Research Article
Boundary Conditions in 2D Numerical and 3D Exact Models for Cylindrical Bending Analysis of Functionally Graded Structures
Table 1
One-layered FGM plate with
. Analytical 3D versus 2D numerical models. Frequency
in Hz.
| | Mode | 3D exact | 2D FE | 2D FE (CB) | 2D GDQ | 2D GDQ (CB) |
| | | I | 40.19 | — | 39.07 | — | 39.21 | | I | 40.19 | — | 39.07 | — | 39.21 | | I | 80.37 | 80.06 | — | 80.36 | — | | I | 160.7 | — | 158.0 | — | 158.4 | | I | 160.7 | — | 158.0 | — | 158.4 | | I | 200.8 | 200.1 | — | 200.8 | — | | I | 200.8 | 200.1 | — | 200.8 | — | | I | 321.2 | 320.2 | — | 321.1 | — | | I | 361.3 | — | 356.8 | — | 357.7 | | I | 361.3 | — | 356.8 | — | 357.7 | | I | 401.4 | 400.2 | — | 401.3 | — | | I | 401.4 | 400.2 | — | 401.3 | — | | I | 521.5 | 520.2 | — | 521.5 | — | | I | 521.5 | 520.2 | — | 521.5 | — | | I | 641.6 | — | 635.4 | — | 636.5 | | I | 641.6 | — | 635.4 | — | 636.5 | | I | 681.6 | 680.1 | — | 681.5 | — | | I | 681.6 | 680.1 | — | 681.5 | — |
| | | I | 200.2 | — | 195.1 | — | 195.1 | | I | 200.2 | — | 195.1 | — | 195.1 | | I | 398.9 | 399.5 | — | 398.8 | — | | I | 791.6 | — | 786.4 | — | 779.7 | | I | 791.6 | — | 786.4 | — | 779.7 | | I | 985.8 | 995.4 | — | 985.7 | — | | I | 985.8 | 995.4 | — | 985.7 | — | | I | 1560 | 1588 | — | 1560 | — | | I | 1749 | — | 1767 | — | 1729 | | I | 1749 | — | 1767 | — | 1729 | | I | 1936 | 1980 | — | 1936 | — | | I | 1936 | 1980 | — | 1936 | — | | I | 2490 | 2566 | — | 2490 | — | | I | 2490 | 2566 | — | 2490 | — | | II () | 2775 | 2773 | — | 2775 | — | | II () | 2775 | 2773 | — | 2775 | — | | I | 3034 | — | 3124 | — | 3007 | | I | 3034 | — | 3124 | — | 3007 |
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