Closing a door is non-linear. FE is linear. End of story.
Less pessimistically, there are aspects of the door-closing-quality-sytem that are analysable by a linear approach - primarily the structural properties of both the door and the body. You could also look at the vibration modes of the panels and see what sort of sound they make when the catch strikes, and then apply damping sheet to those modes to get rid of the bad sounding ones.
You'll need to make a lot of assumptions, or get a fair amount of experimental work, to get a handle on this.