Speedy iterations for speedier cars

Based in Alfta, Sweden, Leanders Brothers Racing is a team that won the 2006 FIA European Drag Racing Championship, and is the current grand champion. Leanders uses a custom clutch unit that provides enhanced heat dissipation to make the clutch more durable. The 10-in. unit has three discs and no bolted facings, which is what improves heat dissipation during races and makes maintenance easier. "Our clutch is a result of experimentation with different designs," says Jorgen Leanders, the team's chief engineer. "Software helped me capture the best design through trial and error." Leanders uses software from IronCAD LLC, Atlanta. Changes are possible even far into the design process. In fact, Leanders is currently developing an 11-in. clutch (with and without a ring gear) that will be used to transfer torque from the starter motor pinion to the flywheel. Adds Cary O'Connor of IronCAD, "Parametric capabilities allow constraint-driven variations of the clutch design, or changes can be made that do not abide by constraints."

Under the hood: Math

There are a myriad of algorithms utilized in simulation software. For solving one-parameter nonlinear systems, for example, some software might use the iterative Brent method; it usually works better than simple linear interpolation, because usually, nonlinear functions are not particularly smooth.

For multidimensional optimization, where results depend on several parameters, the Nelder-Mead method is a classic. Here, the minimum is approached by steps, one coordinate at a time. A function's behavior is extrapolated to generate new test positions. Each reiteration, the algorithm replaces one test point with a new one — replacing the worst with one reflected through remaining points — until the software reaches a tipping point, and shrinks the simplex towards the best.

But turning it up a notch is modeling vibration — one of the most computationally demanding tasks in analysis. Algorithms abound: Rayleigh quotient iteration, Jacobi-Davidson, Davidson, LOBPCG, and subspace iteration. One new software based on eigensolvers combines the memory savings of iterative solvers with the robustness of Lanczos. "Our PCG Lanczos eigensolver determines natural frequencies and mode shapes using less computational power, often in less time," adds Jeff Beisheim, senior development engineer, ANSYS Inc., Canonsburg, Pa.

One command is its level of difficulty, which fixes convergence problems that typically occur when elements are oddly shaped. Higher levels replace the PCG with a Sparselike direct solver, so the program behaves more like a Block Lanczos.

FEA for the masses

Even 50 years ago, finite element analysis existed, but was used only by those bold enough to develop an FEA system themselves. There was no need for an easy user interface or quality results presentation, because the pioneers of FEA were highly trained specialists, often working at universities, with detailed understanding of mathematics and programming. Platforms were mainframes or UNIX workstations.

Fast forward: When computers spread in industry, PCs became powerful enough to handle the huge processing job of meshes and matrixes for systems of equations so essential to realistic models. "FEA programs are now more polished, but can still require deeper understanding," says Podnos.