The pilot was conducting a solo navigation exercise, which involved an enroute landing. Turbulence was encountered during the latter stages of the landing approach and a heavy touchdown occurred. The aircraft bounced and again touched down heavily before the pilot was able to regain control of the landing. After taxying to the parking area, the pilot discovered damage to the nosegear leg and adjacent structure. Relatively strong and gusty wind conditions existed at the time of the accident. Sink had been encountered on short final approach and the pilot had been unable to prevent a heavy touchdown.