Issue 48

B. Chen et alii, Frattura ed Integrità Strutturale, 48 (2019) 385-399; DOI: 10.3221/IGF-ESIS.48.37 393 Source model Sum of Squares Df Mean Square F Value P-value Prob > F Model 230.04 35 6.57 6.873E+5 < 0.0001 significant t 1 0.036 1 0.036 3735.32 < 0.0001 significant F 1 17.85 1 17.85 1.867E+6 < 0.0001 significant F 2 26.41 1 26.41 2.762E+5 < 0.0001 significant F 3 1.91 1 1.91 2.0E+5 < 0.0001 significant F 4 51.34 1 51.34 5.369E+6 < 0.0001 significant F 5 24.41 1 24.41 2.552E+6 < 0.0001 significant F 6 2.37 1 2.37 2.48E+5 < 0.0001 significant … … … … … … … Residual 9.562E-5 10 9.562E-5 Lack of Fit 9.562E-5 5 1.912E-5 1.125E6+5 < 0.0001 significant Pure Error 8.500E-10 5 1.700E-10 Cor Total 230.04 45 Table 8 : ANOVA for response surface X quadratic model. Source model Sum of Squares Df Mean Square F Value P-value Prob > F Model 498.34 35 14.24 9191.84 < 0.0001 significant t 1 9.08 1 9.08 5860.00 < 0.0001 significant F 1 1.326E-3 1 1.326E-3 0.86 0.3766 non-significant F 2 0.026 1 0.026 16.82 0.0021 non-significant F 3 0.041 1 0.041 26.19 0.0005 non-significant F 4 206.54 1 206.54 1.33E+5 < 0.0001 significant F 5 94.29 1 94.29 60871.61 < 0.0001 significant F 6 9.65 1 9.65 6229.75 < 0.0001 significant … … … … … … … Residual 0.015 10 1.549E-5 Lack of Fit 0.015 5 3.098E-3 Pure Error 0.000 5 0.000 Cor Total 498.36 45 Table 9 : ANOVA for response surface Y quadratic model The control points value in consideration of parameter uncertainty In order to calculate the mean stress and stress amplitude of control points more accurately, this study uses the important sampling method to select the sample points of uncertainty parameters. Important sampling method is one of the most effective Monte Carlo techniques, the basic principle is that it doesn't from a given probability distribution function of sampling, but modifies the given probability distribution so as to shift the sampling center towards the failure region to gain information more efficiently [18]. Probability of structural failure can be expressed in the following form [ ( )] ( ) [ ( )] ( ) ( ) = ( ) ( ) X X X X f V V V I g v f v I g v f v P p v dv E p v p v + −    =       (5)