As engineering software has evolved into comprehensive packages, the root function seems to be "solid modeling." That is, before any kind of development can be done, the first item of business is to get a numerical 3-D model of the object -- whether a bracket or a complete chassis -- into the computer. Once that is done, many analysis operations can be performed on it. FEM can be used to determine its strength, once boundary conditions are defined, such as space and geometry limitations, material properties, and all load inputs. In fact, there are even automatic optimization routines which can identify weak areas, reconfigure the design, and rerun the analysis, the same as an engineer would. If airflow is involved, say it's an intake manifold, CFD may be available to study different flow path designs. If it's a moving mechanism such as steering components, a combination of parts may be joined and then animated, to see what interferences may exist. If high temperatures are involved, as in header pipes, a thermal analysis can show how that heat is transferred and dissipated. Then, as the design is finalized, cumulative tolerance checks can be run automatically before having components fabricated. The final digital model can then be sent directly to a CNC machine such as an automatic mill or lathe -- or even the latest rapid prototyping methods of stereolithographic production, or the laser-generation of models layer-by-layer out of fluid materials.
There is nothing magical about the mathematics; it is just a matter of degree. Even without a computer, a good structural engineer can estimate the location of the worst stresses and easily calculate the worst loads. From there he can work down through less and less critical areas. But a computer can just as easily go to extremes of refinement, breaking a structure into hundreds of thousands of "elements," as shown in the computer-generated drawing of Fig 53. In this way it is possible to optimize the strength-to-weight ratio so that no area is either unnecessarily weak or unnecessarily heavy. The process is independent of the type of material or the type of structure. It could be used on a balsa monocoque or a spaghetti-tube frame. With that introduction, let's consider the actual procedure, using the parent program "NASTRAN" (NASA Structural Analysis) as an example.
First you have to define the necessary shape, and certain locating points such as the suspension and engine mounts. You have to provide space for the driver and fuel and a hundred other bits. This is as far as most people get in their consideration of chassis design. But for computer analysis, all of this information must be represented by numbers, and not drawings. Every point must be defined by three-dimensional co-ordinates, which in some cases means locating thousands of three-digit dimensions.
For each point, the computer needs to know what material properties apply. In the case of a sheet metal monocoque, this is relatively simple, because the material will have uniform thickness and symmetrical properties. With fiberglass or graphite composites, however, both the thickness and the direction of maximum stiffness are infinitely variable (as discussed in chapter 10). This is a structural advantage but an analytical nightmare.
The most comprehensive FEA programs can run any conceivable stress test on the structure: static or dynamic, linear or non-linear, impact or fatigue. Dynamic tests are primarily for vibration frequency analysis; non-linear tests are for investigation of structures as they yield; fatigue is not usually a problem in the short life of a race car; and thermal or aerodynamic studies don't apply to the tub. So for our purposes (race cars) the simplest test is adequate--and expensive enough. A simple static torsion test is not only the most appropriate for a race car, but it is the easiest to verify in the finished product--and to compare to previous empirical designs.
At some point it's necessary to make an educated guess as to what loads will be encountered and what stiffness is required. It is commonly assumed that a chassis which is torsionally stiff enough will be adequate in beaming. It also used to be assumed that 3,000 foot-pounds per degree of stiffness provided a rigid enough chassis for the suspension springs and anti-roll bars to balance the handling. With the incredible aerodynamic loads now seen, it's hard to say what is adequate, but the best Formula One cars are probably over 40,000 foot-pounds per degree. The scientific way to determine the loads would be to instrument a car for vertical, longitudinal, and lateral g loads, and get a recording of the conditions at every track in the series. This would provide not only stiffness requirements, but peak bump loads and bump amplitude/frequency plots for fatigue analysis.
Ideally, a designer could keep modifying the structure, changing the location and thickness of panels until all stresses were equal at the limit. This would give the ultimate optimum strength-to-weight ratio. However, this assumes that the real world loading conditions are accurately known, and that there is only one worst case. In fact, there are unanticipated situations which must be allowed for, like an off-course excursion, or combinations of load such as hitting the brakes and a bump at the same time. When you get right down to it, it's hard to even make a subjective decision: What kind of safety factor does one select? 1.5?...2.5?...ten? But given a complete historical survey of what the vehicle should encounter, and leaving the consequences of deviation up to the driver, continual redesign and rerunning is certainly better than experienced guessing.
The actual costs of running a finite element analysis are a little hard to predict, given all the unknowns and the potential complexity. Most teams probably don't even know what it costs to analyze their cars, but we can use one early model as an extreme example for estimation of a professional analysis. The structure was broken down into about 800 elements. Based on computer time and man-hour costs, just the input or setup time would take about two weeks and cost roughly $3,000. From then on, each computer run on each configuration change might be about $500, the number of runs depending on the brilliance of the first layout and the final refinement desired. So the total computer development time could have cost less than $10,000. The weight saving due to graphite fibers was said to be 35% less than an aluminum tub, but how much can be credited to the computer is unknown. However, if we estimate the tub to be around 50 pounds, and the finite element analysis reduced the weight by 10%, that is 5 pounds at $2,000 per pound--which is certainly within reason.
On the other hand, assuming you already have a decent PC, a slightly less ambitious analysis can be done in your spare time for a fraction of the cost. Simplified versions of NASTRAN currently sell for a few thousand dollars, and with them, you can make as many runs as your spare time and deadlines allow. Even if you had to buy a more powerful PC, the extra few grand or so would be easily amortized over a lot of other applications.
The cost/benefit tradeoff is always hard to pin down. If you expect to be doing structural optimization on a lot of race cars, then the equipment and experience will definitely pay off in the long run. But for a few applications, the best value might be hiring out the analysis, or merely making a few simplified calculations on a pocket computer. Or, as is usually the case, relying on intuition.
In any case, the process is not bulletproof. Those who have done FEA a few times recommend experienced specialists who can save a lot of time, money, and mistakes. While the designer can't keep up with the latest in computer technology, neither can the programmer be aware of all the race car design requirements. It takes a combination of talents with expertise in many areas to make it all come together. But with the success of existing examples, the availability of computers, and the weight and safety advantages of finite element analysis, we are going to be seeing a lot more efficient chassis on the track -- whether we know it or not.
McLaren had asked Hercules Aerospace of Salt Lake City, one of the largest graphite fiber producers in America, to produce the first one-piece true monocoque structures ever seen in racing. So naturally when Hercules took the job, they decided to use the standard aerospace technique of finite element analysis to optimize the design. Eventually Hercules admitted that the original hand-calculated design by McLaren's John Barnard was intuitively "pretty close," but this was still a dramatic first application.
At the time of this writing, FEA had even reached NASCAR, the last bastion of intuitive race car design. Factory assisted efforts from Chevrolet and Ford were being quietly used to improve the torsional strength-to-weight ratio of Winston Cup cars -- but of course that information is never generally available to privateer racers or constructors. However, a strong racing-oriented engineering program under Harry Law at Clemson University produced a number of valuable publicly available SAE papers (See numbers 983051, -53, and -54), that demonstrated what FEA could contribute. Graduate level students used it, with carefully measured dimensions from some familiar chassis, to establish that the baseline torsional rigidity was about 10,000 foot-pounds per degree. They then ran dozens of cases in which they added or strengthened structure to see what the relative effects were.
The analysis easily showed that the weakest areas were at the cowl and the un-triangulated engine bay. Eventually, repeated computer runs brought the rigidity up to about 23,000 foot-pounds per degree, a number that was felt adequate in maintaining the desired suspension dynamics. Being realistic, they also analyzed the engineering tradeoffs in terms of added weight and CG height. The final configuration was plus 40 pounds and a 1/2-inch higher CG, numbers which could be related to laptimes through the use of a racetrack simulation. However, it appears these handicaps could have been minimized by utilizing just the most cost-effective structural modifications. Finally, to verify the FEA, other students constructed a precise torsional test rig -- also to resolve the precision and repeatability of testing. After running a number of different chassis, their figures indicated that some common chassis were less than 60 percent as stiff as the original baseline chassis in this study.
Cost and compatibility with your existing hardware may be of first importance to the non-professional non-commercial user, although an engineering professor once told me the most effective strategy for a department of five or more engineers would be to fire one engineer and buy the best software package. At the time of this writing, apparently the most popular and most powerful package was I-DEAS (Integrated Design Engineering Analysis Software), which with all added modules could be in the $50,000 range. Other packages that should be investigated include CATIA (more design and surfaces oriented), Unigraphics (more manufacturing oriented), ProEngineer, and Autocad. The FEA techniques they use may be based on NASTRAN, ANSYS, ABAQUS (primarily non-linear), and STRUDL (civil structures). Although an adequate full-bore program could be in the $5-10,000 range, simplistic training programs are as little as a few hundred. A good mid-range compromise is currently the MacNeal-Schwendler version of NASTRAN, which runs on a PC with enough accessories. This will be adequate for most racers, when selection is based on the following capability considerations:
Types of analysis include statics and dynamics, 2D or 3D, and heat transfer, which is hardly critical in race car structures.
Variety of components that can be modeled includes plates (panels), beams (including tapered beams), and shafts. One small drawback in some scaled-down program is that they only accept point loads. That is, aerodynamic or gravity loads cannot be distributed over a surface, but must be reduced to point loads at nodes or analysis intersections.
Graphics capabilities can include input visualization, zoom/rotation/pan of the image, overlaying of the strain-deformed image, and animation of the image in dynamic analysis. Other features not usually available in these lower cost programs are automatic generation of meshes, or panel breakdowns, and automatic input data error checking.
Output variations beyond graphics include transfer capability to larger computers for more detailed analysis -- a strong point for a NASTRAN-compatible program. And of course there may be CNC-compatible output, which is irrelevant unless CNC machinery is available, even on a contract basis.
Ease of use may be a key question for occasional users. Procedures and commands are easily forgotten without interactive input, or automatic prompting. To reduce memory requirements, some packages have minimal prompting. For initial familiarization, a good interactive package might take a few days to learn, while a poor non-interactive program might take few weeks. But then as procedures become familiar, the repetitive prompting isn't there to slow down the process.
The last consideration might be speed and capacity. At worst, a maximum capacity analysis on a PC might take overnight -- which is human downtime anyhow. But that may still allow a structure with thousands of nodes (the original McLaren example was about 600 nodes). It's simply a matter of learning to live with limitations, by first analyzing with a "broad brush" and then focusing in on critical areas with increased element densities.
As problems are simplified to accommodate smaller computers, accuracy of results may begin to suffer somewhat. Considering that real-world race car loads are only approximated anyhow, errors are probably not significant. But this points out that FEA's greater value is in showing relative effects rather than absolute values. That is, it is better to run a computer analysis on a known, existing chassis (perhaps comparing output to real test results), and then make simulated changes in the chassis, such as thinner material sections, to study the change in performance. In other words, what is the predicted tradeoff in reduced weight versus reduced stiffness?
In the near future, expect to be able to lease software just as needed from application service providers, and to be able to run analyses at home via the Internet. Massively parallel processing will soon make analyses a thousand time faster, and a hundred times more efficient. But in the fast-changing world of software, no book can be up to date. The only way to get the latest information on FEA products is from monthlies such as Mechanical Engineering, Machine Design, SAE Journal, and your own specific PC magazine.
pvanvalken@aol.com