When arriving after dark at a major airport, I usually go to the national departure terminal and find the quietest, most hidden corner, and sleep on the floor there. There are usually less people around departure terminals...

Keep your flight tickets with you just in case security checks you out, but being in the departure terminal gives the impression that you got to the airport the evening before to catch an early flight

You've got your sleeping bag with you, I presume, so it can be a good night's sleep (and free), just bring some extra food for the evening and breakfast...

sorry if this wasn't the answer you were looking for...