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I want to try to minimise weight and cost of the screen by optimising the thickness of the board and the size of the stiffening aluminium. A board 12 mm thick, for example, won't need as much stiffening as a 6 mm board, but it would be twice the weight.

Regarding the aluminium, I can obtain three types: L-shape, U-shape, and box-shape in various thicknesses. There are two variables: T (thickness) and L (length of cross-section). For a given weight of aluminium, how do I optimise the stiffness? Do I use a section which is thin (T = 1.6 mm) but with a large cross-section (L = 40 mm), or a thicker piece (T = 3 mm) with a smaller cross-section (L = 20 mm)?

I have the problem, then, of optimising the board thickness combined with the shape/thickness of the aluminium.

I am hoping there are simple equations that relate stiffness to T and L, given that the aluminium will be fixed to the back of the MDF board. Does anyone know those equations?

Without resorting to equations, what is the likely optimum stiffness combination: 6 mm, 9 mm, or 12 mm board; combined with what cross-section and thickness of aluminium: L, U or box-section?

I don't know if this is of any use, but MDF has a specific gravity of about 0.75; aluminium 0.25.