10. APPENDICE 10.1

10. APPENDICE

10.1 Catalogazione degli articoli sull’ instabilità e sulle vibrazioni di “shell”

cilindriche in composito

Art. N°

Argomento Geometria Materiale Shell Theories

Carichi Vincoli Metodo di Soluzione [17] -Buckling Cir. Cyl. Shell Composito -Donnel

-R. Love -As. Com. -Mom. Fl. S2-S2 Galerkin [18] -Buckling -Vibrazioni

Cir. Cyl. Shell Composito Cross-ply

-Donnel -As. Com. -Pres. Lat.

-

S2-S2 Sol.esatta (autoval.)

[19] -Buckling Cir. Cyl. Shell Composito Ortotopo + Stiffeners

-Donnel -As. Com. -Pres. Lat. -Combin.

S2-S2 Sol.esatta (autoval.)

[20] -Vibrazioni Cir. Cyl. Shell Composito Ortotropo

-R.Donnel -R. Love

- S3-S3 Sol.esatta (autoval.)

[21] -Vibrazioni Cir. Cyl. Shell Composito -Love - C4-C4 S3-S3 C4-S3

-Fin. Diff. -Fin.Com. Four. Tras. [22] -Buckling Cir. Cyl. Shell Composito

Ortotropo

-Flügge -Non Uni. As. Com.

S3-S3 -Fin.Com. Four. Tras. [23] -Buckling

-Vibrazioni

Cir. Cyl. Shell Composito Ortotropo

-Flügge -Non Uni. As. Com. S3-S3 -Fin.Com. Four. Tras. [24] -Bending -Buckling -Vibrazioni

Cir. Cyl. Shell Composito Cross-ply -Love -1st Order -3rd Order -S Dis. Tr. -As. Com. -Dis. Tr. S-S C-C F-F Spazio di Stato [25] -Buckling -Vibrazioni

Cir. Cyl. Shell Composito Antisym. Angle-ply

-Donnel -As. Com. -

S-S Galerkin

[27] -Buckling Cir. Cyl. Shell Composito Angle-ply

10.2 “Buckling” e resistenza delle dieci sequenze di impilamento

TYPE 1

(

0/90/0/90/0

)

S CARICO CRITICO [N] FRECCIA CRITICA [m] MAXF (layer 9 top) TWSI (layer 9 top) TWSR (layer 9 top) CON. C-E 18588 3 10 279⋅ − 1.178 (31) 1.271 (51) 1.190 (51) CYL. C-E 19324 3 10 216⋅ − 1.177 (31) 1.265 (51) 1.185 (51) CON. G-E 5302 3 10 351⋅ − 0.775 (31) 0.608 (31) 0.780 (31) CYL. G-E 6112 3 10 299⋅ − 0.882 (31) 0.787 (31) 0.887 (31) (Tab.10.1) TYPE 2

(

90/0/90/0/90

)

S CARICO CRITICO [N] FRECCIA CRITICA [m] MAXF (layer 1 bot) TWSI (layer 1 bo) TWSR (layer 1 bot) CON. C-E 18608 3 10 387⋅ − 1.848 (11) 2.382 (11) 1.831 (11) CYL. C-E 19276 3 10 299⋅ − 1.875 (11) 2.435 (11) 1.858 (11) CON. G-E 5278 3 10 455⋅ − 1.116 (11) 1.216 (11) 1.103 (11) CYL. G-E 6082 3 10 382⋅ − 1.262 (11) 1.555 (11) 1.247 (11) (Tab.10.2) TYPE 3

(

45/−45/45/−45/45

)

S CARICO CRITICO [N] FRECCIA CRITICA [m] MAXF (layer 10 top) TWSI (layer 10 top) TWSR (layer 10 top) CON. C-E 8424 3 10 638⋅ − 2.436 (51) 6.271 (51) 2.583 (51) CYL. C-E 9282 3 10 514⋅ − 2.611 (51) 7.191 (51) 2.770 (51) CON. G-E 4401 3 10 435⋅ − 1.483 (621) 2.202 (621) 1.484 (621) CYL. G-E 5018 3 10 366⋅ − 1.458 (51) 2.338 (51) 1.529 (51) (Tab.10.3) TYPE 4

(

90/0/0/0/0

)

S CARICO CRITICO [N] FRECCIA CRITICA [m] MAXF (layer 1 bot) TWSI (layer 1 bot) TWSR (layer 1 bot) CON. C-E 18903 3 10 212⋅ − 0.977 (11) 0.957 (11) 0.968 (11) CYL. C-E 19432 3 10 168⋅ − 1.002 (11) 0.991 (11) 0.993 (11) CON. G-E 6167 3 10 330⋅ − 0.806 (11) 0.636 (11) 0.797 (11) CYL. G-E 7035 3 10 279⋅ − 0.910 (11) 0.810 (11) 0.900 (11)

(Tab.10.4) TYPE 5

(

0/90/90/90/90

)

S CARICO CRITICO [N] FRECCIA CRITICA [m] MAXF (layer 9 top) TWSI (layer 9 top) TWSR (layer 9 top) CON. C-E 14086 3 10 507⋅ − 2.256 (31) 3.267 (31) 2.249 (31) CYL. C-E 15501 3 10 418⋅ − 2.456 (31) 3.728 (31) 2.447 (31) CON. G-E 4238 3 10 505⋅ − 1.134 (31) 1.288 (31) 1.135 (31) CYL. G-E 5026 3 10 421⋅ − 1.266 (31) 1.603 (31) 1.266 (31) (Tab.10.5) TYPE 6

(

30/−30/30/−30/30

)

S CARICO CRITICO [N] FRECCIA CRITICA [m] MAXF (layer 10 top) TWSI (layer 10 top) TWSR (layer 10 top) CON. C-E 10431 3 10 293⋅ − 1.484 (741) 3.311 (741) 2.108 (741) CYL. C-E 12283 3 10 251⋅ − 1.341 (51) 2.574 (681) 1.810 (681) CON. G-E 4616 3 10 312⋅ − 0.935 (701) 0.977 (701) 0.988 (701) CYL. G-E 5396 3 10 269⋅ − 0.951 (51) 0.938 (51) 0.968 (51) (Tab.10.6) TYPE 7

(

60/−60/60/−60/60

)

S CARICO CRITICO [N] FRECCIA CRITICA [m] MAXF (layer 10 top) TWSI (layer 10 top) TWSR (layer 10 top) CON. C-E 8900 3 10 1016⋅ − 3.489 (31) 11.701 (31) 4.359 (31) CYL. C-E 9534 3 10 828⋅ − 3.782 (31) 13.530 (31) 4.722 (31) CON. G-E 4192 3 10 590⋅ − 1.470 (541) 2.704 (31) 1.644 (31) CYL. G-E 4667 3 10 488⋅ − 1.437 (31) 3.321 (31) 1.822 (31) (Tab.10.7) TYPE 8

(

0/0/0/90/90

)

S CARICO CRITICO [N] FRECCIA CRITICA [m] MAXF (layer 7 top) TWSI (layer 7 top) TWSR (layer 7 top) CON. C-E 12906 3 10 196⋅ − 0.865 (31) 0.821 (31) 0.864 (31) CYL. C-E 15171 3 10 173⋅ − 0.993 (31) 0.985 (31) 0.989 (31)

CON. G-E 4235 3 10 282⋅ − 0.643 (11) 0.406 (31) 0.637 (31) CYL. G-E 4904 3 10 238⋅ − 0.724 (11) 0.513 (11) 0.716 (11) (Tab.10.8) TYPE 9

(

90/90/90/0/0

)

S CARICO CRITICO [N] FRECCIA CRITICA [m] MAXF (layer 10 top) TWSI (layer 10 top) TWSR (layer 10 top) CON. C-E 17340 3 10 350⋅ − 1.467 (31) 1.720 (31) 1.469 (31) CYL. C-E 17920 3 10 272⋅ − 1.489 (31) 1.754 (31) 1.490 (31) CON. G-E 5914 3 10 495⋅ − 1.087 (31) 1.190 (31) 1.091 (31) CYL. G-E 6573 3 10 408⋅ − 1.195 (31) 1.438 (31) 1.199 (31) (Tab.10.9) TYPE 10

(

0/0/0/0/0

)

S CARICO CRITICO [N] FRECCIA CRITICA [m] MAXF (layer 10 top) TWSI (layer 10 top) TWSR (layer 10 top) CON. C-E 13239 3 10 129⋅ − 0.639 (961) 0.772 (921) 0.825 (921) CYL. C-E 15206 3 10 113⋅ − 0.397 (961) 0.468 (861) 0.561 (861) CON. G-E 4794 3 10 221⋅ − 0.440 (821) 0.261 (821) 0.511 (821) CYL. G-E 5715 3 10 195⋅ − 0.360 (821) 0.182 (801) 0.426 (801) (Tab.10.10)

10.3 Matrice Omega per le dieci sequenze di impilamento

⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⋅ ⋅ ⋅ ⋅ ⋅ = Ω 63 . 12 0 0 0 0 0 0 71 065 . 4 0 0 0 0 065 . 4 676 . 119 0 0 0 0 0 0 10 425 . 2 0 0 0 0 0 0 10 515 . 1 10 805 . 7 0 0 0 0 10 805 . 7 10 146 . 2 7 8 6 6 8 (1) GLASS-EPOXY ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⋅ ⋅ ⋅ ⋅ ⋅ = Ω 021 . 13 0 0 0 0 0 0 709 . 18 593 . 2 0 0 0 0 593 . 2 172 . 27 0 0 0 0 0 0 10 5 . 2 0 0 0 0 0 0 10 856 . 3 10 979 . 4 0 0 0 0 10 979 . 4 10 953 . 4 7 7 6 6 7 (2) CARBON-EPOXY ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⋅ ⋅ ⋅ ⋅ ⋅ = Ω 63 . 12 0 0 0 0 0 0 676 . 119 065 . 4 0 0 0 0 065 . 4 71 0 0 0 0 0 0 10 425 . 2 0 0 0 0 0 0 10 146 . 2 10 805 . 7 0 0 0 0 10 805 . 7 10 515 . 1 7 8 6 6 8 (2) GLASS-EPOXY ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⋅ ⋅ ⋅ ⋅ ⋅ = Ω 021 . 13 0 0 0 0 0 0 172 . 27 593 . 2 0 0 0 0 593 . 2 709 . 18 0 0 0 0 0 0 10 5 . 2 0 0 0 0 0 0 10 953 . 4 10 979 . 4 0 0 0 0 10 979 . 4 10 856 . 3 7 7 6 6 7 (3) CARBON-EPOXY ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = Ω 273 . 91 169 . 12 169 . 12 0 0 0 338 . 24 017 . 56 387 . 43 0 0 0 338 . 24 387 . 43 017 . 56 0 0 0 0 0 0 10 752 . 1 10 579 . 1 10 579 . 1 0 0 0 10 157 . 3 10 076 . 1 10 33 . 8 0 0 0 10 157 . 3 10 33 . 8 10 076 . 1 7 7 7 7 8 7 7 7 8 (3) GLASS-EPOXY

⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = Ω 347 . 20 116 . 2 116 . 2 0 0 0 232 . 4 277 . 19 256 . 6 0 0 0 232 . 4 256 . 6 277 . 19 0 0 0 0 0 0 10 907 . 3 10 745 . 2 10 745 . 2 0 0 0 10 49 . 5 10 701 . 3 10 201 . 1 0 0 0 10 49 . 5 10 201 . 1 10 701 . 3 7 6 6 6 7 7 6 7 7 (4) CARBON-EPOXY ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⋅ ⋅ ⋅ ⋅ ⋅ = Ω 63 . 12 0 0 0 0 0 0 365 . 93 065 . 4 0 0 0 0 065 . 4 312 . 97 0 0 0 0 0 0 10 425 . 2 0 0 0 0 0 0 10 833 . 8 10 805 . 7 0 0 0 0 10 805 . 7 10 778 . 2 7 7 6 6 8 (4) GLASS-EPOXY ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⋅ ⋅ ⋅ ⋅ ⋅ = Ω 021 . 13 0 0 0 0 0 0 597 . 22 593 . 2 0 0 0 0 593 . 2 283 . 23 0 0 0 0 0 0 10 5 . 2 0 0 0 0 0 0 10 758 . 2 10 979 . 4 0 0 0 0 10 979 . 4 10 051 . 6 7 7 6 6 7 (5) CARBON-EPOXY ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⋅ ⋅ ⋅ ⋅ ⋅ = Ω 63 . 12 0 0 0 0 0 0 312 . 97 065 . 4 0 0 0 0 065 . 4 365 . 93 0 0 0 0 0 0 10 425 . 2 0 0 0 0 0 0 10 778 . 2 10 805 . 7 0 0 0 0 10 805 . 7 10 833 . 8 7 8 6 6 7 (5) GLASS-EPOXY ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⋅ ⋅ ⋅ ⋅ ⋅ = Ω 021 . 13 0 0 0 0 0 0 283 . 23 593 . 2 0 0 0 0 593 . 2 597 . 22 0 0 0 0 0 0 10 5 . 2 0 0 0 0 0 0 10 051 . 6 10 979 . 4 0 0 0 0 10 979 . 4 10 758 . 2 7 7 6 6 7 (6) CARBON-EPOXY

⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = Ω 612 . 71 499 . 5 579 . 15 0 0 0 998 . 10 735 . 24 556 . 33 0 0 0 157 . 31 556 . 33 959 . 106 0 0 0 0 0 0 10 375 . 1 10 134 . 7 10 021 . 2 0 0 0 10 427 . 1 10 749 . 4 10 443 . 6 0 0 0 10 042 . 4 10 443 . 6 10 054 . 2 8 6 7 7 7 7 7 7 8 (6) GLASS-EPOXY ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = Ω 515 . 18 363 . 1 302 . 2 0 0 0 726 . 2 045 . 13 341 . 5 0 0 0 604 . 4 341 . 5 341 . 27 0 0 0 0 0 0 10 555 . 3 10 768 . 1 10 986 . 2 0 0 0 10 536 . 3 10 505 . 2 10 025 . 1 0 0 0 10 972 . 5 10 025 . 1 10 249 . 5 7 6 6 6 7 7 6 7 7 (7) CARBON-EPOXY ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = Ω 612 . 71 579 . 15 499 . 5 0 0 0 157 . 31 959 . 106 556 . 33 0 0 0 998 . 10 556 . 33 735 . 24 0 0 0 0 0 0 10 375 . 1 10 021 . 2 10 134 . 7 0 0 0 10 042 . 4 10 054 . 2 10 443 . 6 0 0 0 10 427 . 1 10 443 . 6 10 749 . 4 8 7 6 7 8 7 7 7 7 (7) GLASS-EPOXY ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = Ω 515 . 18 302 . 2 363 . 1 0 0 0 604 . 4 341 . 27 341 . 5 0 0 0 726 . 2 341 . 5 045 . 13 0 0 0 0 0 0 10 555 . 3 10 986 . 2 10 768 . 1 0 0 0 10 972 . 5 10 249 . 5 10 025 . 1 0 0 0 10 536 . 3 10 025 . 1 10 505 . 2 7 6 6 6 7 7 6 7 7 (8) CARBON-EPOXY ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⋅ ⋅ ⋅ ⋅ ⋅ = Ω 63 . 12 0 0 0 0 0 0 639 . 23 065 . 4 0 0 0 0 065 . 4 038 . 167 0 0 0 0 0 0 10 425 . 2 0 0 0 0 0 0 10 515 . 1 10 805 . 7 0 0 0 0 10 805 . 7 10 146 . 2 7 8 6 6 8 (8) GLASS-EPOXY

⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⋅ ⋅ ⋅ ⋅ ⋅ = Ω 021 . 13 0 0 0 0 0 0 474 . 10 593 . 2 0 0 0 0 593 . 2 406 . 35 0 0 0 0 0 0 10 5 . 2 0 0 0 0 0 0 10 856 . 3 10 979 . 4 0 0 0 0 10 979 . 4 10 953 . 4 7 7 6 6 7 (9) CARBON-EPOXY ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⋅ ⋅ ⋅ ⋅ ⋅ = Ω 63 . 12 0 0 0 0 0 0 038 . 167 065 . 4 0 0 0 0 065 . 4 639 . 23 0 0 0 0 0 0 10 425 . 2 0 0 0 0 0 0 10 146 . 2 10 805 . 7 0 0 0 0 10 805 . 7 10 515 . 1 7 8 6 6 8 (9) GLASS-EPOXY ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⋅ ⋅ ⋅ ⋅ ⋅ = Ω 021 . 13 0 0 0 0 0 0 406 . 35 593 . 2 0 0 0 0 593 . 2 474 . 10 0 0 0 0 0 0 10 5 . 2 0 0 0 0 0 0 10 953 . 4 10 979 . 4 0 0 0 0 10 979 . 4 10 856 . 3 7 7 6 6 7 (10) CARBON-EPOXY ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⋅ ⋅ ⋅ ⋅ ⋅ = Ω 63 . 12 0 0 0 0 0 0 114 . 13 065 . 4 0 0 0 0 065 . 4 562 . 177 0 0 0 0 0 0 10 425 . 2 0 0 0 0 0 0 10 518 . 2 10 805 . 7 0 0 0 0 10 805 . 7 10 409 . 3 7 7 6 6 8 (10) GLASS-EPOXY ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⋅ ⋅ ⋅ ⋅ ⋅ = Ω 021 . 13 0 0 0 0 0 0 644 . 8 593 . 2 0 0 0 0 593 . 2 236 . 37 0 0 0 0 0 0 10 5 . 2 0 0 0 0 0 0 10 66 . 1 10 979 . 4 0 0 0 0 10 979 . 4 10 149 . 7 7 7 6 6 7