Proceedings to divide or redivide a district comprising less than two hundred thousand acres into director divisions, or to redivide the director divisions heretofore established for districts comprising more than two hundred thousand acres, may be initiated by a petition filed with the county commissioners of the county in which the principal office of the district is situated. The petition shall designate the name of the district and pray that it be divided into director divisions, or that existing director divisions be redivided, and shall be signed by at least two-thirds of the directors of the district or in lieu thereof by at least twenty electors of the district. A petition to divide or redivide a district shall not be filed more than once in each five-year period except for redivisions necessitated by reason of a change in the total number of directors of the district.