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E. Maggiolini et alii, Frattura ed Integrità Strutturale, 25 (2013) 117-123 ; DOI: 10.3221/IGF-ESIS.25.17 120 To achieve a sufficient approximation, it is not necessary to compute the integral across the whole domain, but it is faster to only make the integration in a subdomain (a circular subdomain with a radius equal to 5.5c has been verified as suitable). Differences between these two estimations can be assumed to be the intrinsic scatter between the two methods so that if the “integral” value is available, the “IG effective” value can be computed by this correction (Tab. 1). A NALYSIS BY SOFTWARE WITHOUT A BUILT - IN PDE SOLVER ost FEM software does not have the PDE solver or integration option; nevertheless, it is possible to have a reasonable approximation by means of the knowledge of nodal coordinates and nodal local stress. One possibility is to transform the integral into a summation, with a quadrature rules approximation [7]. For this calculation it is necessary to define a weight coefficient, called N, built on the distance between nodes:             V eff ,int eff ,sum V ψ x,y σeq(y)dV N x,y ψ x,y σeq(y) N x,y ψ x,y ψ x,y dV          in V (4) In a uniform mesh, i.e. with elements having the same dimension and constant distance between nodes, N should be constant. In any other case, N shall be computed depending on element dimension and actual node distances. This approach suggests using the nodal reaction (at each node constrained) as the N approximation, when the body is loaded by a uniform distributed load, such as the gravity load. Consequently, the bigger the element, the bigger the reaction. Fig. 4 shows the nodal reaction in a subdomain in the case of a fairly regular, but not uniform, mesh. Figure 4: Plot of reaction N in a subdomain For any kind of FE software, it is simply necessary to export coordinates of the node inside the subdomain, the first principal stress in each of those nodes, and the reaction of the same nodes. Any mathematical tool (i.e. Matlab or even a spreadsheet such as Excel) can compute σ eff,sum of Eq. (4). Figure 5: Trend of σ eff,int Vs σ eff,IG Vs σ eff,sum . 0 1 2 3 4 5 6 7 8 9 10 0 30 60 90 120 150 180 σ /σ nom 2α [°] σ eff,IG σ eff,int σ eff,sum M