PSI - Issue 80

Luke Wyatt et al. / Procedia Structural Integrity 80 (2026) 31–42 L. Wyatt et. al. / Structural Integrity Procedia 00 (2023) 000–000

40

10

1 . 05

1 . 02

1

1

0 . 98

0 . 95

¯ K 1 B

¯ K 1 B

0 . 96

0 . 94

0 . 9

0 . 92

VEMQuad VEMVor

VEMQuad VEMVor

0 . 85

0 . 1

0 . 2

0 . 1

0 . 2

0 . 05

0 . 15

0 . 05

0 . 15

h mean / c

h mean / c

(a) t / c = 0 . 1

(b) t / c = 0 . 5

Fig. 7. Convergence of K 1 B for thick and thin plates with mesh size

VEMQuad VEMVor Reference

VEMQuad VEMVor Reference

4

6

3

K 1 B / ( M 0 √ π a )

K 1 B / ( M 0 √ π a )

4

2

2

1

0

0 . 2 0 . 4 0 . 6 0 . 8

1

0 0 . 2 0 . 4 0 . 6 0 . 8 1

a / c

a / c

(a) t / c = 0 . 1

(b) t / c = 0 . 5

Fig. 8. Converged VEM results of K 1 B for crack problem 1 with varying crack size

6. Conclusions

In this paper further extensions and applications have been proposed to the newly formulated reduced order shear projection Mindlin plate virtual element. The construction of the element mass matrix has been proposed, and it has proven to be e ffi cient at the analysis of free vibrations for both clamped and simply supported thin and thick plates. The VEM results converge to within 0.4% of those from the equivalent FEM formulation, and agree with the analytical solutions. The VEM formulation of the geometric sti ff ness matrix for in plane buckling of the plate has been proposed, and tested on mixed clamped / simply supported and simply supported plates. The VEM compares well against the FEM results, especially for thin plates where it converges more accurately to the analytical solution by 1-2%. The calculation of the bending stress intensity factor by the J-integral technique was also proposed, and was found to be e ff ective, even on relatively coarse meshes when compared to previously published results. Further