13th International Conference on Fracture June 16–21, 2013, Beijing, China -10- efficiency. The time consumption from the high precise analysis is about 4980 minutes, accounting for nearly 70% of the total time cost. The method pays some cost. However for accurate turbine blade design, the high precise numerical method is indispensable on the optimization. Considering the efficiency, the paper calculates the correction factor to correct the approximation function so that the optimal value could have the high precision and high feasibility. Table.3 Result before and after optimization on shrouded blade 1 2 { , } Y Y Y = Constraints Initial value Optimal value Effect Strength constraints ( 1Y) xtip d /MPa 0.0035 0.00295 -15.71% shroud σ /MPa 435.024 450.3 3.51% chamfer σ /MPa 270.125 295.364 9.25% blade σ /MPa 593.141 575.364 -3.00% contact σ /MPa 80.1019 105.673 +31.92% Aerodynamics constraints ( 2Y ) fm / 1 . kg s− 107.363 106.825 -0.50% T/K 1234.86 1187.75 -1.3% Object Initial value Optimal value Effect Strength object ( ) m X /g 203.27 189.7 -6.68% Aerodynamics object ( ) Xη 0.874964 0.92353 5.55% Weight object ( ) F X 1.100 1.0379 -5.65% Table.4 Cost of multiple precision MDO strategy on turbine Discipline Analysis type Model accuracy DOE number Calling number Cycling number Cost （min） Strength Strength analysis medium 136 8 —— 518 Approximation low —— —— 9528 …… Aerodynamics Aerodynamics analysis medium 28 8 —— 1665 Approximation low —— —— 6864 …… Couple closely coupled analysis high —— 9 —— 4980 —— Total cost 7201 0 20 40 60 80 100 0 200 400 600 800 1000 1200 1400 1 2 4 6 8 1 1 1 1 1 2 2 2 2 2 3 3 3 3 J value run counter J1 J2 Figure.8 Convergence curve of the Compatibility constraints 1 2 , J J ∗ ∗ on the system layer The compatibility constraint is an important index measuring convergence in the CO strategy. Fig.8 shows the convergence curve of the compatibility constraint 1 2 , J J ∗ ∗ during the system layer. J1 represents 1J ∗ and J2 represents 2J ∗ . Because the value has huge difference, two kinds of longitudinal axis are adopted. The eight convergence phases show that the whole process constructs and updates 8 times of the approximate function. Because the 1 i + th optimization starts with the
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