Senior Engineer
Algor Inc.
Pittsburgh, Pa.
Edited by Paul J. Dvorak






Over the past 30 years, finiteelement analysis has gone from a technology used mostly by experts and academics to an everyday engineering tool. How did that happen?
FEA companies say it's because they've taken care of previously complex issues so you don't have to. Indeed, FEA tools have become easy enough so that with proper training, nonanalyst professionals such as designers and medical doctors are finding uses for it.
Analysis for the millennium
Admittedly, early FEA versions were difficult to use. Engineers needed significant expertise to build and analyze models. The required expertise level has since diminished so rapidly that most engineers can now produce accurate results. Expert analysts still have their place solving the most difficult problems and mentoring their juniors. But for the rest of the user audience, modern FEA packages automatically and intelligently deal with geometry, material, and control settings so users are free to be more creative. This article focuses on several behindthescenes features in the better FEA programs. These let engineers perform more analyses more accurately and in less time. For example:
There's no need to make assumptions about loads, especially in scenarios involving motion. Calculating or estimating loads has always been a tough job. Although applying them in linearstatic FEA is not difficult, it sometimes takes significant expertise to properly estimate their magnitude and direction. Estimating loads is particularly complex when modeling parts or assemblies that undergo largescale motion.
To solve problems with motion, many FEA vendors use a twostep approach. First, a kinematics package obtains loads (reaction forces and moments at joints), which represent the effects of motion. Linearstatic FEA then calculates stresses based on the obtained loads. This approach requires a leap of faith, an assumption that deformations caused by the loads do not affect the loads. A question to ponder is: Why on earth would you use linearstatic FEA for models that move?
It is possible to bypass this assumption altogether with a method that couples motion and stress analysis. This technique is used by software that simulates moving events, such as Algor's Mechanical Event Simulation (MES). MES uses nonlinear timedependent FEA to account for the changing inertia, shape, and material behavior of the moving model all in one process. There is no need to calculate or estimate loads when using the software. Forces and moments are automatically balanced according to Newton's laws of motion. This rigorous technique is required when models come in contact with surfaces, as in drop tests. Without this software, common practice would have been to approximate the effects of such impacts using loads estimated outside FEA.
In contrast, MES does not estimate loads but rather simulates the event: the falling body, the impact, and how the deformed body rebounds. Throughout the event, the software calculates stresses and other quantities important to the user.
Specifying contact locations in scenarios with motion is also a task of the past. The technical details behind simulating surfaces in contact are mathematically complicated and should be automatically handled by FEA software. Nevertheless, contact methods employed by some FEA tools require users to specify locations on each body at which contact will be made. But it's not always possible to know in advance which surface points will contact. This is particularly true in dynamic events in which areas making contact change with time. Thus, the software should automatically determine where parts contact.
What's more, the software should have builtin intelligence that prevents it from considering contact between locations that cannot physically interact. Consider an FEA model of an actuating cone clutch. It engages and disengages as the shaft rotates. The rotation combined with frictional effects, makes it nearly impossible to specify the locations making contact. This is easily resolved in software such as MES that only requires users to specify which parts or surfaces can make contact.
There should be no need to adjust the time step in nonlinear timedependent analyses. Nonlinear FEA is integral to the better FEA programs. Unfortunately, it has been difficult to use because it required significant experience to set parameters necessary to obtain convergent solutions. Uptodate nonlinear FEA techniques free users of the burden by automatically setting appropriate values for models.
An accurate, automatic timestep method uses the underlying physics to determine optimal time steps throughout an event. Generally, the faster an event unfolds, the smaller the timestep needed. Software has two primary challenges in this area: Determine when an event happens quickly, and when it is safe to increase time steps to reduce computational effort.
The timestepping method, available in MES, for example, lets the software automatically set appropriate values based on continual examination of convergence with the goal of an accurate solution.
Users should simply specify a capture rate for the event, then let the software adjust timestep sizes throughout. Of course, the software should also have the flexibility to let advanced users assign time steps rather than using the automation.
Parameters for integration schemes should be automatically set in nonlinear timedependent analyses. The schemes, additional features in timedependent nonlinear FEA, integrate the equations of motion and should be transparent to users. They are complicated and require numerous parameters. The analysis goal is to produce accurate renditions of physical events. This is sometimes at odds with the finiteelement method, which occasionally produces spurious highfrequency behavior. An integration scheme should eliminate erroneous behavior by introducing numerical dissipation in highfrequency modes. However, adding dissipation algorithms to the software should not reduce its accuracy or damp important lowfrequency modes. Parameters in one classical scheme, called the Newmark method, can be adjusted by users to produce algorithmic dissipation, but at the price of accuracy. Thus, the task of setting integration parameters to ensure accuracy should be handled by the software, not the user.
There should be no need to learn curvefitting techniques when working with raw material data. Material properties are an inherent component of any FEA model, and the properties for common materials are readily available. Most FEA vendors provide libraries of material data. But what happens when only raw data is available for an unusual material under consideration? Certainly, users shouldn't have to calculate materialdependent parameters associated with a material model. They should be confident that the FEA program will calculate appropriate material parameters from raw data. To this end, some FEA vendors are providing easytouse, graphically driven curvefitting modules. It should be clear from plots of experimental data that parameters calculated by the curvefitting module closely characterize the raw data.
Say goodbye to setting parameters to capture and mesh CAD models. Engineers should rarely need to know how CAD data is transformed into finite elements. Thus, automatic meshing technologies usually generate FEA models, particularly those from CAD systems. A modern FEA system simply generates the best possible elements — those whose shape gives the most accurate results.
And lastly, there should be no need to transfer analysis data from one solver to another for multiphysics problems. In a multiphysics analysis, two or more physical phenomena interact, such as one in which thermal effects influence mechanical behavior. A single model should handle both physical processes.
Standard practice, in a thermalmechanical example, has been to first calculate a temperature distribution using heattransfer FEA, and use the temperatures as input for an FEA stress analysis. Because both models are geometrically identical, the engineer should not have to know the details of how data transfers from one solver to the other. In addition, it's also possible to couple other analyses, such as fluid and thermal or fluid and stress.
Furthermore, the real world is not limited to just two phenomena, so the software shouldn't be either. Good FEA software incorporates as many disciplines as needed and may include any combination of mechanical, vibration, thermal, electrical, and fluidflow effects.
Properly designed FEA software lets engineers conduct analysis without burdening them with technical details. The software should tell users how it resolved any of the issues mentioned and let them override its decisions when necessary. Expect the automation trend to continue. As we've seen here, even what's considered difficult today will soon be an everyday event.
A brief stroll down FEA's memory lane
Developments in FEA software have come so steadily over the last few decades that looking back provides a revelation at how far it has come. What FEA today does for the user, the user had to do for the software 20 years ago. For instance, users had to:
 Estimate loads, especially in scenarios involving motion.
 Specify contact locations, again in models involving motion.
 Adjust the timestep size in a nonlinear timedependent analysis.
 Set integration scheme parameters in a nonlinear timedependent analysis.
 Use curvefitting techniques, probably in separate programs, before working with raw data from material tests.
 Build models in the FEA program and mesh them manually. "Advanced" programs still required setting parameters to mesh a CAD solid model.
 Transfer analysis data manually from one processor or solver to another when problems involved combinations of mechanical, vibration, thermal, electrical, and fluidflow effects.