PSI - Issue 39

7

Author name / Structural Integrity Procedia 00 (2019) 000–000

Davide Leonetti et al. / Procedia Structural Integrity 39 (2022) 9–19

15

Fig. 4. Finite element model, boundary conditions and mesh.

The comparison between the normalized stress distribution extracted by the finite element model and the one calculated according to the proposed procedure is depicted in Figure 5. The stress distributions showed in each graph of Figure 5 are normalized with respect to the maximum stress, in absolute value, resulting from the finite element model. In particular, the stresses are related to two sections: the symmetry section, at x =0mm and the section at x =10mm, arbitrary selected. It results that a reasonable agreement is obtained between the two models, when the underlying assumptions are verified: (1) the beam dimensions are significantly larger than the extension of the line load, and (2) the length of the beam is significantly larger than each of the dimensions associated to its section, so that it can be considered infinitely long. The deviation in the normal stress along the x -direction, see Figure 6c, are attributed to a different distribution of the bending moment along the beam estimated with the two models. A maximum deviation of 15% is observed, corresponding to the valley in Figure 5c.

0,0 0,2

-1,2 -1,0 -0,8 -0,6 -0,4 -0,2 0,0

-1,2 -1,0 -0,8 -0,6 -0,4 -0,2

ANSYS Proposed

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σx/max{σx,FEM}

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(a) in the section at x =0 mm z [mm]

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-1,4 -1,2 -1,0 -0,8 -0,6 -0,4 -0,2 σ x /max{σ x,FEM }

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(d) in the section at x =10 mm

(e) in the section at x =10 mm

Fig. 5. Comparison between the stresses resulting from the finite element model and the proposed approach.