I can't even use the Kirchhoff thin plate theory by itself anyway because the breaking boards are borderline moderately thick plates not thin ones. For example, a google search for wooden boards to break in karate shows boards with the dimensions: 6" x 12" x 0.5" so the ratio of the thickness...
I was hoping I would only need to calculate for small deflections because at first glance, the calculations for large deflections look a lot more complicated and I haven't been able to understand them yet. They involve non-linear equations that have to solved numerically.
I found this source https://www.academia.edu/36316365/Chapter_13_Flat_Plates which had a more generous definition of a small deflection than the book by Szilard. For this paper, the deflection is less than half of the plate thickness. With a thickness t of 18 mm over a maximum deflection w_max...
Maybe I just need a source with a thicker board so that the deflection decreases as described here:
A thicker wooden breaking board will generally require a greater force to achieve the same amount of deflection as a thinner board, and will also exhibit less deflection under the same force. This...
I was so happy that the deflections are small because that means I don't have to use nonlinear equations but then I looked at the book "Theories and Applications of Plate Analysis" by Rudolph Szilard the capital with the title "Classical Small Deflection Theory of Thin Plates" and one of the...
The problem is that I have a book by Ugural that I attached and he only has the options of simply supported, free, sliding, and clamped/built-in for the boundary conditions of the edges of a plate. He discusses these in Chapter 1.7 that has the title Boundary Conditions. I need a boundary...