By Laura Carrabine

When a tool or technique has won acceptance and begins to approach indispensability, it is easy to overlook its origins, if only because the tool's effectiveness helps its users forget how they ever got the job done without it. (Where would doctors be without first the X-ray and now the MRI?) Talking to those who developed and popularized a tool can give us a sense not only of where the innovation came from, but also of where the technology is headed as it continues to evolve.

Finite element analysis (FEA) has a long legacy that extends as far back as 1915 with the publication by Boris Grigorievich Galerkin (1871-1945) of a method for the approximate integration of differential equations, thereafter known as the Galerkin method. But it took roughly half a century before this important technology began to have a significant effect on the practice of mechanical engineering.

Among the pioneers of FEA to whom we spoke for this article are: Edward L. Wilson, professor emeritus of civil engineering at the University of California at Berkeley and founder of Computers and Structures Inc. (Berkeley); John Swanson, retired founder and chief technologist of Swanson Analysis Systems (later renamed ANSYS Inc., Pittsburgh); Richard MacNeal, founder of and currently consultant for the MacNeal-Schwendler Corp. (Los Angeles); Klaus-JŸrgen Bathe, professor of mechanical engineering at MIT and founder and director of ADINA R&D Inc. (Cambridge, Mass.); Jason Lemon, founder of SDRC (Cincinnati) and currently founder and president of International TechniGroup Inc. (ITI, Cincinnati); K.K. Wang, professor emeritus of mechanical engineering at Cornell University (Ithaca, N.Y.), current director of the Cornell Injection Molding Program (CIMP), and co-founder and chairman of the board of C-MOLD; Richard Miller, founder of Aries and currently an industry consultant; and Michael Bussler, president and CEO of Algor Inc. (Pittsburgh).

The term "finite element" method is thought to have been coined around 1957 by Raymond Clough, then a professor of mechanical engineering at the University of California at Berkeley. Edward L. Wilson, who earned a master's and a doctoral degree under Clough, says the first publication to use the term "finite element" was Clough's "The Finite Element Method in Plane Stress Analysis," which was presented at the Proceedings of the 2nd annual ASCE Conference on Electronic Computation in 1960. The paper was based on early work at the Boeing Co. that used two-dimensional elements to include the skin stiffness in the analysis of wing structures.

"By 1960," Wilson said, "many other groups in the United States and Europe were conducting significant research on matrix analysis of structures in which continuous structures were modeled with discrete elements. However, most researchers used the terminology 'direct stiffness method.' It was not until the application of the finite element method to the solution of heat transfer problems in 1964 that the finite element method was accepted as the most descriptive terminology for the method." Wilson's Structural Analysis Program (SAP) products, first developed at the University of California at Berkeley, are still in use today and are marketed by Computers and Structures Inc.

From 1963-65, Wilson worked as a senior research engineer for Aerojet General Corp. in Sacramento, Calif. "This was an excellent opportunity to apply the finite element method to several different types of complex problems," Wilson said. "One of the first Aerojet problems I solved using my 2-D finite element program was the stress analysis of a cross section of a solid rocket propellant subjected to internal pressure. The first analysis was compared to a photoelastic analysis that had been previously conducted. At the point of maximum stress, the FEA produced a stress approximately 5 percent larger than the photoelastic results. Since a finite element (displacement-based) analysis always produced a lower bound on displacements and stresses, a new photoelastic analysis was conducted. The new experimental results were closer to the computer results; however, due to 3-D effects near the stress concentration, the photoelastic method had inherent errors that were not previously recognized. I then introduced a special mesh generation for rocket propellants in which only the boundary nodes were specified. The internal nodes were iteratively generated by averaging the values of the coordinates of the four adjacent nodes. Within the next two years, the photoelastic group at Aerojet reduced the size of the rocket propellants significantly, and most of the experimental engineers were writing or using FE programs."

While Wilson was working at Aerojet, John Swanson joined Westinghouse Astronuclear Labs in Pittsburgh in 1963. As a staff member of the stress analysis group, Swanson was responsible for stress analysis of the components in NERVA nuclear reactor rockets. He used computer models to predict transient stresses and displacements of the reactor system due to thermal and pressure loads. In the next several years, Swanson continued to develop 3-D analysis, plate bending, nonlinear analysis for plasticity and creep, and transient dynamic analysis, using a finite element heat conduction program that was a result of Wilson's work at Aerojet.

Swanson said, "I recognized that Westinghouse and other companies could save time and money by using an integrated, general-purpose FEA code to do complex calculations that engineers typically did manually. I believed that such a code would perform tedious mathematical tasks, such as those associated with heat transfer."

Westinghouse balked at the idea, and Swanson subsequently left the company in 1969 to establish Swanson Analysis Systems in his home outside Pittsburgh. He developed his flagship product ANSYS using a keypuncher and time-shared U.S. Steel's mainframe. "In those early days," said Swanson, "I paid a very high price for less computer power than many kids now have sitting on their desks." By the end of 1970, the first version of ANSYS was coded, and Westinghouse was Swanson's first customer.

Since then, Swanson has launched one innovation after another. Today, ANSYS software is comprised of a full suite of capabilities, including multiphysics, computational fluid dynamics, electromagnetic, mechanical, LS-DYNA, and pre- and postprocessing capabilities. Wilson, Richard Miller, and others credit Swanson as the most successful distributor of FEA technology. "John not only developed a world-class FEA program, but also devised a novel approach to distributing ANSYS worldwide," said Wilson.

Richard MacNeal founded the MacNeal-Schwendler Corp. in 1963 in Los Angeles. The company's first analysis code was called Sadsan. MacNeal said, "In 1965, we became involved with a NASA procurement project to develop an FE system that resulted in our own version of Nastran. The company's commercial version of Nastran was first offered in 1971."

MacNeal called the years 1955-70 the Finite Element Revolution. "During that time frame," he said, "there was an industry-specific need for better methods to analyze jet engines, spacecraft, and nuclear reactors. The digital computer was the enabling technology for stored programs, floating point arithmetic, higher-order languages, and core memory. The finite element method was the key to enable these requirements."

As one of Wilson's students at the University of California at Berkeley, Klaus-JŸrgen Bathe began developing the ADINA code. "After graduation," said Bathe, "I accepted a teaching position at MIT. However, I continued developing ADINA, FEA software for structural analysis, fluid flow, and fluid/structure interaction." Later, Bathe established ADINA R&D, a company that continues to develop and distribute ADINA.

In 1967, after leaving his teaching position at the University of Cincinnati's mechanical engineering program, Jack Lemon established the Structural Dynamics Research Corp. (SDRC). "I established the company to help solve problems that plagued manufacturers," said Lemon. "At the time, Computervision and Applicon were the software leaders, but they focused their efforts on the 2-D drafting marketplace. Our vision was to integrate design, FEA, testing, and systems to overall product design. We were among the first to integrate 2-D drafting with CAE. This effort prompted the need for solid modeling. This was the impetus behind Geomod, a product that provided capabilities to do FEA more efficiently to increase productivity." Later, while still with SDRC, Lemon's development team introduced Superb FEA; Modal Plus, a modal testing analysis and analysis program; and SuperTAB, the first commercial modeling package that ran on DEC workstations.

As the finite element method became better established, its application areas began to expand. The Cornell Injection Molding Program, which began in 1974 with a grant from the National Science Foundation, used calculations that consisted of both finite element and finite difference methods. According to program director K.K. Wang, "Our early work from 1974 through the early 1980s allowed us to make predictions of polymer flow in a relatively simple cavity such as a disk or a plate. The FEA program we developed was not able to analyze a flow of a polymer in a complex shape, such as a telephone case or TV cabinet. That technology wasn't available until one of my former students, V.W. Wang, made a major technological breakthrough that extended the simulation using FE and finite difference/hybrid computational method to 3-D space. That breakthrough, in the form of his Ph.D. thesis, enabled the technology to become a viable commercial tool. Previously, if users wanted to analyze the filling of a complex part, they had to cut the object into little pieces to approximate the geometry."

K.K. Wang went on to co-found C-MOLD with V.W. Wang (no relation), who remains C-MOLD's president and CEO.

In the early 1980s, Richard Miller established Aries to offer FEA and solid modeling together on a PC. He said, "We wanted to address the age-old problem associated with an FE model being an abstract representation of the real world. Historically, engineers created elements and forced them to conform as closely as possible to a real world object. Using automatic meshing that is combined with solid models, users didn't have to create the abstract model, but the actual model and the computer created the FE model. This approach focused on precision. If an engineer, for instance, had a geometric modeler that only allowed him or her to model cubes, the user could model a sphere if enough cubes were put together. Looking closely at the cube, it appeared as a pretty jagged object because the representation of a sphere was a series of cubes. That's not very good model fidelity. Whereas, if the package offered a spherical element, then users were able to model a sphere exactly. That's high fidelity and that's what we brought to the marketplace."

The MacNeal Schwendler Corp. acquired Aries in 1983. "At the time," Miller said, "both Dick MacNeal and John Swanson realized that they had to broaden their appeal by offering analysts the ability to work with geometry. That's why MacNeal-Schwendler bought Aries. We had expertise in the FE method and geometry."

Algor launched its first general-use FE code for PCs in 1984. Michael Bussler said, "The product allowed users to do preprocessing with graphics, processing for static stress analysis, and view results in a modern postprocessing graphical context. Today, everyone is doing automatic mesh generation in CAD. However, before 1990, the CAD interfacing that we were doing allowed users to create a mesh in AutoCAD, push a button, and the AutoCAD mesh would automatically become a mesh in Algor."

According to Bussler, Algor was the first company to offer an FE program on the IBM PC that went beyond the 640K memory limit. "As a result, users were able to work on much bigger problems," stated Bussler. By 1989, Algor offered a nonlinear calculating capability that performed material nonlinearities and large deformations involving geometric nonlinearity on PCs.

Algor's Accupak/VE, announced in 1997, combines kinematics, rigid/flexible body dynamics, and nonlinear stress analysis in one package. "The ability to do the physics-based virtual prototyping using one system," said Bussler, "is the only rational way to perform motion of assemblies that have parts made up of finite elements. Using Accupak/VE, users model the part, set up the mechanism, and incorporate the real-world variables. There's no need to figure out the forces. It's possible for a nonengineer to set up the model and run it."

Several FEA suppliers are offering analysis products that are integrated with popular CAD programs, but the engineering community has not fully embraced the approach. Analysts are leery of handing over FEA capabilities to less experienced users; some designers and mechanical engineers are hesitant to conduct a finite element analysis. Organizations fret over training, implementation, and related expenses.

MacNeal said, "I believe that the trend toward involving the designer in the analysis will continue—however, not at the rate that some of the FEA vendors would like to see it happen. I think the momentum will build because the process is something that will add more competitiveness to companies using the FEA tools early in the design cycle. I believe it's something very good to have happen, but that it will happen at a slower rate than predicted."

"The issue needs to be initially addressed at the university level," noted Wilson. "As teachers, we have to show students the benefits of integrating FEA in the design cycle. In other words, when we teach elementary mechanical engineering, we need to teach it with design in mind. There is a lack of attention to this issue at the moment. Movement has been made, but not sufficient movement. FEA methods are still fairly difficult to use. Software vendors might claim that it's easy, saying 'Just press a button.' However, 'garbage in, garbage out' still applies."

Wilson said that ideally designers ought to be able to read a CAD drawing into an analysis package to set up the mathematical models for analysis. "Of course, the CAD geometry might be very complex with details that have no bearing on what the user wants to get out of the analysis. What is necessary is that the designer uses tools that allow him to quickly change the CAD geometry to a mathematical model, such as a beam or a shell structure. The meshing and the analysis are done automatically. There must be error messages and help for the designer if certain processes have been done incorrectly. Today, the process has not matured enough to allow that process to happen. More research is necessary. The problem of integrating FEA with CAD has not been solved completely. I think eventually that analysis will become an integral part of design," Wilson said.

Miller is a proponent of providing the FEA tools to designers to help bolster productivity and expertise. He said, "An FEA program allows an engineer to make mistakes at a rapid rate of speed. It doesn't change the fact that the engineer may make mistakes anyway. You have to make sure that the engineer knows the fundamentals and that he or she is schooled in the tools. Today, it's possible for an analyst to sit at the control panel and set the rules that the engineer works under and the parameters for failure, arranging to be notified by the Internet if and when problems arise. In that scenario, the engineer uses the tools, but is supervised by the person who has advanced skills. Software that provides advanced tools to people with certain controls to assure that they get the right answers is a good thing."

The main difference between an analyst and a design engineer, according to Miller, is that analysts historically have never worked with geometry. "They've only developed the FE model. When you send a design engineer to do an analysis, he generally starts off with geometry; he wants to model the geometry and then will analyze it. The world that the analyst works in is the world of abstraction—nodes and elements. Engineers live in the world of geometry.

"Design engineers are really concerned about usability," continued Miller. "They want something like Quicken [the popular bookkeeping program]—easy to use, friendly interfaces, no hassles, wizards, etc. Analysts want command lines, strings of variables, and customized programming. They are interested in tickling the innards. Both worlds can exist because if software suppliers give the analysts the tools to do the customization and the control, and provide design engineers with the usability on the systems that they want, you have the best of both worlds."

Sounds simple enough. Why hasn't it happened? Miller said, "There's no end to what people can do technically. They can write code all day. However, their applications become increasingly more esoteric. To expand the technology to mass markets means software suppliers should focus on usability."

The other issue is the pain or anxiety that an analyst might feel as a result of implementing FE capabilities for the design engineer. Miller noted, "Most CEOs don't understand the technology. Fear, uncertainty, and doubt loom. Threatened analysts fan the fires and the boss caves in to their demands. Those CEOs aren't willing to take chances."

MacNeal said, "I see the future of FEA as being a process of continuing to make progress on automation and its integration with CAD. For example, meshing is a very important part of FEA. It's automated, but it's not rugged. A lot of work needs to be done in this area. The integration from CAD to meshing to analysis is not really available. The link back—where you can automatically take results from an analysis and download them to CAD so a designer can see the effects of FEA and determine what changes need to be made to the design—has a long way to go."

Fierce global competition is forcing manufacturers to do business more efficiently, and the technology they use must help them. MacNeal said, "A huge improvement in CAD with the introduction of parametric, feature-based solid modeling is a factor. Designers can make changes to CAD models rapidly, and analyze and optimize the changes at the same rate. Today, it's possible to design and optimize a structural component or a whole structure on the computer. Software developers need to make structural analysis more relevant to the design. As developers, we should integrate the CAD model that the designer builds so that by pressing a button, the designer will obtain the analysis results automatically."

There will always be the need for high-end analysis and analysts, MacNeal said. Automation of the process helps the analyst be more effective. "He or she can work faster and do more work on larger models."

Bussler noted, "Most engineers react in fright to the growing trend of increasingly more nontechnical people using virtual prototyping technology. Everything is becoming virtual. Why not engineering? In medicine today, doctors have the ability to perform helpful simulations without knowing anything about classical engineering. They can obtain the results or predictions they need. Previously, scientists would have to involve an outside consulting firm to do the work. Surgeons and other health professionals can't wait around. They need the data now."

"Of course," said Bathe, "we must still teach students how to use and develop finite methods. However, new curriculums must be developed. Currently at MIT, we are in the tedious process of developing new undergraduate materials. A whole new set of textbooks is being written for the mechanical engineering undergraduate courses. There is still a very pervasive demand among university professors to 'publish or perish.' The underlying trend is that if you want to do research, you had better do it in an area in which you can publish a paper quickly. In the real world, however, some tough problems cannot be solved quickly. Therefore, issues like these won't lead to immediate publication so the impetus to pursue the problem is lost."

Bathe wants to continue doing research to push the state of the art of the technology for industry to solve its problems. "There are many areas to do research," he noted. "You have to be able to identify them, and the only way to do that is to be close to the needs of industry."


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