Research Article
A Refined Higher-Order Hybrid Stress Quadrilateral Element for Free Vibration and Buckling Analyses of Reissner-Mindlin Plates
Table 8
Convergence of six lowest nondimensional frequency parameters (
, 0.1 and SSSS, CCCC).
| | Boundary | Mesh | Mode sequence number | 1 | 2 | 3 | 4 | 5 | 6 |
| (a) QH8 with modified consistent mass matrix (QH8-RCV, ) | 0.001 | SSSS | | 2.0208 | 5.1600 | 5.1600 | 8.5457 | 10.7782 | 10.7782 | | 2.0044 | 5.0290 | 5.0290 | 8.0832 | 10.1251 | 10.1251 | | 2.0010 | 5.0066 | 5.0066 | 8.0174 | 10.0268 | 10.0268 | Ref. sol | 2.000 | 5.000 | 5.000 | 8.000 | 10.000 | 10.000 | CCCC | | 3.6986 | 7.7478 | 7.7478 | 11.8207 | 14.7803 | 14.9043 | | 3.6563 | 7.4895 | 7.4895 | 11.1031 | 13.5317 | 13.5943 | | 3.6484 | 7.4478 | 7.4478 | 10.9922 | 13.3726 | 13.4356 | Ref. sol | 3.646 | 7.436 | 7.436 | 10.964 | 13.332 | 13.395 |
| 0.1 | SSSS | | 1.9440 | 4.6822 | 4.6822 | 7.3572 | 8.9607 | 8.9607 | | 1.9335 | 4.6062 | 4.6062 | 7.0516 | 8.5663 | 8.5663 | | 1.9321 | 4.6062 | 4.6062 | 7.0581 | 8.5881 | 8.5881 | Ref. sol | 1.931 | 4.605 | 4.605 | 7.064 | 8.605 | 8.605 | CCCC | | 3.3008 | 6.3401 | 6.3401 | 9.0667 | 10.7861 | 10.8677 | | 3.2925 | 6.2555 | 6.2555 | 8.7327 | 10.2492 | 10.3400 | | 3.2943 | 6.2743 | 6.2743 | 8.7752 | 10.3198 | 10.4162 | Ref. sol | 3.292 | 6.276 | 6.276 | 8.792 | 10.356 | 10.455 |
| (b) QH8 with lumped mass matrix (QH8-LV) | 0.001 | SSSS | | 1.9997 | 4.9970 | 4.9970 | 7.9691 | 9.9694 | 9.9694 | | 2.0000 | 4.9999 | 4.9999 | 7.9986 | 10.0001 | 10.0001 | | 2.0000 | 5.0000 | 5.0000 | 7.9998 | 9.9999 | 9.9999 | Ref. sol | 2.000 | 5.000 | 5.000 | 8.000 | 10.000 | 10.000 | CCCC | | 3.6452 | 7.4121 | 7.4121 | 10.8713 | 12.9885 | 13.0468 | | 3.6461 | 7.4365 | 7.4365 | 10.9637 | 13.3312 | 13.3935 | | 3.6460 | 7.4363 | 7.4363 | 10.9644 | 13.3318 | 13.3949 | Ref. sol | 3.646 | 7.436 | 7.436 | 10.964 | 13.332 | 13.395 |
| 0.1 | SSSS | | 1.9427 | 4.6385 | 4.6385 | 7.0569 | 8.5511 | 8.5511 | | 1.9452 | 4.6710 | 4.6710 | 7.1895 | 8.7670 | 8.7670 | | 1.9457 | 4.6784 | 4.6784 | 7.2173 | 8.8157 | 8.8157 | Ref. sol | 1.931 | 4.605 | 4.605 | 7.064 | 8.605 | 8.605 | CCCC | | 3.3019 | 6.2524 | 6.2524 | 8.6322 | 10.0169 | 10.0917 | | 3.3155 | 6.3496 | 6.3496 | 8.9075 | 10.4886 | 10.5773 | | 3.3181 | 6.3688 | 6.3688 | 8.9622 | 10.5759 | 10.6670 | Ref. sol | 3.292 | 6.276 | 6.276 | 8.792 | 10.356 | 10.455 |
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