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Thin is in: Engineering tool targets plastics, other slender parts

Skeleton-based finite element analysis for thin parts

A thin three-dimensional part (left) and a skeletal representation of it (right) created with Mechanical Engineering Assistant Professor Krishnan Suresh's new technique and software. Suresh's "skeleton-based" finite element analysis promises to let engineers much more quickly and accurately design thin parts ranging from plastic components to those of tiny machines, like microelectromechanical systems (MEMS). (large image)

The world abounds with objects that are thin and lightweight, yet strong, including cell phone cases, car body panels, and aircraft hulls, just to name a few. But engineering these parts isn't as easy as their commonness might suggest, says Mechanical Engineering Assistant Professor Krishnan Suresh.

In fact, objects that are thin relative to their overall size tend to confound established engineering techniques, like standard finite element analysis. The situation has led Suresh, a former industry researcher, to create his own method and software for analyzing the structural, thermal and fluid properties of thin parts.

The technique might one day help engineers much more quickly and accurately design molds for injection-molded plastic parts — an industrial sector with an annual U.S. market value of $180 billion. Poorly designed molds can cause problems like warped and weak plastic, or incomplete filling of the mold cavity. And injection-molded parts are usually thin and complex in shape, making them a perfect match for Suresh's method.

His new “skeleton-based” finite element analysis isn't limited to plastics, however; any part whose longest dimension greatly exceeds its shortest could benefit. This includes the components of tiny machines such as microelectromechanical systems (MEMS) and microfluidic devices.

Krishnan  Suresh

Krishnan Suresh (large image)

“Thin components are everywhere and if anything their applications are increasing,” says Suresh.

Thin parts are so prevalent because when designed right, they often achieve the highest strength to weight ratios. “If you look at nature, natural selection has designed many things to be locally thin,” says Suresh. “A good example is the tortoise shell. The tortoise, although slow, wants to move around as quickly as it can. So the shell must be light, but it's also strong.”

Although materials play a role, “the geometry of thinness, the shell design, is also very important,” he says.

When engineers optimize a design, they start by building a three-dimensional model inside a computer. Then, they use finite element analysis to simulate physical phenomena within the part, such as temperature gradients that develop as molten plastic flows through a mold, or the response of an auto body shell to an impact. But finite element analysis was originally created to analyze regularly shaped objects whose three dimensions match closely in size. As a result, it yields unreliable results when applied to thin components, says Suresh.

To overcome this well-recognized problem, engineers have created a “mid-surface-based” finite element analysis. The technique removes the “thin” dimension by taking a 2-D slice through an object's middle, and uses this as the basis for analysis. The tool works well for very simple solids, such as flat, circular plates.

“But if the part is even slightly more complex, the concept of the mid-surface breaks down. There is no such thing as a single cross-section that unambiguously defines the entire object,” says Suresh. “So, you can use this technique but it requires a lot of manual labor. It's not easily automated because everything is so ill-defined.”

What Suresh has invented is an analysis that rests instead on a mathematically well-defined skeletal representation of a solid. Given the proper algorithm, a computer can readily calculate the skeleton of any object, whether thin, thick, simple, complex, 2-D or 3-D, he says. In 3-D, the skeleton resembles a tight net that covers the part's entire surface. It is this net, or mesh, of finite elements that allows Suresh to calculate the average temperature or stress of specific regions within the part.

By virtue of being fast, highly accurate and easily automated, the new technique combines the best features of its predecessors, says Suresh. He hopes to see it adopted by industry, and to this end has developed software that integrates the technique with existing packages. Suresh has applied for a patent on the technology through the Wisconsin Alumni Research Foundation, the patent and licensing organization for UW-Madison.