PSI - Issue 33

I.J. Sánchez-Arce et al. / Procedia Structural Integrity 33 (2021) 149–158 Sánchez-Arce et al. / Structural Integrity Procedia 00 (2019) 00 –000

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Figure 3. Vertical displacement of the upper right corner. Comparison between NNRPIM and ABAQUS' solutions.

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Figure 4. Normal stress, in the loading direction (  xx ), at x=1 m.

The normal stresses along the horizontal directions (  xx ) were obtained for both solutions, as shown in Figure 5. There is a stress concentration in the upper left corner, where the edge is constrained. Such a condition was expected because of the coarse nodal distribution used. Moreover, Khosrowpour et al., (2019) found, in a similar exercise, that the stresses predicted using FEM are slightly higher than those obtained using meshless, with calculated differences of around 2.5%. In Figure 5, it can be clearly seen that the difference between the meshless and FEM solution is around the same value, confirming a successful implementation. The shear stress (  xy ) distributions of both solutions were also compared, as shown in Figure 6. Although the shear stress distributions are not widely available in the literature, these give an indication about the correctness of the deformation gradient and the polar decomposition of the left Cauchy-Green tensor. The  xy magnitudes between the two models are rather similar. More importantly, the patterns were similar, indicating that the deformation gradient was properly calculated as it was the polar decomposition. The stress concentration on the upper left corner is more evident in the FEM solution than in the meshless solution. This could be attributed to mesh size, as it was verified using a FEM model with four times more divisions on all edges (2673 nodes), which leads to a mesh around 14 times denser. Thus, supporting the idea that meshless methods provide accurate results with coarser nodal distributions.