This question cannot be answered without some acceptance criteria. However stiff you make it there will always be an element of 'bend'. Acceptance criteria are usually provided by a relevant design code based either on deflection and or stress limits. The footprint of the mass is also an issue, is it uni or bi directional bending? Does selfweight need to be considered? What shape ribs? Bulb? Flats? Angles? More info please.
This problem having 2 phase 1) Phase to calculate the plate thickness which can avoid the bending, ie minimum thickness of plate 2) Ones we have minimum plate thickness, then reduce the plate thickness and use the rib for stiffness, Rib in rectangular or square cross section, which welded diagonally or horizontally depends plate material normal steel, to make problem little simple, if the plate is mounting on pillar, pillars are40x40x100 thickness at four corner(normal steel material) and plate welding with pillars, and same mass acting on center. in this case calculating 1) and 2) If you know how to do and if you are missing something , you can assume somethings which required for calculation, And let me know..looking forward your reply
For general rule, if you calculate (FEM) the actual bending of your structure (self mass included as well), you can easily decide if it is wrong or not. Use this formula: Max deflection<L/250 (or200 if you are brave enough, ot it is not really important). Where L=main lenght. The goodness in this method is that you can check it in the real structure. And you can add auxiliary supports, if you need some correction afterwards.