Issue 66

K. Saada et alii, Frattura ed Integrità Strutturale, 66 (2023) 191-206; DOI: 10.3221/IGF-ESIS.66.12

Source

Sum of Squares df

Mean Square 475.13 82.39 0.8368 1114.95 0.0028 3.97

F-value

p-value

(a) ANOVA for Stress Model

2375.66 82.39 0.8368 1114.95 0.0028 3.97

5 1 1 1 1 1 9

42.93 7.44 0.0756 0.3588 100.74 0,0003

< 0.0001 0.0233 0.7895 0.5639 < 0.0001 0.9876

significant

A-geometry B-section(mm 2 )

AB A²

significant

B²

Residual Cor Total

99.60

11.07

2475.27 14 R 2 =0.9598, R 2 adjusted = 0.9374, R 2 predicted = 0.9267and Adequate precision =14.8008 (b) ANOVA for Young's Modulus

Model

3-014E+06 1-941E+05 1993-83 10258-86 1-016E+06

5 1 1 1 1 1 9

6-028E+05 1-941E+05 1993-83 10258-86 1-016E+06

31-40 10-11 0-1039 0-5344 52-91 0-0002

< 0.0001 0-0112 0-7546 0-4834 < 0.0001 0-9903

significant

A-geometry B-section(mm 2 )

AB A²

B²

2-99

2-99

Residual Cor Total

1-728E+05

19196-36

3-187E+06 14

R 2 =0.9458, R 2 adjusted = 0.9157, R 2 predicted = 0.8678 and Adequate precision =12.4394

Table 3: ANOVA of quadratic model obtained for stress and Young’s Modulus. To develop empirical models for mechanical properties and analyze the influence of selected parameters, an experimental plan was designed using the Response Surface Methodology (RSM) technique, ANOVA (Analysis of Variance) is a statistical method used to assess the significance of different factors in a regression model, including quadratic models. In the context of a quadratic model, ANOVA helps to determine whether the quadratic term makes a significant contribution to the overall fit of the model. A quadratic model is a type of regression model that includes both linear and quadratic terms The ANOVA table for a quadratic model breaks down the total variation in the data into different components, each corresponding to the variation explained by the model or its components. It helps to evaluate the significance of each term (linear and quadratic) in the model and how much of the variation they account for. The ANOVA table typically consists of several components: - Sum of Squares (SS): This represents the sum of the squared differences between the observed values and the predicted values from the model. - Degrees of Freedom (DF): The degrees of freedom for each component represent the number of independent pieces of information available for estimating that component. - Mean Square (MS): The Mean Square is obtained by dividing the Sum of Squares by its corresponding Degrees of Freedom. - F-ratio (F-value): The F-ratio is calculated by dividing the Mean Square for a given component by the Mean Square of the residual (error) term. - P-value: The p-value represents the probability of obtaining an F-ratio as extreme as observed, assuming that the null hypothesis is true (i.e., the term does not contribute significantly to the model). If the p-value associated with the quadratic term ( β 2) is small (usually less than a chosen significance level, often 0.05), it indicates that the quadratic term is statistically significant, and its inclusion in the model improves the fit significantly. On the other hand, if the p-value is large, it suggests that the quadratic term does not contribute significantly to the model, and a simpler linear model might be more appropriate. ANOVA of a quadratic model assesses the significance of the quadratic term (x^2) and helps determine if it improves the model's performance compared to a simpler linear model. RSM was used, which was used in the previous literature in the case of tensile tests and its results were good [43,44]. The

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