The pilot in the retractable landing gear-equipped airplane reported that he had been flying an instrument flight rules cross-country flight for about 6 continuous hours. He reported that he felt fatigued and anxious to get out of the airplane, so he decided to refuel enroute. He contacted a nearby tower, and, at that time, he was notified of two aircraft in the pattern. He was able to identify only one airplane before he initiated the approach. During the approach about 100ft above ground level, the tower controller informed the pilot that he needed to go around but did not say why. The pilot thought it to be unwise to abort the landing because he did not know the location of the second airplane in the pattern and continued the approach and landing. He reported that he did not accomplish the GUMPS (Gas Undercarriage Mixture Props) checklist because of the distractions, and the airplane touched down with the landing gear retracted. The airplane sustained substantial damage to the lower fuselage longerons and bulkhead. The pilot reported that there were no mechanical malfunctions or failures with the airplane that would have precluded normal operation.