I once spoke to a very well known British (world championship winning!) chassis designer about exactly this. Although this was probably about 10 years ago, I doubt things have changed for the reasons vizard has already pointed out.
My mate, who was also there, was studying engineering at the time and had loads of questions ready along the lines of 'how do you model/analyse...', etc. The replies he got surprised him.
The chassis designer said they didn't even draw the chassis, but did note down tube lengths and angles etc. He simply watched his kart lapping tracks and got feedback from drivers. Then it simply came down to experience and trial and error followed by more testing of prototypes.
Sounds like more of an art than a science to me.
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