PSI - Issue 80

Luke Wyatt et al. / Procedia Structural Integrity 80 (2026) 31–42

38

8

L. Wyatt et. al. / Structural Integrity Procedia 00 (2023) 000–000

1 . 04

VEMQuad VEMVor FEMQuad

VEMQuad VEMVor FEMQuad

1 . 01

1 . 02

1

¯ λ 1

¯ λ 1

0 . 99

1

0 . 98

0 . 98

0 . 97

0 . 04 0 . 06 0 . 08 0 . 1 0 . 12 0 . 14

0 . 04 0 . 06 0 . 08 0 . 1 0 . 12 0 . 14

h mean / a

h mean / a

(a) t / a = 0 . 01

(b) t / a = 0 . 1

Fig. 4. Convergence of the first buckling load of a thick and thin clamped / simply supported square plate with mesh size

1 . 02

VEMQuad VEMVor FEMQuad

VEMQuad VEMVor FEMQuad

1 . 03

1 . 01

1 . 02

1 . 01

¯ λ 1

¯ λ 1

1

1

0 . 99

0 . 99

0 . 04 0 . 06 0 . 08 0 . 1 0 . 12 0 . 14

0 . 04 0 . 06 0 . 08 0 . 1 0 . 12 0 . 14

h mean / a

h mean / a

(a) t / a = 0 . 01

(b) t / a = 0 . 1

Fig. 5. Convergence of the first buckling load of a thick and thin simply supported square plate with mesh size

simply supported plates were tested. In the mixed boundary condition case the clamped boundaries were parallel to the applied load, and the simply supported boundaries perpendicular. The initial load σ 0 xx = 1MPa ,τ 0 xy = σ 0 yy = 0 was used in both tests. Figures 4 and 5 show the convergence of the first buckling load, normalised by the analytical solution [17], ¯ λ 1 with decreasing average element diameter. For thick plates the convergence of both VEM and FEM results are very similar, both in terms of rate and absolute value. However the accuracy for the thin plates is 1-2% better for the VEM results than the FEM. Tables 3 and 4 show the converged VEM and FEM results and the analytical solution where available. The results show that all the analysis methods are very similar, and for λ 1 coincide closely with the analytical solution. It can be seen that the VEM may slightly under predict λ 4 when compared to the FEM results, as was seen for ω 4 in Section 5.1. Increasing the scaling parameter of the stability part of the sti ff ness makes the VEM results more similar to the FEM, but without the analytical solution, it is not certain that this is improving the accuracy of the result.