I don't quite know how you want to apply the function.
There is a cylindrical surface that has dents. Where are the dents?
You say the cylindrical surface has six different faces with different axes. How are the axes different? The faces look like they are all concentric.
You can apply a load as a function of a coordinate dimension. Create a coordinate frame so that zero is at the center of the function. Probably best to split the face so that the face is only 2 mm wide.
What is the physical mechanism that creates the load?