Jacek Marczyk, chief scientist of stochastic simulation for MSC.Software, has a theory when it comes to design: "Failure is an option," he says. "It's part of physics."
When a car crashes into a wall, for example, the automaker may have already accounted for such a failure with multiple crash tests, using FEA software and dummies buckled into the seats. However, what about a car crashing just slightly off-center into a wall? Or what if the car just happens to be made with a material thickness a fraction off the standard for its make and model?
According to Marczyk, FEA does not account for this variability in nature. "Classic methods of CAE software are excessively optimistic," he says. So instead, Marczyk has expanded MSC's traditional CAE software to include MSC.Robust Design, a system based on stochastic simulation that, he claims, more closely mimics reality than FEA.
And he's not the only one leading the charge. ANSYS too has embedded its own version of random testing, which they call probabilistic analysis, into its ANSYS Structural, Mechanical, and Multiphysics software products.
Both MSC.Software and ANSYS, big players in automotive and aerospace design , are pushing their respective versions of random testing software. So it should come as no surprise then that this trend of accounting for uncertainties in analysis is most apparent in the auto and aerospace industries, where the catastrophic potential and liability for failure is greatest.
The distinction between traditional FEA software and stochastic simulation is complex. While traditional FEA consists of optimization to develop the best design under set conditions, stochastic simulation uses random variables of uncertainty to develop the best design for a range of conditions for FEA software, an analysis is a single run of tests and is deterministic; a stochastic simulation is a collection of Monte Carlo-type analyses—several iterations with coarse models," says Marczyk. "A coarse model run many times is better than a less coarse model run fewer times," he says.
Other CAE companies, including ALGOR and SolidWorks, do not incorporate stochastic simulation analysis into their products. "Other than the high-end niche market space, I don't see probabilistic analysis software growing much with mainstream users," says Suchit Jain, vice president of analysis products for Solidworks, in explaining why he does not plan to use stochastic simulation in its COSMOS analysis tools.
Time is money
Intended for more accuracy and significantly reduced product development cost-time profiles, MSC.Robust Design operates as a pre- and post-processor for driving multiple runs of MSC.Nastran finite element models, with similar plans for other MSC.Software products.
MSC.Robust Design works independently of the number of variables. Engineers must determine the degree of uncertainty in the response variables. The software enables them to create tolerances for the design/input variables, and then run a Monte Carlo simulation to achieve a statistical response. The system generates a meta-model (see graph p. 34) that shows both the most likely behavior, as well as the outliers generally not captured by classic CAE—that is, the chance that something could go wrong, which could lead to a lawsuit, warranty, or recall. "The most likely response is not equal to the nominal response," says Marczyk. "This is why systems fail."
Engineers rely on a decision map that uses a give-and-take system of information. When they provide the input variable (stresses, frequency, material thickness, etc.), they get the output variable (information on how it performs under that stress, frequency, material thickness, etc.). In this way, random input variables can be entered to determine the outcome under uncertainty. The strength of the two variables, referred to as the correlation, is ranked in a pie chart (see chart), which engineers can access by clicking on any of the color-coded output variable buttons. Knowing the variable rankings enables engineers to decide where to concentrate their efforts.
Stochastics in use
In 1997, BMW ran the first stochastic crash analysis, consisting of 128 Monte Carlo simulations on a Cray T3E/512 over a weekend; today, that same analysis takes one day on a Linux machine. With the goal of reducing 15 kg of weight without limiting performance, BMW's final stochastic design resulted in a savings of 15.3 kg, requiring an analysis of 90 executions of 200 hours each. In the end, by cutting down on mass, the stochastic design saved BMW $36 million per car over five years. Audi, Toyota, Jaguar, Mercedes, and Nissan are also currently investing in stochastic simulation.
Competing analyses
ANSYS insists that probabilistic analysis is fast becoming a necessary add-on in design testing. "Most companies are heading in this direction because the deterministic approach isn't good enough," says Ravi Kumar, Manager of New Business Development. "The deterministic approach tells you that the design is safe based on the design input. But how do I know my design input is safe? The answers were good enough ten years ago but not anymore."
Whirlpool is one company to reap the benefits of ANSYS' probabilistic analysis. Using ANSYS Mechanical, they were seeking to design a more reliable, but cheaper refrigerator. To cut down on costs, they replaced the copper heat loop tube with steel in the condenser unit. Consequently, however, the two steel tubes could potentially cause a crack in the heat loop tube. With single pass analysis and optimization, the cause of the stresses went undetected. With probabilistic analysis though, Whirlpool noticed that the maximum stress exceeded the limit, and they were able to make the necessary design changes. The result: they ultimately saved $800,000 per year and received fewer maintenance service calls.
The migration from traditional CAE to stochastic simulation may be catching on only with those software companies involved in high-risk applications. Nevertheless, Marczyk says common sense is the driving mantra behind MSC.Robust Design, and it boils down to the bottom line.
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