Issue 48

Y. Khalfi et alii, Frattura ed Integrità Strutturale, 48 (2019) 208-221; DOI: 10.3221/IGF-ESIS.48.22 217 2 3 2 cr N a N E h  (32) where a is the length of the square plate and h is the thickness of the plate. The following dimensionless of Winkler’s and Pasternak’s elastic foundation parameters, as well as the critical buckling temperature difference are used in the present analysis 4 4 1 2 , W g a a k K k K D D   (33) where 3 2 2 / 12(1 ) D E h        (34) a/h Theories k 1 =0, k 2 =0 k 1 =10, k 2 =0 k 1 =10, k 2 =10 k 1 =0, k 2 =0 k 1 =10, k 2 =0 k 1 =10, k 2 =10 Isotropic v = 0.3 Orthotrophic E 1 / E 2 =10 25 40 Orthotrophic E 1 / E 2 =10 25 40 Orthotrophic E 1 / E 2 =10 25 40 5 present CPT FSDT HSDT 2.9512 3.0440 4.8755 3.6152 3.7080 5.5395 2.9498 3.0042 3.9345 2.9512 3.0440 4.8755 6.3487 9.1039 10.578 11.1628 23.4949 35.8307 6.1804 8.2199 9.1085 6.3487 9.1039 10.578 6.4378 9.1939 10.6685 11.2528 23.5849 35.9207 6.2265 8.2666 9.1564 6.4378 9.1939 10.6685 8.2156 10.9717 12.4463 13.0306 25.3627 37.6986 7.0759 9.1356 10.0504 8.2156 10.9717 12.4463 10 present CPT FSDT HSDT 3.4224 3.5151 5.3466 3.6152 3.7080 5.5395 3.4222 3.5088 5.1996 3.4224 3.5151 5.3466 9.3732 16.7719 22.2581 11.1628 23.4949 35.8307 9.2733 15.8736 20.3044 9.3732 16.7719 22.2581 9.4632 16.8620 22.3482 11.2528 23.5849 35.9207 9.3531 15.9501 20.3789 9.4632 16.8620 22.3482 11.2410 18.6397 24.1260 13.0306 25.3627 37.6986 10.9144 17.4460 21.8356 11.2410 18.6397 24.1260 20 present CPT FSDT HSDT 3.5650 3.6578 5.4893 3.6152 3.7080 5.5395 3.5650 3.6569 5.4711 3.5650 3.6578 5.4893 10.6534 21.3479 31.0685 11.1628 23.4949 35.8307 10.6199 20.9528 30.0139 10.6534 21.3479 31.0685 10.7435 21.4380 31.1586 12.0634 25.7465 39.4333 10.7085 21.0405 30.1009 10.7435 21.4380 31.1586 12.5212 23.2158 32.9364 13.0306 25.3627 37.6986 12.4555 22.7709 31.8171 12.5212 23.2158 32.9364 50 present CPT FSDT HSDT 3.6071 3.6999 5.5314 3.6152 3.7080 5.5395 3.6071 3.6998 5.5303 3.6071 3.6999 5.5314 11.0780 23.1225 34.9717 11.1628 23.4949 35.8307 11.0721 23.0464 34.7487 11.0780 23.1225 34.9717 11.1681 23.2125 35.0618 11.2528 23.5849 35.9207 11.1621 23.1360 34.8386 11.1681 23.2125 35.0618 12.9458 24.9903 36.8396 13.0306 25.3627 37.6986 12.9379 24.9105 36.6118 12.9458 24.9903 36.8396 100 present CPT FSDT HSDT 3.6132 3.7060 5.5375 3.6152 3.7080 5.5395 3.6132 3.7060 5.5373 3.6132 3.7060 5.5375 11.1415 23.4007 35.6120 11.1628 23.4949 35.8307 11.1400 23.3810 35.5538 11.1415 23.4007 35.6120 11.2315 23.4907 35.7021 11.2528 23.5849 35.9207 11.2300 23.4711 35.6438 11.2315 23.4907 35.7021 13.0093 25.2685 37.4798 13.0306 25.3627 37.6986 13.0076 25.2484 37.4210 13.0093 25.2685 37.4798 Table 2 : Comparison of nondimensional critical buckling load of square plates subjected to uniaxial compression. In order to verify the mechanical buckling solutions determined in this work, the results of composite plates under uniaxial and biaxial loading are obtained and compared with those predicted by CPT, FSDT, and HSDT as indicated in Tables 2 and 3.It is clear that the results show significant differences between the shear deformation theories and the classical plate theory, due to the shear deformation effect. In addition, an excellent agreement is obtained between the current theory and the HSDT for all side-to-thickness ratio values a/h and the modulus ratios E 1 /E 2 . The disagreement between the present theory RPT and HSDT on the one hand and the first order shear theory FSDT on the other hand increases as the side-to- thickness a/h and the modulus ratios E 1 /E 2 increases. It can also be noted that the dimensionless critical load of buckling increases rapidly with the increase of the side-to-thickness ratio a/h , while this dimensionless load ceases to increase when