The pilot reported that during the sixth and final landing of the day, he was aware of another airplane in the landing pattern that disrupted his routine. He did a mental checklist, and thought that the landing gear was down; however, it was not. The airplane subsequently landed with the landing gear retracted, which resulted in substantial damage to the fuselage. The pilot reported no preimpact mechanical malfunctions or failures with the airplane that would have precluded normal operation.