PSI - Issue 41

Christos F. Markides et al. / Procedia Structural Integrity 41 (2022) 351–360 Christos F. Markides et al. / Structural Integrity Procedia 00 (2019) 000 – 000

357

7

Vertical downwards displacement

Point K

Material interfaces

Rigidly clamped

Fig 8. The geometry and the meshing of the numerical model.

94

93

92

σ eqv [MPa]

91

90

0

50000

100000

150000

200000

Number of elements

Fig. 9. The convergence analysis.

4. Results 4.1 Stresses

Adopting for the parameters of the problem the numerical values considered in sub-section 2.1, the stress distri butions according to the analytic formulae obtained are plotted along some strategic loci (shown in Fig.10a), in juxtaposition to the results provided by the numerical analysis, for comparison reasons. More specifically, in Figs.10(b, c) the non-zero normal stresses are plotted along y - and x -axis, respectively. As it is seen, there is a quite satisfactory agreement between analytical and numerical results, in favour of the soundness of the mathematical solution introduced in this study. Some minor discrepancies observed (see for example Fig.10c) are attributed to the fact that while for the analytic solution the material points of the flat edge are considered ideally stuck with the stamp (i.e., the points on – LL remain stationary in the x -direction, allowed to move only in the y -direction), corresponding to an infinite friction coefficient between the flat edge of the FBD and the stamp, in the numerical model a finite coefficient of friction was considered, allowing a slight slip of the points of the flat edge of the FBD with respect to the corresponding points of the rigid stamp.