Wood to Metal

In what direction?

<...aluminium...> doesn't have a "grain". Woods are stronger in one particular direction and weaker in others.

It is possible to split <...14mm thick Beech...> along the grain with a sharp blow and significantly more effort will be needed to do that with <...aluminium...>, because it is more likely to bend than split.

This is akin to comparing apples with raspberries; they are both fruit and they have different properties.

Load will be downwards. The Shelf is supported on all edges by a metal frame 40mm wide size of shelf about 450mm x 500mm with a hole cut out in the middle about 150mm x 200mm.
Shelf will be bolted down to the frame.
My estimate is a 4-5 mm thick plate will be enough.

It depends on what the <...shelf...> is supporting, and how heavy it is. It could be that <...14mm...Beech...> is overkill, for example.

<...Beech...> is not usually available in widths of <...450mm...500mm...> and it is possible that, to reach this width, several pieces have been laminated together with glue, in which case the <...strength...> of the assembly has to take this feature into account.

Beech is not a "durable wood" and is not suited to being left outdoors without substantial surface treatment; paint and marine varnish being examples. It is not suited to continuous immersion in water. Its light colour makes it suitable for small-scale furniture manufacture and can often be found facing plywood in large sheet form. If either immersion or outdoors are features of this <...shelf...> then <...aluminium...> might be a better alternative; if there is a furniture character to the <...shelf...> then <...Beech...> might be a better selection.

If the <...metal frame...> is made of something other than <...aluminium...> then the possibility of galvanic corrosion needs to be taken into account in both the <...strength...> and the appearance where dissimilar metals come into contact, particularly is there is an electrically-conducting fluid nearby.

Is there some overthinking going on (which occurs in Engineering circles on occasions)?

Why do you want aluminum?

Because of Weight, don't want steel. Is only used in a dry dust free position will be carrying a big chunk of electronics in a Steel case weight probably aroung 20 kgs.
Also the wood has to be treated with Fire-retardent materials and then sealed against Dust and Moisture.
Hole in the middle is to let air circulate in the Cabinet.
Frame is Aluminium Profile, Bolts are Stainless steel ofr gavanised / Cromated, so no galvanich action to consider.

The frame and the <...aluminium...shelf...> will therefore require equipotential bonding to local earth/ground, under many applicable local electrical standards, to obviate the risk of electric shock from the <...big chunk of electronics in a Steel case...>.

Stiffness is proportional to the cube of the thickness.

Can you add support beams under the shelf?

One might try <...4-5 mm thick plate...> experimentally, and go from there.

Doubling-up the <...plate...> would appear to be an option, given that the <...Beech...> being replaced is <...14mm...thick...>. Adding bracing/stiffening bars to the underside of the <...plate...> would appear to be another, as indicated in #6⇑.

It seems to depend largely upon what materials are either available or to hand, and unlikely to yield to calculation beforehand.

5mm <...aluminium...plate...500mm...> x 500mm is available here for £36GBP plus taxes and shipping.

Do get back to this forum with details of the preferred solution after it has been tried.

I would suggest 4mm aluminium propeller or floor plate would be adequate as the making of the plates increases the stiffness. Where the hole is to be made cut the plate slightly smaller and fold the excess into an angle, even 12mm will make the hole surround more rigid. The plate is not that hard to bend if a simple folder is made from angle iron bolted together with a long handle. Remember to allow for the thickness of the metal if the insert is to fit neatly. Corner brackets can be attached for added strength.

I have used 6mm for a washdown bench but that would be overkill for your requirements as the washdown bench was made to hold a 300Kg antique diesel engine for cleaning before stripping down.

My gut says 5mm ( I haven't asked my brain).
TBF there are a variety of grades of Ali'
Del