Couple of points. In any object in general, the most efficient (read weight-wise efficiency) cross section for strength to weight is material at the outermost fiber. That is to say, the strongest objects for their weight will have the bulk of their material at the outermost points of the shape, and the least amount of material everywhere else. In certain instances, such as in pure tension, compression or shear this is no longer true. But the overwhelming majority of the time, objects are subjected to some sort of bending, and most objects are weakest when exposed to that type of loading. So in general, if you make an object strong enough to resist any bending forces, it will handle tension, compression and shear pretty well also.
All of that was a rather long winded way of saying if you want stronger prints, use more (thicker) shells, floors and ceilings, and don't worry about the infill at all. View infill as a way of supporting the shells, floors and ceilings of a model to keep them in place during printing. But after the model is complete, the large majority of the strength will come from the perimeters.
This is true in real life as well as in 3D printing. For example, a pipe is almost as strong as a solid rod of the same diameter in bending, but much lighter. And a pipe can be much longer than a solid rod and not bend a lot under it's own weight. So when making 3d prints make them more like a pipe, than a solid rod. They will be stronger and lighter in general. Again there may be some exceptions to this rule of thumb depending on how a part might be used. But in general this is the way to go, to get maximum strength while minimizing weight.