What You Do Not Need to Know to Do FEA

By Ulises Gonzalez, Ph.D.
Senior Engineer
ALGOR, Inc.

Over the past thirty years, Finite Element Analysis (FEA) has gone from a technology available mostly to expert analysts to a commonly used engineering design tool. Why has FEA undergone such an evolution? FEA companies claim that it is the "things that you do not need to know to do FEA" that have made FEA tools available to more engineers. Indeed, FEA tools have become so easy to use that non-engineering professionals such as designers and medical doctors are finding uses for this technology.

In the past, FEA software products were difficult to use by today’s standards. Specifically, users had to possess significant expertise in order to build their FEA models. Then, as now, an FEA model consists of the geometry of the object(s) being considered, loads, material properties, and parameters used to control how the analysis is to be carried out. As FEA technology matured, the level of required expertise has diminished as software has become easier to use. This is not to say that analysts are no longer needed. However, for many engineering design problems, a modern FEA software package should automatically and intelligently deal with most geometry, material and control settings. These "behind the scenes" features free engineers from needing to have in-depth knowledge about the inner workings of FEA software.

In this article, we focus on the "behind the scenes" features that FEA software packages should have so that design engineers do not need to worry about:

• estimating loads, especially in scenarios involving motion;

• specifying contact locations in scenarios involving motion;

• adjusting the timestep size in a nonlinear time-dependent analysis;

• setting integration scheme parameters in a nonlinear time-dependent analysis;

• using curve fitting techniques to work with raw material data;

• setting parameters to automatically capture and mesh a CAD solid model; and

• transferring analysis data from one processor to the other for multiphysics.

No Need to Estimate Loads, Especially in Scenarios Involving Motion

For many years, linear FEA packages have demanded very little expertise from the engineer except in one regard: calculating or estimating loads. Applying loads in linear static FEA is not difficult, but significant expertise may be required to properly estimate their magnitude and direction. What engineers need to know to estimate loads is particularly involved when modeling a part or assembly that is undergoing large-scale motion. To solve such problems, many FEA vendors use a two-step approach that uses a kinematics package to obtain the loads (reaction forces and moments at joints), which are meant to represent the effects of motion, and linear static FEA to obtain the stresses based on those loads. This two-step approach requires a leap of faith – the deformations caused by the loads are assumed to not affect the loads themselves. One may ask, why is linear static FEA used for models involving motion?

It is possible to bypass these assumptions altogether by utilizing a method that couples motion and stress analysis. Such a technique is employed by ALGOR’s Mechanical Event Simulation (MES) software. MES uses nonlinear time-dependent FEA to properly account for the changing inertia, shape and material behavior of the model as it undergoes motion. There is no need to calculate or estimate loads when using MES; the forces and moments are automatically balanced according to Newton’s laws of motion. This rigorous technique is highly desirable when analyzing models that experience surface contact, as is the case when modeling drop tests. Common practice is to approximate the effects of such impacts using loads estimated outside FEA. In contrast, MES eliminates the need to estimate these loads by simulating the entire event associated with the impact, including the falling body, the impact, and how the deformed body rebounds. Throughout the event, MES outputs stresses and other quantities important to the designer.

No Need to Specify Contact Locations in Scenarios Involving Motion

The technical details behind the simulation of surface contact are mathematically complicated and should be automatically handled by the FEA software. Nevertheless, contact methods employed by some FEA tools require the user to specify locations on each body at which contact will be made. It is not always possible to know in advance which surface points will contact. This is particularly true in dynamic events in which the points making contact change with time. Thus, the software must automatically determine where contact occurs throughout the event.

In order to be computationally efficient, the software should have "built-in" intelligence that prevents it from considering the contact between locations that cannot physically interact. In Figure 1 we show two instances of an MES model of an actuating cone clutch that engages and disengages as the shaft rotates. This rotation combined with frictional effects makes it basically impossible to specify which locations will make contact. This problem is easily resolved because the MES method only requires that the user specify which parts or surfaces can make contact.

Figure 1: In this MES, an actuating cone clutch mechanism is modeled using surface contact in conjunction with frictional effects. The motion consists of the clutch engaging and disengaging as the shaft rotates, as illustrated with results at two moments in time.

No Need to Adjust the Timestep Size in a Nonlinear Time-Dependent Analysis

As mentioned above, nonlinear FEA is an integral part of MES. Historically, nonlinear FEA has been difficult to use and required significant experience in order to set the parameters necessary to obtain a convergent solution. The spirit driving the development of techniques like MES is to insulate the user from having to be an expert to apply nonlinear FEA methods. Thus, today’s nonlinear FEA techniques should automatically set appropriate parameter values for the user’s model. In other words, the engineer should not have to be concerned with the details of these features.

One feature that should be inherent to time-dependent nonlinear FEA analysis is an automatic time-step method. An accurate, automatic time-step method should utilize the underlying physics to ascertain the optimal time-step size throughout an event. Generally, the faster an event is unfolding, the smaller the time-step size required. There are two primary challenges: (1) how to diagnose when a relatively fast event is occurring, and (2) when it is safe to increase the time-step size, thus reducing the computational effort. With this time-stepping method, the software automatically sets the appropriate time-step size based on continual examination of convergence with the aim of obtaining an accurate solution. The user should simply input a capture rate for the event, and let the automatic time-stepping scheme adjust the time-step size throughout the event. Of course, the software should also have the flexibility to enable advanced users to stipulate a time-step size rather than using the automatic time-stepping scheme.

The model of the flyball governor shown in Figure 2 was analyzed using MES to verify the accuracy of the automatic time-stepping scheme. The simulation of the event was begun with the whole apparatus spinning. When the base is lowered, the spin rate should increase, just as ice skaters spin faster by pulling their arms closer to their body. This simplified model was chosen because it has an exact analytical solution. The MES, which utilizes an automatic time-stepping scheme, was able to reproduce the analytical solution to within 0.4%.

Figure 2: The spinning motion and resulting stresses for this flyball governor were calculated simultaneously by one software tool, ALGOR’s Mechanical Event Simulation (MES).

No Need to Set Integration Scheme Parameters in a Nonlinear Time-Dependent Analysis

The scheme used to integrate the equations of motion is another feature of time-dependent nonlinear FEA analysis that should be transparent to the users. These schemes are complicated not only in their details, but in that they require numerous input parameters. The goal is to produce an accurate rendition of a physical event. This is sometimes at odds with the finite element method, which occasionally produces spurious and unphysical high-frequency behavior. The integration scheme can be used to eliminate this erroneous behavior by introducing numerical dissipation in the higher frequency modes. However, the addition of such algorithmic dissipation should not result in a loss of accuracy nor damp the important low frequency modes. The parameters in the classical Newmark method can be adjusted by a user to produce algorithmic dissipation, but at the price of accuracy.

What is needed is an integration scheme that filters out the effects of erroneous high frequencies without reducing the accuracy, and yet requires no user-intervention. MES uses just such a method. This method’s ability to damp only the unphysical high frequencies can be demonstrated by simulating the motion of a repetitive mechanism. Figure 3 shows the displacement time trace of several points on a repetitive indexing mechanism. It can be inferred from the nodal displacement time traces that no damping occurs in any of the physically relevant modes.

Figure 3: The plots of nodal displacements (lower right) for this repetitive indexing mechanism (upper left) demonstrate how the results are cyclical – as expected.

No Need to Use Curve Fitting Techniques to Work with Raw Material Data

As mentioned above, material properties are an inherent component of any FEA model. The question is: what do users need to know about a material before they can conduct FEA on a model that utilizes that material? If the material is a common substance, then its properties are easily available. In fact, most FEA vendors provide users with libraries of such material data. But what happens in the increasingly common event that the user is considering a proprietary or new material for which he or she only has the raw experimental data? Certainly, the user should not need to know the curve fitting techniques used to manipulate this data into a form appropriate for FEA. In other words, the user should not need to know how to calculate the material-dependent parameters associated with a given material model. The user should simply be confident that the appropriate material parameters have been automatically calculated from the raw data.

To this end, FEA vendors should provide users with easy-to-use, graphically driven curve-fitting modules. It should be clear from plots of the experimental data that the parameters calculated by the curve-fitting module closely characterize this data. Figure 4 shows the results of an MES model of a rubber expansion valve. This analysis was conducted using material parameters that were obtained using the curve-fitting interface also illustrated in the figure. Note how closely the tabular (experimental) data is matched by the fitted curve. In this case, the combination of a graphical user interface and curve-fitting methods eliminates the need for the engineer to calculate material parameters using some complicated data manipulation scheme.

Figure 4: In an MES of a rubber expansion valve (lower right), the Ogden material model was used to characterize the rubber. The material parameters were obtained using a built-in curve fitting utility (upper left).

No Need to Set Parameters to Automatically Capture and Mesh a CAD Solid Model

Engineers should never need to know how CAD data is transformed into finite elements. Thus, automatic meshing technologies are commonly employed to generate FEA models, in particular those originating from CAD geometrical representations. Users should not need significant experience in order to apply these meshing methods. The methods should simply generate the best possible elements; that is, elements whose shape gives the most accurate results. Figure 5 shows a finite element model generated from a Solid Edge assembly using ALGOR’s InCAD technology, which employs an automatic solid mesh engine. The user did not have to know how to set any parameters in order to properly capture the complex CAD geometry and obtain a good mesh. Notice the regularity of the surface elements, which is where most loads are applied and thus where element quality usually matters most. The mesh shown is a hybrid mesh with brick elements on the surface and tetrahedral element inside.

Figure 5: This valve assembly was captured from Solid Edge using ALGOR’s InCAD technology, which employs an automatic solid mesh engine. No special knowledge was needed to automatically capture the complex CAD geometry without file translation and obtain a good mesh consisting of regular surface elements, which is where most loads are applied and thus where element quality usually matters most. Some minor features were suppressed because they were outside the area of the engineer’s interest.

No Need to Transfer Analysis Data From One Processor to the Other for Multiphysics

Finally, consider a scenario in which multiple physical phenomena interact, requiring a multiphysics analysis. In such an analysis, the same model should be applicable under each process. For example, consider the case of a model in which thermal effects influence mechanical behavior, as illustrated by the model of a casing depicted in Figure 6. Standard practice is to first calculate the temperature distribution using heat transfer FEA, and to then use these temperatures as input for an FEA stress analysis. Because both models are geometrically identical, there should be no need for the engineer to have to know the details of how data is transferred from one process to the other. In addition to coupling thermal and stress processors, it is also possible to couple other analysis processors, such as fluid and thermal or fluid and stress. Furthermore, multiphysics analysis should not be limited to just two processors working in unison, but should incorporate as many as the physics of your event requires and may include any combination of stress, vibration, heat transfer, electrostatic and fluid flow analysis processors.

Figure 6: The same geometrical model of a casing was used for both a heat transfer (upper left) and a linear static stress (lower right) analysis. The FEA software automatically transferred the heat transfer results to the linear static stress analysis.

More Options for More Engineers

In this article, we discussed several important issues that should be automatically dealt with by FEA software. Certainly, the software should inform the engineer how it resolved these issues, and let the user override its decisions. Nevertheless, the engineer should, with the aid of a properly design software package, be able to perform FEA without knowing many technical details. The fact that some vendors have implemented automatic features into their software is why FEA has become such a widely used engineering design tool.