How to apply the bending effect to objects that are already beveled I'm going to make a shape that looks like speed bumps. Make sure that the edges of the object are rounded as shown in the following picture:


However, in order to bend an object using Simple deform, the object must be subdivided, which does not apply to the internal side, as shown in the following picture:


Is there a good way to bend these objects without loss of volume and corner vertex roundness?

blender 2.80, Used Solidify Modifier.
Edit: Ok so I screwed my answer because I've imported your object as an .obj into 2.79, so it has applied the modifier, but my answer will help to fix the problem with the face.

You've made a mistake with your object. Actually you have a series of parallel edges made of a series of vertices and that are not filled with faces, and on the bottom you have a big face.



As I suppose it's not what you want, select this face and delete it (X (Delete) > Only Faces). You now have your edges.



Make sure you have your LoopTools addon activated, select all and RMB (in 2.8) or W (in 2.7) > LoopTools > Loft, it will fill the whole thing with faces.




Now you have a shape that is already bent, so I'm not sure what you're trying to do. Also I think you might get rid of some edge loops but again, it depends on your final purpose...