Issue 48

E. Maiorana, Frattura ed Integrità Strutturale, 48 (2019) 459-472; DOI: 10.3221/IGF-ESIS.48.44

between the portions of plate divided by the stiffener; there are four half-waves instead of the three found in the other cases. Group OF1-III shows behavior more similar to that of the first two groups, although there is less deformation as the value of the rigid stiffener in OF1-IV is approached. Therefore, an optimal cross-section stiffener in terms of relative flexural stiffness, corresponds to the curve described by group OF1-III and its interpolation equation, Eqn.10, which shows that the optimal position on varying  is the following:

h  / h = (  0.055  3  0.005  2 + 0.219  + 0.341)

(10)

with coefficient of determination R 2 = 0.9991. Alternately, the linear interpolation equation is:

h  / h = (0.179  + 0.339)

(11)

with coefficient of determination R 2 = 0.9902. Tab. 10 compares the results numerically, according to Eqn.10 and Eq.11, showing a good match.

h  / h



-1

-0.75 -0.5 -0.25 0

0.25 0.5 0.75 1

FEM 0.17 0.20 0.24 0.28 0.34 0.40 0.44 0.48 0.50 [Eq.10] 0.17 0.20 0.24 0.29 0.34 0.39 0.44 0.48 0.50 [Eq.11] 0.16 0.20 0.25 0.29 0.34 0.38 0.43 0.47 0.52

Table 10: Results from numerical analyses, Eq.10 and Eq.11.

Fig. 10 shows the curve of the optimum value of stiffener position with respect to stress gradient  for optimal cross section stiffener, in terms of relative flexural stiffness, together with results for the optimum location of stiffener determined according to an energy formulation and a sequential quadratic programming algorithm described in Bedair 1997 [7].

0.60

0.50

0.40

h' / h

0.30

y = -0.0549x 3 - 0.0048x 2 + 0.2192x+ 0.3409 R 2 = 0.9991

0.20

0.10

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 

Figure 10: Optimum value of h  / h vs.  for optimal cross-section stiffener. Comparison between results of Eq.10 and results reported in Bedair, 1997 . The comparison shows a good match considering the different approach and schematization of the beam web panel and stiffening. Lastly, the following observations may be derived: for  < 0, the optimal position of the longitudinal stiffener depends on relative stiffness, and flexible and rigid stiffeners can be distinguished, particularly for  = -1; the best position

470