PSI - Issue 80

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

37

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

7

1

1

0 . 95

0 . 9

¯ ω 1

¯ ω 1

0 . 9

0 . 8

0 . 85

VEMQuad VEMVor FEMQuad

VEMQuad VEMVor FEMQuad

0 . 04 0 . 06 0 . 08 0 . 1 0 . 12 0 . 14 0 . 8

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. 2. Convergence of the first natural frequency of a thick and thin clamped square plate with mesh size

1 . 01

1 . 01

1 . 005

1 . 005

1

1

¯ ω 1

¯ ω 1

0 . 995

0 . 995

VEMQuad VEMVor FEMQuad

VEMQuad VEMVor FEMQuad

0 . 99

0 . 99

0 . 985

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. 3. Convergence of the first natural frequency of a thick and thin simply supported square plate with mesh size

Table 2. Comparison of the natural frequencies of the thick simply supported square plate Vibrational Mode VEMQuad VEMVor

FEMQuad

Analytical [16]

ω 1 a ρ/ G ω 2 a ρ/ G ω 4 a ρ/ G

0.930 2.225 3.400

0.931 2.225 3.414

0.931 2.227 3.417

0.930 2.219 3.406

5.2. Buckling Results

The buckling tests were carried out on the same domain with the same dimensions and material constants as in Section 5.1. In order to be able to compare to available analytical results, mixed clamped / simply supported and