This paper highlights the design of finite element analysis (FEA) without the finite element. The analysis can use the same information, the CAD system used to create the geometry in the first place. The geometry as well as the analysis fields-like displacement or temperature all uses the non-uniform rational B-spline mathematical representation. Software makers generally use the NURBS mathematical model to generate curves and surfaces in a digitized image. The framework lets mechanical engineers run quick, what-if scenarios to determine how changing a piece of a subassembly would affect the entire assembly. The full assembly need not be remeshed.


With many of today’s analysis systems, design engineers can essentially analyze as they design. Yet, one step in the modern-day design-analysis process can be done away with to make everything work together even quicker than it does already, according to a Purdue University mechanical engineering professor. He envisions an analysis without the very finite elements that put the “FE” in FEA.

Although many analysis packages claim to let mechanical engineers design and analyze, there’s still a lag between those two processes, said Ganesh Subbarayan, a professor of mechanical engineering at the university in West Lafayette, Ind. Subbarayan said he’s working on software that will merge design and analysis seamlessly by actually doing away with the meshing preprocess that has been the standard way to analyze shapes since the finite element method came into vogue in the mid-1950s.

Most of the current desktop FEA software can now be integrated with computer-aided design software through various means. With those systems, engineers model their design with CAD, then move over to the analysis system (which can often be accessed through the CAD interface) where a preprocessor automatically generates the mesh needed to analyze the piece. In this step, the engineer’s design is overlaid with a mesh that looks a lot like a fishing net but is really a complex system of points—called nodes—that form a grid, or mesh, across a model.

The engineer assigns nodes throughout the model, according to considerations like the anticipated stress levels of a certain area and the detail wanted in the results. The mesh contains the data on material and structural properties that define how the part will react to certain load conditions. If the analysis finds fault with a design, the engineer takes it back to CAD for remodeling. Then it’s time to analyze again. And so on.

On some setups the design and analysis handoff is done so easily that designers don’t really think overly much in terms of the separate steps—now I’m analyzing, now I’m designing. But bigger analysis problems, as for large assemblies, often must be run on standalone FEA software that can take some time to return results—perhaps 24 hours or more. That time lapse certainly calls attention to the analysis step.

With a new analysis system, engineers can change the size of particles like these within a composite material and immediately get analysis results.

More than time is lost when the geometrical shapes that make up an engineering design are laid over with a finite element mesh, Subbarayan maintains.

“Designers generally have a good feel for how to construct complex geometry. They break it into little pieces that they assemble and compose,” Subbarayan said. “That’s how most CAD systems work. Then, analysts throw away all the information used to make this geometry and they start with a mesh. We’ve lost all that design information.

“If we could make analysts use the same procedure used to make the geometry, then redoing the analysis would be much more efficient if the shape needed to be changed,” he said.

The Same Tree

By incorporating the mathematics that power the analysis software with the mathematics that power the CAD software, Subbarayan said he can do away with the finite-element method of analysis altogether. He said that analysis can use the same information the CAD system used to create the geometry in the first place.

Because his system doesn’t rely on a now-vital part of FEA—the finite element mesh—it makes for truly simultaneous design and analysis, Subbarayan said. When you take away preprocessing times, engineers get more design time. Because analysis and design run together inside the same software system, they can be done together with no passing the design back and forth, he said.

“We are trying to speed up this process to make it more efficient by rethinking the way analysis is carried out,” he said. “Instead of waiting until the end of the CAD process to do the analysis, we are trying to unify both the CAD design and analysis so that they are carried out concurrently.”

Subbarayan and a former doctoral student, Xuefeng Zhang, developed their software based on work by another doctoral student, Devendra Natekar. The geometry as well as the analysis fields—like displacement or temperature—all use the non-uniform rational B-spline mathematical representation. Software makers generally use the NURBS mathematical model to generate curves and surfaces in a digitized image, which is why it’s popular with CAD vendors. The Purdue system is powered by a software application Zhang wrote, which Subbarayan calls jNURBS because it uses the Java language.

That common language means that when engineers make changes to their part, they see at the same time on the same monitor how those changes would affect the part’s displacement or temperature.

The Purdue system would speed analysis, Subbarayan said, because engineers wouldn’t have to reanalyze the entire part after every small design change. This is possible because the analysis system maintains the same hierarchical design history—sometimes called the design tree—as does the CAD system. Each step in the design is logged and tallied, much the way your Internet browser maintains an ordered history of the Web sites you’ve visited on a particular day. The analysis then need only tease out from that history the steps that correspond with the piece of the design they want to analyze.

“You’re only analyzing the thing you’ve changed in relation to everything else,” Subbarayan said. “You can make geometric changes and can analyze it without having to reconstruct the geometry.”

Unlike Baking a Cake

To better understand how this type of analysis would work, think about baking a cake. Let’s say you’re healthconscious. You want to figure out if you could use a mild-flavored olive oil instead of regular cooking oil in your cake batter and still have it taste good. You bake the cake with nothing but olive oil, then taste it. Disgusting. You try again—this time with a certain blend of olive and cooking oil. You cook the cake and have another piece. Still not so good. You continue to experiment in that way until you’ve come up with the proper mix of olive and cooking oil that makes the cake edible.

In the same way, with many of today’s software tools the analyst or engineer can isolate potential design flaws only by analyzing a design after it has been completed and subjected to preprocessing. With the Purdue system, you could throw in a little change and immediately get the results. Instead of adding olive oil, though, you might be increasing part thickness around a hole. No need to bake a cake and sit down with a piece of it. If the tweaking isn’t what you need, you can fine-tune it right there and keep doing that until you get it just so. Only then do you make the cake—or, in the case of an engineer, the prototype.

Or, let’s say a material engineer needs to create a 50-particle composite material for use in a microprocessor. Microprocessors—the central processing units in computers—usually include a silicon chip and a copper heat spreader. But the chip and heat spreader can’t be coupled directly because copper and the silicon expand at different rates; coupling them could break the chip.

You want a layer in between them that will give. The composite would make up this layer.

“To design the composite, the materials engineer begins by figuring out how many particles it’ll be made up of, what size they should be, and how densely they should be arranged,” Subbarayan said.

“Typically, you’ll need to distribute particles of different sizes throughout the material to find a tradeoff between viscosity and heat,” he added.

With his system, engineers could change the location or the size of one particle—without modifying the location and size of all the others—and see results as they change that location. Only the particle that changes is modified and analysts can immediately study the interaction of all the particles. They don’t have to remesh the 50-particle composite to determine stiffness.

“Right now, CAD systems have one framework for geometry and materials distribution, and analysis systems have another for behavior,” Subbarayan said. “We’ve provided a mathematical framework that unifies geometry, material distribution, and behavior.”

That framework also lets mechanical engineers run quick, what-if scenarios to determine how changing a piece of a subassembly would affect the entire assembly. The full assembly need not be remeshed. The changes to the subassembly’s design information would ripple through the entire system and return analysis results.


In the same way, the Purdue researchers’ method could shield suppliers’ proprietary design information while still letting the customers test supplier parts virtually to see how they perform. The supplier sends over only the applicable design history needed for the analysis.

In the future, Subbarayan and his fellow researchers would like their software to be able to analyze for the coupled physical phenomena that are often a part of real-life engineering problems. This could make it an invaluable tool for MEMS development. While MEMS actuators need to be analyzed for electrostatic, temperature, and displacement problems all at once, they also contain a variety of different materials, Subbarayan said.

He plans to seek a business partner that will help commercialize the software in the near future.

Not alone without a Net

The Purdue researchers can’t lay claim to the only software method to boast analysis without finite elements. Procision software from Procision Analysis Inc. of Mis-sisauga, Ontario, is a meshless structural analysis software. The analysis package uses a mathematical technique that differs from Subbarayan’s but can calculate accurate analysis results from precise solid models, according to the developer.

Field Magic from Intact Solutions LLC of Madison, Wis., is also a commercial meshfree solver that analyzes problems in heat transfer, electro- and magnetostatics, plate vibration, and plane and thermal-plane stress, says that developer.

But some engineers say that meshless technology may not help them much. Many FEA vendors have integrated their analysis software with the CAD systems these engineers use every day, so analysis is easy and relatively seamless and the analysis time suits these engineers fine.

For instance, one engineer who posted to an online forum discussing the Purdue software wrote: “Nearly all of us have some in-house FEA and we adopt a system where we can move smoothly between the CAD application and the FEA package. All of the better FEA packages have model creation ability embedded anyway. However, CAD packages are better at the CAD side, so everyone tends to draw in the CAD package and import the file into the FEA package.”

Such FEA packages would include NET Works from Noran Engineering Inc. of Westminster, Calif., which integrates its analysis program within the Solid Works CAD system. That vendor’s software application does feature geometry associativity, which means loads, boundary conditions, and meshes are updated interactively whenever changes are made in Solid Works. Engineers need not remesh a part for reanalysis. The system does the work for them.

Cosmosworks from Solid Works of Concord, Mass., is also accessed from that company’s CAD software for design analysis.

Other FEA vendors, whose products generally target the analyst rather than mechanical engineers, feature more general CAD interfaces. These vendors’ products aren’t so tightly coupled. Most CAD designs can be translated to the software for analysis. Such companies include Algor of Pittsburgh and Abaqus Inc. of Providence, R.I.

Subbarayan’s system may represent the march of engineering software toward ever faster and more useful analysis. Stay tuned.