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Your customer is an pig-head!
Hi John, the "formula" for a finite element analysis is too complex to answer in a general response. My suggestion is that you show your client the validity of the results by doing some traditional calculations (Roark's Formulas for Stress & Strain is a good source for these.) and repeat these calculations in COSMOS. When he sees that the answers match (they should...if they don't, check your model set-up or calculations), he should be more inclined to believe the results on the more complext model. There are also a couple of White Papers on the SolidWorks website that provide some background to FEA theory without getting too deep into the math.
Try this and let me know if you need anything else...