Issue 48

Y. Khalfi et alii, Frattura ed Integrità Strutturale, 48 (2019) 208-221; DOI: 10.3221/IGF-ESIS.48.22 218 this ratio exceeds 25 (the plate becomes thinner more and more), and the results obtained by shear deformation theories (current RPT theory and first-order shear theory FSDT and high order theory HSDT) become identical to that obtained by conventional CPT theory, implying that the effect transverse shear becomes useless. Indeed, the non dimensional critical load of the buckling does not depend on the variation of side-to-thickness according to the classical theory which neglects the effect of the transverse shear. It is clear to note the considerable increase in dimensionless critical load of buckling when the plate rests on an elastic foundation. It should be noted that the unknown function in present theory is 4, while the unknown function in FSDT and HSDT is 5. It can be concluded that the present theory is not only accurate but also simple in predicting the critical buckling load of rectangular composite plates. 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 1.4756 1.5220 2.4378 1.8076 1.8540 2.7698 1.4749 1.5070 2.1138 1.4756 1.5220 2.4378 2.8549 3.3309 3.4800 5.5814 8.4069 10.8715 2.8319 3.1422 3.2822 2.8549 3.3309 3.4800 2.8729 a 3.3489 a 3.6905 a 5.6264 8.4249 a 10.8895 a 2.8341 a 3.1453 a 3.2859 a 2.8729 a 3.3489 a 3.6905a 4.1078 4.2378 a 4.5794 a 6.5153 9.3138 a 11.7783 a 2.9976 a 3.3390 a 3.4994 a 4.1078 4.2378 a 4.5794 a 10 present CPT FSDT HSDT 1.7112 1.7576 2.6733 1.8076 1.8540 2.7698 1.7111 1.7552 2.6208 1.7112 1.7576 2.6733 4.6718 6.0646 a 7.2536 5.5814 8.4069 10.8715 4.6367 5.8370 6.6325 4.6718 6.0646 a 7.2536 4.6898 a 6.0826 a 7.2716 a 5.6264 8.4249 a 10.8895 a 4.6765 5.8491 a 6.6444 a 4.6898 a 6.0826 a 7.2716 a 5.5787 a 6.9714 a 8.1604 a 6.5153 9.3138 a 11.7783 a 5.2882 a 6.4367 a 7.2181 a 5.5787 a 6.9714 a 8.1604 a 20 present CPT FSDT HSDT 1.7825 1.8289 2.7446 1.8076 1.8540 2.7698 1.7825 1.8286 2.7380 1.7825 1.8289 2.7446 5.3267 7.6643 a 9.6614 a 5.5814 8.4069 10.8715 5.3100 7.5546 9.3049 5.3267 7.6643 a 9.6614 a 5.3717 7.6823 a 9.6794 a 5.6264 8.4249 a 10.8895 a 5.3542 7.5716 a 9.3217 a 5.3717 7.6823 a 9.6794 a 6.2606 8.5711 a 10.5682 a 6.5153 9.3138 a 11.7783 a 6.2277 8.4083 a 10.1518 a 6.2606 8.5711 a 10.5682 a 50 present CPT FSDT HSDT 1.8036 1.8500 2.7657 1.8076 1.8540 2.7698 1.8036 1.8499 2.7653 1.8036 1.8500 2.7657 5.5390 8.2784 a 10.6576 a 5.5814 8.4069 10.8715 5.5361 8.2566 10.5810 5.5390 8.2784 a 10.6576 a 5.5840 8.2964 a 10.6756 a 5.6264 8.4249 a 10.8895 a 5.5810 8.2744 a 10.5989 a 5.5840 8.2964 a 10.6756 a 6.4729 9.1853 a 11.5645 a 6.5153 9.3138 a 11.7783 a 6.4689 9.1597 a 11.4835 a 6.4729 9.1853 a 11.5645 a 100 present CPT FSDT HSDT 1.8066 1.8530 2.7687 1.8076 1.8540 2.7698 1.8066 1.8530 2.7687 1.8066 1.8530 2.7687 5.5707 8.3744 a 10.8172 a 5.5814 8.4069 10.8715 5.5700 8.3687 10.7972 5.5707 8.3744 a 10.8172 a 5.6158 8.3924 a 10.8352 a 5.6264 8.4249 a 10.8895 a 5.6150 8.3867 a 10.8151 a 5.6158 8.3924 a 10.8352 a 6.5046 9.2813 a 11.7241 a 6.5153 9.3138 a 11.7783 a 6.5038 9.2752 a 11.7035 a 6.5046 9.2813 a 11.7241 a a Mode for plate is ( m, n ) = (1,2). Table 3 : Comparison of nondimensional critical buckling load of square plates subjected to biaxial compressive load Figures 4 show the effect of the side-to-thickness ratio (a/h) on the dimensionless critical buckling N when the square plate ( a/b = 1) without elastic foundation or resting on Winkler’s or Pasternak’s elastic foundations using the present refined shear deformation theory. It is noted that N increases rapidly with increasing side-to-thickness ratio. However, for the plate without elastic foundation or resting on one parameter Winkler’s foundation, the variation of the dimensionless critical buckling N is almost independent of the side-to-thickness ratio (a/h) when this latter is higher than 25 . It can be also seen that the presence of elastic foundations lead to an increase of the dimensionless critical buckling N . Figures 5 and 6 show the variation of the critical load of the dimensionless buckling N of the rectangular composite plates without elastic foundation or resting on Winkler’s or Pasternak’s elastic foundations as a function of the modulus ratio ( E 1 /E 2 ). The plate is assumed to be subjected to axial loading shown in Fig. 3 (uniaxial compression and biaxial compression). It is found that the critical load of dimensionless buckling increases monotonically as the the modulus ratio ( E 1 /E 2 ) increases. It is also noted that the critical dimensionless load N of the rectangular composite plates under unaxial compression is greater than that of a plate under biaxial compression.