On July 17, 2015, about 1545 central daylight time, a Cessna 172RG airplane, N6511V, was substantially damaged when it landed gear up at the Anoka County-Blaine Airport (KANE), Minneapolis, Minnesota. The flight instructor and the commercial pilot receiving instruction were not injured. The airplane was registered to Kilo Delta LLC and operated by a private individual under the provisions of 14 Code of Federal Regulations Part 91 as an instructional flight. The flight originated from KANA about 1500.According to the pilot after conducting a landing at another airport, they taxied and departed. On departure, when the commercial pilot retracted the landing gear, they heard a loud "clang" sound from the vicinity of the left main landing gear. They lowered the landing gear and were unable to get the left main landing gear to extend. Using the normal and emergency extension procedures, they were still unable to get the left main landing gear to extend. They decided to land gear up at KANE. An examination of the airplane found damage to the bulkhead and a fractured left landing gear actuator. Numerous attempts to obtain the broken actuator from the operator were unsuccessful and a detailed examination of the actuator was not possible.