That partly answers as to the nature of the material. Since it's RTM epoxy it'll likely be 50–60% fibre volume fraction. Since the tow size is mentioned it's quite likely to be woven. If it's plain weave that would make a likely cured ply thickness maybe 0.008"/0.2 mm, maybe a dry fabric areal weight of 200 gsm.
These are very largely guesses. You really need to find this sort of thing out. However, we can estimate the probable sort of properties of the material based on what's commonly available. My own bias is towards aerospace; a marine engineer or sports equipment designer might well have different estimates.
You used metric units so I'll do so too. A woven carbon/epoxy is likely to have a strength of maybe 900 MPa in tension undamaged, maybe 680 MPa in compression undamaged. These will be about 240 MPa for a quasi-isotropic layup (as many ±45° plies as 0/90s) with an open hole present in compression. If compression after impact allowables are needed they will be less.
The likely stiffness (Young's modulus or E) for a woven carbon 0/90 is 55000 MPa. A quasi-isotropic layup will be have an E of maybe 42000 MPa. Shear stiffness of a quasi-isotropic layup is likely to be maybe 15000 MPa.
Emphasis: These are guesses. You need to find out this stuff for your material.
For thicknesses the only numbers you give are a deflection, for an undefined loading direction but a magnitude of 2900 N, of 0.1 mm for a plate 220 mm square.
If the loading is simple tension:
[tt] ___________
/| | ->
/| | ->
/| | -> total load 2900 N.
/| | ->
/|___________| ->
220 mm
[/tt]
Deflection is given by d = strain * 220
Strain is stress/E = stress/42000
Stress = load/A = 2900/(220*t)
So 0.1 <= 2900/(220*t) / 42000 * 220. Thus required t is a minimum of 2900/0.1/42000 * 220/220 = 0.7 mm or maybe 4 plies (perhaps a layup of 0/45/45/0) if the assumptions above are valid.
The direction of the 2900 and whether it is some sort of point load or disributed and whether it puts the plate in tension/compression or shear or bending needs defining.
You are presumably doing this as some sort of home job. If it matters more than simple inconvenience then you need to get a structural/stress engineer involved. A mech eng graduate or someone who has studied engineering at a technical college level should be ok.
While we're usually willing to help out a raw beginner we're not here to size your structure for you or indeed to teach you how to do so in detail. If you want to learn how to size structures for yourself I'm sure someone can advise on a suitable course if you share your location.
