The first picture is in French and I don't know French as a language so I can't say too much about. Please post English worded pictures.
Something in the 2nd picture doesn't look possible to me. The beam has non-zero deflection at the ends yet zero shear force at the ends. Force causes deflection so I don't see how this possible. Non-zero deflection at the ends must be caused by non-zero deflection at the ends.
Anyway, this seems to be the beam discussed in section 11.5 here:
This is an infinite length beam over elastic support over the entire length and a small patch of uniformly distributed load at the center. This case requires an infinite length beam. Then sheare force and deflection could approach zero at the ends. In your picture your beam is rather short compared to the length. You should model a very long beam to approach the theory. Also, beam theory in general requires a beam to be long relative to its cross section dimensions, and for beam delfections to be small compared to its length.
Aso your patch of the area of uniformly distributed load does not span the cross section dimension of your beam.
Are you trying to match the theory by modeling a solid? Or does your image depict a 1D entity geometry with cross section displayed?
And to match the model, you should have an elastic support over the entire length on one side of the beam (bottom of your picture).