Let's say I'm designing a table surface which has to be stiff, rigid, but at the same time, not too heavy. It is rectangular in shape and ratio of length:width is quite large. It is only supported on both ends of its length. If I use a 50 mm slab of gray cast iron for the surface of the table, during maximum loading the table will bend and the Z-axis displacement at the center would be 0.04 mm, which is not acceptable. The allowable value is 0.005 mm. So I have to find way to increase the stiffness and reduce this Z-axis displacement. Problem is, even with 50 mm steel slab, the maximum weight criterion is already exceeded. Increasing material thickness is not an option, on the contrary I have to reduce the weight of this structure so it can stay within the allowable range.

What if instead a simple flat 50 mm slab I make it like 20 mm slab with extra stiffener profile on its underside? Like honeycomb pattern, or any other stiffener configuration. which is possible because it's a cast iron anyway, just have to create the mould.. by doing that I could reduce the weight by almost 40kg

The question is: Is it theoretically possible? 50 mm slab gives 0.04 mm bending displacement, now I want to make it like 20 mm slab to reduce weight, but with intricate stiffener pattern underside and I'm hoping for it to reduce the displacement significantly at the same time. Am I wasting my time?

EDIT: My mistake, the requirement was not 0.005 mm but 0.005 in (0.127 mm). However, this +- 0.127 mm figure is basically the machining tolerance of the workpiece that will be made on top of this table, so I guess the tolerance of table itself should be much lower than that, I don't know the exact number yet but it just won't go as low as 0.005 mm that's probably too extreme. I'm still in the early stage of the design so a lot of design requirements is still open to revision..