Ulises Gonzalez
Senior Engineer
Algor Inc.
Pittsburgh, Pa.

Edited by Paul J. Dvorak

Over the past three decades, FEA developers have automated  many complex tasks while adding capability to the software. Mechanical  Event Simulation (MES) software from Algor Inc., for example, lets users  study more than stress at one moment in time. Results from an indexing  mechanism, for example, shows displacements for several points. The graphs  show no damping in any of the physically relevant modes or spurious high-frequency  vibration that solvers occasionally find.

Over the past three decades, FEA developers have automated many complex tasks while adding capability to the software. Mechanical Event Simulation (MES) software from Algor Inc., for example, lets users study more than stress at one moment in time. Results from an indexing mechanism, for example, shows displacements for several points. The graphs show no damping in any of the physically relevant modes or spurious high-frequency vibration that solvers occasionally find.


Estimating static loads is difficult enough without  having to consider how they change with motion and impact. In this Algor  MES, an engineer modeled an actuating cone clutch using surface contact  and frictional effects. The motion consists of the clutch engaging and  disengaging as the shaft rotates. Results show stress at two different  times.

Estimating static loads is difficult enough without having to consider how they change with motion and impact. In this Algor MES, an engineer modeled an actuating cone clutch using surface contact and frictional effects. The motion consists of the clutch engaging and disengaging as the shaft rotates. Results show stress at two different times.


A simulation of this flyball governor begins with the  whole apparatus spinning. Lowering the base should increase the spin rate,  just as ice skaters spin faster by pulling their arms closer to their  body. MES technology uses an automatic time-stepping scheme and reproduces  the analytical solution for the governor's motion to within 0.4% of published  values. This simplified model was chosen because it has an exact analytical  solution.

A simulation of this flyball governor begins with the whole apparatus spinning. Lowering the base should increase the spin rate, just as ice skaters spin faster by pulling their arms closer to their body. MES technology uses an automatic time-stepping scheme and reproduces the analytical solution for the governor's motion to within 0.4% of published values. This simplified model was chosen because it has an exact analytical solution.


The Ogden material model was used to characterize the  rubber in an MES analysis of a rubber expansion valve. The analysis was  conducted using material parameters obtained from a curve-fitting interface.  In this case, the combination of a graphical-user interface and curve-fitting  methods eliminate the need for calculating material parameters using separate  and complicated data-manipulation schemes.

The Ogden material model was used to characterize the rubber in an MES analysis of a rubber expansion valve. The analysis was conducted using material parameters obtained from a curve-fitting interface. In this case, the combination of a graphical-user interface and curve-fitting methods eliminate the need for calculating material parameters using separate and complicated data-manipulation schemes.


The valve assembly was modeled in Solid Edge, from Unigraphics  Solutions Inc., Maryland Heights, Mo., and meshed using Algor's InCAD  technology. Users did not have to set parameters or work with a translated  file to properly capture the complex CAD geometry and obtain a good FEA  mesh. Elements on the surface are well formed where most loads are applied  and thus where element quality usually matters most. Minor features, such  as bolts, were suppressed because they fell outside the area of design  interest. To optimize run times, the mesh is a hybrid of brick elements  on the surface where stress concerns are greatest and tetrahedral elements  inside.

The valve assembly was modeled in Solid Edge, from Unigraphics Solutions Inc., Maryland Heights, Mo., and meshed using Algor's InCAD technology. Users did not have to set parameters or work with a translated file to properly capture the complex CAD geometry and obtain a good FEA mesh. Elements on the surface are well formed where most loads are applied and thus where element quality usually matters most. Minor features, such as bolts, were suppressed because they fell outside the area of design interest. To optimize run times, the mesh is a hybrid of brick elements on the surface where stress concerns are greatest and tetrahedral elements inside.


The finned engine cylinder requires a study to find  how well it transfers heat to air and what stresses the thermal loads  might induce. Not long ago, users would have to manually transfer analysis  data from the thermal analysis to a separate stress model. Today, the  two analyses are done with the same model. Algor's FEA software, for example,  automatically transfers thermal results to the linear static-stress analysis.

The finned engine cylinder requires a study to find how well it transfers heat to air and what stresses the thermal loads might induce. Not long ago, users would have to manually transfer analysis data from the thermal analysis to a separate stress model. Today, the two analyses are done with the same model. Algor's FEA software, for example, automatically transfers thermal results to the linear static-stress analysis.


Over the past 30 years, finite-element 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 behind-the-scenes 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 linear-static 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 large-scale motion.

To solve problems with motion, many FEA vendors use a two-step approach. First, a kinematics package obtains loads (reaction forces and moments at joints), which represent the effects of motion. Linear-static 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 linear-static 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 time-dependent 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 out-side 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 inter-act. 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 time-dependent 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. Up-to-date nonlinear FEA techniques free users of the burden by automatically setting appropriate values for models.

An accurate, automatic time-step method uses the underlying physics to determine optimal time steps throughout an event. Generally, the faster an event unfolds, the smaller the time-step 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 time-stepping 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 time-step 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 time-dependent analyses. The schemes, additional features in time-dependent 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 finite-element method, which occasionally produces spurious high-frequency behavior. An integration scheme should eliminate erroneous behavior by introducing numerical dissipation in high-frequency modes. However, adding dissipation algorithms to the software should not reduce its accuracy or damp important low-frequency 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 en-sure accuracy should be handled by the software, not the user.

There should be no need to learn curve-fitting 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 material-dependent 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 easy-to-use, graphically driven curve-fitting modules. It should be clear from plots of experimental data that parameters calculated by the curve-fitting module closely characterize the raw data.

Say good-bye 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 multi-physics 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 thermal-mechanical example, has been to first calculate a temperature distribution using heat-transfer 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 fluid-flow 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 time-step size in a nonlinear time-dependent analysis.
  • Set integration scheme parameters in a nonlinear time-dependent analysis.
  • Use curve-fitting 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 fluid-flow effects.