Issue 48

B. Chen et alii, Frattura ed Integrità Strutturale, 48 (2019) 385-399; DOI: 10.3221/IGF-ESIS.48.37 392 1 1 2 3 4 5 6 -3 -3 -3 -3 -3 1 1 1 2 1 3 1 4 -3 -3 - 1 5 1 6 1 2 5.272 0.267 0.844 0.958 0.184 0.536 1.131 0.129 2.828 10 6.505 10 4.691 10 4.041 10 3.900 10 3.205 10 1.383 10 1.838 10 X t F F F F F F t F t F t F t F t F t F F F = + +  +  +  +  +  +  −  +    +    +    +    +    +    +    +  3 -4 1 3 1 4 -3 -4 -4 -4 -4 1 5 1 6 2 3 2 4 -3 -4 -3 -4 2 5 2 6 3 4 3 5 3 6 -4 4 5 3.826 10 1.659 10 8.623 10 1.752 10 2.331 10 1.265 10 1.067 10 6.201 10 1.710 10 2.139 10 3.634 10 7.699 F F F F F F F F F F F F F F F F F F F F F F F F   +    −    +    +    +    −    −    +    +    −    +    + -4 -3 -3 2 -3 4 6 5 6 1 2 -3 2 -4 2 -3 2 -3 2 -3 2 1 2 3 4 5 6 10 1.938 10 6.660 10 1.367 10 1.380 10 2.712 10 4.437 10 5.182 10 8.601 10 F F F F t F F F F F F    −    −   −   +   −   +   −   +   (3) 1 1 2 3 4 5 6 -3 -3 -3 -3 1 1 1 2 1 3 1 4 -3 -3 -3 - 1 5 1 6 1 2 66.695 4.045 0.118 1.758 0.617 2.631 5.914 4.453 2.828 10 6.505 10 4.691 10 4.041 10 3.900 10 3.205 10 1.383 10 1.838 10 Y t F F F F F F t F t F t F t F t F t F F F = + +  +  +  −  −  + −  +    +    +    +    +    +    +    +  3 -4 1 3 -3 -4 -4 -4 1 4 1 5 1 6 2 3 2 -4 -3 -4 -3 4 2 5 2 6 3 4 3 5 -4 -4 3 6 4 5 3.826 10 1.659 10 8.623 10 1.752 10 2.331 10 1.265 10 1.067 10 6.201 10 1.710 10 2.139 10 3.634 10 7.699 F F F F F F F F F F F F F F F F F F F F F F F F   +    −    +    +    +    −    −    +    +    −    +    + -4 -3 4 6 5 6 -3 2 -3 2 -3 2 -4 2 -3 2 1 1 2 3 4 -3 2 -3 2 5 6 10 1.938 10 6.660 10 1.367 10 1.380 10 2.712 10 4.437 10 5.182 10 8.601 10 F F F F t F F F F F F    −    −   −   +   −   +   −   +   (4) The accuracy of response surface is the basis for ensuring the validity of experimental design and response surface function, and the premise of further analysis by using this model. The accuracy of response surface function and the significance of choosing design parameters can be obtained by checking the accuracy of response surface function, which is helpful to determine whether the selected design parameters are reasonable or not. In this paper, ANOVA is used to analyze the model. Some results are shown in Tab. 8 and Tab. 9. In order to better observe the fitting accuracy of response surface, the correlation diagrams of experimental and predicted values are given in Fig. 9, in which actual represents the results of finite element calculation and predicted represents the results of response surface calculation. The F and P values in the table represent the significance of correlation coefficients. The larger of the F value, the more significant of the correlation coefficients is. On the contrary, the smaller of the P value, the more significant of the correlation coefficient is. As can be seen from Tab. 8, the response surface model is significant, and the sensitivity of each design parameter to the response is significant, as well. It shows that the fitting accuracy of response surface is high and the selection of design parameters is reasonable. Because of space, the interaction among design parameters can't be given. Through analysis, it is found that the interaction among design parameters in response surface function is relatively low, which indicates that the interaction between design parameters has less influence on response. Similarly, Tab. 9 shows that although the sensitivity of each design parameter to response is not all significant, the response surface model is generally significant. Combining Tab. 8 and Tab. 9, we can see that although the significance of design parameters to X and Y is different, the control points (X, Y) composed of X and Y still show significant characteristics, which indicates that the selected design variables have a greater impact on the control points, and further proves the rationality of the selection of design variables. It can be observed from Fig. 9 that all design points are near the 45 diagonal line, and the residual is small, which shows that the predicted values of response surface functions X and Y are quite close to the actual values. (a) Fitting accuracy of response surface X (b) Fitting accuracy of response surface Y Figure 9 : Fitting accuracy of control points