantages. Besides the mesh, the software also needs to know the material properties for every part is an assembly: the density, stress criteria, elastic behavior, thermal properties, or any other pertinent property. Most FEA programs have a library of standard materials from which the user can select. You can see the mesh as the network of fine lines in Figure 1.

### Correcting CAD Files for FEA

Most FEA software fails to mesh if there are interferences in the model. Fortunately, most CAD programs have the ability to easily identify interferences. Also, complex features in the CAD file may needlessly complicate the meshing, but have no impact on the calculated stress, so they must be simplified before FEA analysis. For at least these reasons, it is useful for FEA consultants to have the same CAD program with which the designer first created the model. Often, the FEA consultant must edit the CAD files to make them FEA friendly. For this reason among others, Glew Engineering keeps PTC Creo™, Dessault Solidworks™ and Autodesk Inventor™.

### FEA Mesh refinement

Meshes must be fine enough to give accurate results, but not so fine as to choke the computer by requiring excessive memory and computational power. This is known as mesh refinement. Basically one can refine the mesh, make it smaller as appropriate, until the results do not change. There are automated routines for doing this, but they come with limited success. Experience and understanding fundamental FEA concepts is the best guide to creating a mesh that is of the proper size. Then, when one refines it, there is hopefully little to no meaningful change in the results.

## Boundary Conditions: Applying Loads and Constraints

Once the component or assembly mesh is fully defined, it needs loads and constraints. The load can be any external operator that affects the component, whether it is gravity, pressure, impact, force, temperature, electric charge, or initial velocity. The component then must be held in place with the right constraints. With no constraints, the object will simply fly to infinity and beyond once a load is applied; with too many constraints, the program might find itself trying to divide by zero or evaluate an infinitely stiff surface.

## Setting the Analysis Type

FEA programs offer a number of different methods of analyzing a model, depending on the type of loading conditions and the expected response. We typically use Autodesk Simulation, which breaks the analysis types into four main selections, each with many sub-options. The main types are as follows:

*Linear:*Linear analysis is useful for simpler systems with small deflections, linear elastic properties, and unchanging loads and boundary conditions.*Nonlinear:*Nonlinear analysis types encompass more complicated problems involving motion, nonlinear elastic or plastic materials, time-dependent changes to loads and constraints, or large deflections and changes in load direction due to those displacements.*Thermal:*Thermal analysis calculates temperature and heat fluxes due to thermal loads, either for steady-state systems or time-variant systems.*Electrostatic:*Electrostatic analysis can calculate current, electric field, and voltage distribution based on induced electrical parameters.

## Preparing the Results and Drawing Conclusions

The results of FEA are generally given in a report. The FEA software will automatically generate the highlights of a report, but the analyst must augment that report with answers to specific questions posed by their client. The raw data is of little or no use to the client, and must be distilled into a usable form.

Along with their analysis suites, most commonly-used finite element analysis programs offer a wealth of reporting options. The FEA programs store the analysis results at each node, so the engineer can examine the stress, strain, displacement, and reaction forces and moments throughout the model. You can see the color overlay in Figure 1, indicating the shear stress on the model. Beyond simply viewing numerical results, most programs allow the engineer to create graphical representations as well, overlaying colored contour plots onto the model surface or outputting to graphs and charts. In addition to their convenience in generating reports, these graphical tools also help the engineer analyze their own work. The FEA consultant must view their results from with at least two goals in mind:

- Answer the original questions that led them to perform FEA.
- Ensure that the results they’re observing are accurate and representative of the actual physical system.

With the right tools and expertise, an FEA consultant or engineer can reap tremendous rewards with the proper use of FEA software. This series of blogs will take a look at getting the most out of an FEA program, and some of the common pitfalls that FEA users encounter.

Glew Engineering has utilized FEA on a variety of projects, from semiconductor chambers and optical systems to vehicle lifts, heat exchanges and smart phone headsets. Most of these we can’t post for proprietary reasons. Take a look at our finite element analysis consulting services, and let us know how we might help you.

### References

Parker, S. (1994). *McGraw-Hill dictionary of scientific and technical terms* (5th ed., pp. 756-757). New York: McGraw-Hill.

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