What is the structural impact on the wing if no fuel is stored in the wings and just in the fuselage and how to counter possible advantages/disadvantages? Has this topic already been researched?
This has been well-studied, here are the basics.
For the case of fuselage tankage for fuel: The structural loads caused by the weight of the fuel in a fuselage tank must be transmitted between the wings and the fuselage. This means beefing up the wing-to-fuselage attachment points, which is not required if the wings carry the tankage instead. Putting the tankage in the fuselage also means less room for passengers and cargo.
The best place for this fuselage tank would be right at the center of gravity so the CG shift with fuel consumption is minimized- which unfortunately puts the tank right where the passengers sit. And because this places fuel in close proximity to passengers, it creates a risk factor during a crash.
There are more subtleties involved, but these are the primary considerations. I invite the experts here to weigh in with more details.
I'm a vibrations guys (although not specifically wing vibration), so let me add one point to complete niels nielsen's answer.
If the mass of the wings is reduced by removing the fuel, but the stiffness of the wings stays the same, then the natural frequencies of the wing will go up. A higher natural frequency would have an effect on flutter margin (probably makes it better). Dynamic loads on the wing (e.g. fan blade out loads) would also be affected, although it would be hard to predict if these would go up or down. Likely for some components, these loads would go up, but for others they would go down. By components here I am referring to things like the engine mounts, pylon, and pylon to wing connections.
On the other hand, if mass is removed, you could keep the natural frequencies the same by reducing the stiffness a comparable amount. This would save weight and likely cost.
I don't have exact numbers for either case, but it should be an appreciable amount.