The pilot reported that while on a right downwind to runway 32 he accomplished the before landing checklist from memory; however, "I forgot to say 'three green'." The pilot said that he touched down about one-third of the way down the runway with the landing gear retracted and came to rest in an upright position on the runway at about the mid-field point. When asked if he had heard the gear warning horn prior to touching down, the pilot stated that he did not, as he had his headset on. An airframe and power plant mechanic reported that the airplane had sustained substantial damage to the lower fuselage. The pilot reported that no anomalies existed with the airplane prior to or during the flight.