Felix,
> I don't think I am qualified enough to answer in a more mathematical term
> however what I wanted would be something similar to the image below:
step-18 and step-44 (along with a couple of code gallery programs) do
something similar, so I would look there.
You will of course have realized that to answer a question, it is necessary to
formulate it. If you cannot describe in mathematical terms what the force is
and how the force enters the formulation of your problem, how are you going to
know what the weak formulation should be, and how are you going to know
whether the computed solution is correct?