The fir-tree root and rim of a turbine blade was optimized by the three-dimensional contact finite element method. A single blade model was adopted to optimize seven characteristic geometrical variables of the fir-tree root and rim by zero-order algorithm and first-order algorithm

intelligence optimization algorithm and pattern search algorithm. A multi-variable model with three blades and their rim which was considered to represent a more true working condition of turbine blades was established

and the structure of the blade root and rim was optimized by pattern search algorithm. The results show that pattern search algorithm is the best algorithm to solve this optimization problem in consideration of the accuracy and computation time according to the results of a single blade model optimization. The optimum structure which leads to significant decrease in the maximum equivalent stress of the blade root and rim can be obtained by using the model with three blades and their rim. Compared with the original design

the position of the maximum equivalent stress of the blade root and rim changes slightly and the maximum equivalent stress of the blade root and rim decreases by 11.96% and 21.63%

respectively.