'Bending' a model

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Hello all,
I am trying to create 'bent' models to fit a curved surface, and am only able to achieve this by extruding a curve with the appropriate dimesions in Patch, thickening that extrusion in Model, and then cutting the appropriate detail into that curved solid. Is there an easier way to achieve this? The ideal scenario would be to create the detail required in a flat solid and then 'bend' the end result into the correct curvature.
I understand that this is a little hard to understand from text alone, so i'll try to provide some clarity with images. I have created a model that will illustrate this situation.
Assume that the model in the attached image was flattened: If I want this design, to curve around a given surface, is there a way to 'bend' it to a shape like in the image?
The only way I have found is to use the method above.
Hope this all makes some sense.
Thanks in advance.