Any process including pen and paper is subject to human error and the same sort of misanalysis in your example. Modeling with FEA isnt infallible but it lets a designer do a far more comprehensive analysis. In the long run that produces more reliable outcomes
FEA is the mathematic process used by just about every automotive designer because it is predictive, accounts for more complex loading, and lets you get prototypes built and "real life" tested faster.
A quick internet search will return many videos showing how to model an automotive suspension using SolidWorks built in modeling engine. I imagine big time OEMs have even better modeling software and design engineers that are experts in applying FEA to their particular area of specialization.
Dan
Many of the bigger engineering companies such as Northrup Grumman use CATiA but not sure what is common in the automotive industries. I'll have to ask my boss what John Deere uses. He was in charge of hundreds of engineers before he left last year.
I'm well aware of what FEA is and how it works. Computational speed is why we have tools such as FEA. I've done calculations by hand to determine the plastic deformation at each node of a part and it's tedious and laborious process. The more nodes the more work. Obviously, with today's processors those calculations can be run millions of times a minute which is ideal for iterative or infinite series such as the Taylor series, Sine and Cosine functions etc. The software can spit out a solution once an acceptable delta (difference between current solution and previous solution) has been reached. Years ago I calculated the deformation of a rubber membrane stretched and sealed over the opening of a square hole. Symmetry helps a lot in those calculations, but I ended up creating a spreadsheet to calculate the deformation at each node for a given pressure and then created a plot showing the deformation. Very little of that was enjoyable with the exception of seeing the predicted shape and then validating the model via experimental process.
My model had nodes on a grid that were spaced 5mm apart, and the solution was limited to the resolution of the grid. Ansys or similar could have nodes every micron if necessary which would increase the accuracy of the predicted deformation. This is where FEA and computers shines.
Like I said, using FEA on a driveshaft on a tractor would be a waste of time and money which could be better invested somewhere else. The maximum stress in a rotating shaft occurs at the outer surface of the shaft. No surprises there so no need to create an elaborate mesh to figure stress profiles.