13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- Main system: MDO on shroud blade Sub1: structure opt on shroud/blade Sub2: aerodynamics opt on blade 1 2 1 2 0 1 1 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2 2 2 2 2 2 : , , min ( ) ( ) * ( ) . . ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) R R T T T T T find X X Y F X W X W m X m s t J X X X X X X X X Y Y Y Y J X X X X Y Y Y Y η ε ε ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ = + = − − + − − + − − ≤ = − − + − − ≤ 1 2 1 1 1 1 1 1 2 2 2 2 1 1 1 1 1 2 3 4 5 tan : , , min ( )( ) ( )( ) ( )( ) . . 0.01 0 645.5 0 516.4 0 697.0 0 173.0 0 ( ) t t T t t T t t T R tip R shroud R chamfer R blade R con ct R find X X Y J X X X X X X X X Y Y Y Y s t g dx g g g g with m X σ σ σ σ = − − + − − + − − = − ≤ = − ≤ = − ≤ = − ≤ = − ≤ [ ] 2 2 2 2 2 2 2 2 2 2 2 6 7 2 : , min ( )( ) ( )( ) . . 78.5,80.5 1273.5 0 ( ) t t T T R R R find X Y J X X X X Y Y Y Y s t g mf g T with X η ∗ ∗ = − − + − − = ∈ = − ≤ Figure.6 Optimization algorithm structure based on the CO strategy Figure 6 shows the optimization algorithm structure of the blade MDO based on the CO strategy. , 1 7 Ri g i = stands for the approximate function. ( ) Rm X and ( ) R X η respectively represent two sub-system targets. ε is the permissible error of compatible constraint taking 3 10 ε − = . 4.4. Optimization Results Analysis The paper establishes the multiple-precision optimization strategy. Present three kinds of analysis model on turbine blade have embodied in the CO framework by the VCM methods. The figure 7 describes shape changes in the blade root, middle and tip. Table 3 is the numerical response contrast. Under the constraints, the total mass drops 6.68% and the blade efficiency increases 5.55%. Figure.7 Compared shapes before and after optimization at the hub, mid and tip section Table 4 shows the optimization cost of the shrouded blade. "——" represents none in the table. Because the approximate function runs quickly, the cost of the inner loop is not easy to statistics indicated with "......". From the table, major time consumption comes from the DOE, the calling number and the number of the inner loop, total of which is 7163 minutes (518+1665+4980), while the approximation function and updating overall occupies only 38 minutes (7201-7163). It shows that the approximate function could greatly improve the efficiency in optimization process. Because the fluid-solid closely coupled analysis costs very huge, the calling number directly affects the
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