What do you mean by weight distribution? Most of the mass is the rider, and the rider moves.
Bicycle construction is very experimental. Analysing dynamic forces is complex, partly because most of the mass is only loosely coupled to the bike. With most mechanical structures the loads are more predictable, for a bicycle you only have to look at flatland bmx riding to see what a bicycle has to handle. A simple case to think about is the rider leaning into a corner. The forces are not vertical with respect to the bicycle, but at an angle. So you have side loads on the wheels and frame.
The usual approach for commercial bikes is to overengineer and test. Manufacturers of racing bikes sponsor riders partly to have crash test dummies to ride experimental bikes. They keep making them lighter until something breaks, then add a bit back. Or not, they might just choose lighter riders or replace the frames more often.
For homebuilders you can deliberately build light and see what happens (as I did with One Less Ute)
Simulating the loads in software will be complex and I think you'll end up trimming your Monte Carlo parameters to the point where you're not getting a very representative sample (or you're buying a lot of supercomputer time). The extremes that I have done on a rigid diamond frame bike include: dropping ~3m onto a gravel road at ~40kph horizontal speed; riding down a twisty gravel road (~10cm high to low points) at 60kph with 15kg on the front panniers and 30kg on the back; riding 450km of sealed road with 20kg front, 40kg rear, 20kg backpack. I weighed about 80kg when I did those, the bike weighed less than 20kg.
My approach is to assume that the entire weight of the bike + load can be applied to one wheel with the bike anywhere from horizontal to vertical. Then allow for some bouncing. I try to get roughly 60% of the weight on the rear wheel when the ride is seated and there's no extra luggage for normal road use. Load bikes don't obey those guidelines at all.