This paper describes features of finite element analysis (FEA), which has become established in nearly all engineering fields, including bioengineering, where it plays a role in studying many parts of the body, such as nasal passages. Advanced FEA programs like Abaqus help engineers evaluate the effect of loading on impeller’s natural frequencies, modelled rotating at 10,000 rpm. FEA software simulates where structures bend or twist and indicates the distribution of stresses and displacements. The everyday FEA software integrated with computer-aided design systems is user friendly and adept at analyzing most FEA engineering problems, when properly programmed by the user. The software programs meant to model complex or unusual problems are built to allow their users to configure the software—to a certain degree—to their own unique needs.
January saw the death of British mathematician Olgierd Cecil Zienkiewicz, an early pioneer of the finite element method who pushed for its computerization and who recognized the potential for using the method to solve problems outside solid mechanics, purview of the famous Euler-Bernoulli beam equation.
With his passing, we pause to assess FEA’s past—looking at the pros and cons of the leap the method has made into the software realm—and to look at what the future holds for finite element analysis and its applications.
From its inception in the 1940s until about a decade and a half ago, finite element analysis had been performed exclusively by specialized analysts who held Ph.D.s in the subject and had devoted their careers to the discipline. But the FEA field has seen great change over the past 15 years, with a jump in the number of computer technologies available to an increasing number of engineers. And like all changes, it has brought risks and rewards.
In his lifetime, Zienkiewicz saw the finite element method move from a powerful technique originally developed to solve complex structural mechanical problems to its use today across nearly all engineering fields, including bioengineering— and its stretch into unrelated fields such as the simulation of weather patterns. Beginning in the 1960s, FEA researchers began to extend the method beyond linear structural analysis to nonlinear FEA and other engineering disciplines such as fluid dynamics, heat transfer, soil mechanics, wave propagation, and electromagnetics.
Zienkiewicz himself sought to move the finite element method from a research tool to a computer-based analysis method that could be called upon by designers and engineers. And in 1968 he founded the first journal dealing with computational mechanics, the International Journal for Numerical Methods in Engineering.
Today, high-end FEA software packages are available to solve complex problems across many disciplines. But they’re still not perfect; that is, the engineers and researchers who use these tools can spend a lot of time kitting them out and programming them for their own unique use.
Other FEA packages introduced within the past 15 years are now commonly integrated with computer-aided design applications, allowing product developers to analyze as they design. The integration is intended to speed up the design cycle because designers can analyze, then immediately update, their designs.
Without a doubt FEA’s move to the computer allowed it to become the widely used tool it is today, said Samer Adeeb, an assistant professor in the department of civil and environmental engineering at the University of Alberta in Edmonton. By helping move the tool to the computer, Zienkiewicz enabled its popularity and its growth, Adeeb added.
The problems we’re now solving with FEA couldn’t have been done ten years ago because you would have needed a mainframe.
In the early 1970s, FEA was run only on mainframe computers owned mainly by companies in the aeronautics, defense, and nuclear industries. With the rapid decline in the cost of computers and the concomitant increase in computing power, today’s personal computers can now produce accurate FEA results. Adeeb pointed out that many engineering technology vendors are currently marketing simplified analysis programs, which walk users through a series of steps that allow them to define the analysis they want to run and then interpret the results.
“FEA has been around forever, but it’s grown to be very powerful because of the computational power that exists right now in computers,” Adeeb said.
“The problems we’re now solving with FEA couldn’t have been done ten years ago because you would have needed a mainframe,” he added. “Now a desktop has enough computation power that anyone can run FEA.”
That jump to the desktop makes for the packages that allow CAD users to run more up-front analysis during design, but it can also mislead untrained analysts, who may not fully understand the finite element method and won’t exactly know how to best input information or how to interpret results, Adeeb added.
“FEA is becoming so easy to run and is so highly integrated with all the CAD software now, but the output from the analysis is still the numbers a designer uses to determine if the part is safe or not Safe,” he said.
“It’s sometimes too easy to toggle back and forth between CAD and FEA without really knowing what you’re doing,” he said. “Some people abuse FEA because it offers such a nice animation; so they try to get to the animation they want rather than to actually solve a problem that returns useful information.”
According to Adeeb, FEA software shouldn’t be relied upon as a black box that spits out numbers. Designers still need to know the proper inputs and to understand what those numbers mean. The old adage holds true, he said: garbage in, garbage out.
To get meaningful analysis results, designers need to know how to identify the problem that needs solving in the first place. That requires at least a basic understanding of the finite method, he added. Before beginning analysis, designers will need to simplify the problem at hand, to ask themselves whether the problem is linear or nonlinear, and to identify the forces that need to be analyzed.
As an instructor, Adeeb knows this line of questioning doesn’t come intuitively to users who have little or no understanding of the finite element method.
As a numerical technique, FEA allows engineers to find approximate solutions of partial differential and integral equations. FEA software simulates where structures bend or twist and indicates the distribution of stresses and displacements. The software uses a complex system of points to form a grid, or mesh, across a model. The engineer assigns nodes at a particular density throughout the material, often depending on the expected stress levels of a certain area. The mesh contains the material and structural properties that define how the part will react to certain load conditions.
“The first question I ask my students on exams is: what is FEA and why do you need it?” Adeeb said. “If people can’t offer the correct definition of what it is I don’t trust them using FEA. Within the definition itself lies the understanding of what they’re doing.”
Companies that hire designers to perform both CAD and FEA should offer new employees an introductory course to FEA, Adeeb said.
“Otherwise what they’re doing is just an animation, and that doesn’t differ from a computer scientist who is just drawing on the computer,” he said.
the simple stuff
Though desktop FEA has come a long way in the past few decades, everyday users—even those well trained in FEA—still face everyday problems when trying to analyze designs and behaviors as part of their jobs, said Rick James, vice president of consulting at the SimuTech Group of Rochester, N.Y.
One problem is that while many FEA applications are integrated with CAD systems today, many of these calculate what James called “the simple stuff”; that is, they perform relatively basic stress and fatigue analyses. Users will need to purchase a third-party analysis application to run advanced fatigue analysis or other types of analyses on top of the simple stuff, he said.
“Most FEA desktop software doesn’t do the niche stuff like crack-growth propagation, where you’re watching a crack form and move on the screen,” James said.
And advanced FEA add-ons require that users have much more information to hand.
According to James, “This advanced fatigue stuff asks for this load history and that load history and then this residual stress from welding.”
Thus, the everyday CAD users will likely need advanced training to best use advanced packages. Training costs and software costs can quickly add up. According to James, extra analysis software on top of the already existing FEA application can run companies anywhere from $30,000 to $60,000 depending on the package, the number of packages needed, and user needs.
But the companies that really need advanced FEA capabilities simply can’t get by with everyday FEA software alone, he said.
But the good news is that for many uses the everyday FEA software of the type integrated with CAD systems has advanced enough to be of great help. In fact, according to Adeeb, the software is very user friendly and— when properly programmed by the user—adept at analyzing most FEA engineering problems.
“For certain applications, like analyzing engineering structures that behave according to theories developed one hundred years ago, FEA software doesn’t need advancing,” he said.
But the story differs when high-end FEA packages are used for applications not strictly related to engineering, such as biomedical problems, he said. The human body, after all, is nonlinear in behavior. So not only is defining the complex problems related to the body a challenge for a researcher, so is determining how to call upon FEA software to best solve them, Adeeb said.
For example, as part of his research, Adeeb needed to create and analyze a model of a human bone as it grew. For this, he used Abaqus, software marketed by Dassault Systèmes of Paris, a powerful, high-end package used to solve complex physical problems.
Software for complex simulations isn’t plug and play, Adeeb said. The software programs meant to model complex or unusual problems are built to allow their users to configure the software—to a certain degree—to their own unique needs.
“I can do the analysis, but it takes me a lot of trying to fool the software and coming up with workarounds; it’s not something I can directly model, and it takes' me a long time to try to model something like that,” he said.
Researchers can be assured the vendors of these customizable, high-end systems like Abaqus and Ansys of Canonsburg, Pa., will be stepping up with software to suit specialized needs in the future. But for new and specialized applications like biomedical software, development takes time, James said.
“But FEA software has proven to be very lucrative so it’s worth it for these guys to work on development,” he added.
Still, whether researchers and engineers call upon FEA software to solve complex problems or to analyze fairly straightforward structures as they design, they’ll need to bring their own judgment to the problem at hand, James said.
“FEA is never going to be the ultimate decision-making tool, nor should it be,” he said. “It’s still used for mathematical equations and modeling physics, and you still have to use engineering judgment when calling out a result you don’t think is true, even if your software can do amazing feats.” .
But the mix of engineering know-how, engineering judgment, and amazing feats of software make for analysis and design never dreamed possible before the age of FEA.
In 1998, upon acceptance of the Timoshenko Medal from ASME, Zienkiewicz speculated about the future of FEA by referring to Charles Duell, commissioner of the U.S. Office of Patents in 1899, who famously speculated that everything that could be invented had already been invented.
For many uses, the everyday FEA software integrated with CAD systems is user friendly and adept at analyzing most FEA engineering problems, when properly programmed by the user.
“I do not share this pessimistic view, and I think we shall see many exciting developments in the coming years,” Zienkiewicz said. “It is evident that both applied mechanicians and mathematicians will continue to contribute to the numerical analysis field.”
He said that more than a decade ago, and it still stands.