Issue 51

A. Chikh, Frattura ed Integrità Strutturale, 51 (2020) 115-126; DOI: 10.3221/IGF-ESIS.51.09 120 R ESULTS AND DISCUSSION n this study, bending; buckling and free vibration investigation on SS FG beam by the present theory is suggested for investigation. The FG beams are made of Aluminum (Al; E m = 70 GPa, ρ m = 2702 kg/m 3 , ν m = 0.3) and alumina (Al 2 O 3 ; Ec = 380 GPa, ρ c = 3960 kg/m 3 , ν c = 0.3) and their properties vary in the direction of the thickness of the beam according to power-law. The lower part of the FG-beam is rich in aluminum, while the upper part of the FG-beam is alumina rich. For convenience, the following dimensionless parameters are used: 2 4 2 4 2 0 4 4 ( / 2)100 , ( / 2) , , , p c c w w p k L AL w L E I k L N L w L K K N EI EI EI EI qL         (26) The buckling answer of an FG beam under axial force   0 N has been studied. A dimensionless; critical-buckling load is shown in Tab. 2. The critical-buckling load was obtained for various values regarding the foundation parameters w K and p K . The results were contrasted with those delivered by Rao et al. [16]. Tab. 2 reveals that this study's results agreed with those available in the literature. Tab. 3 present the comparisons of the dimensionless natural frequency obtained by the present beam theory with other beams theories results of Chen et al. [14] and Ying et al. [15] for three divers values of the thickness-to-length ratio, and for divers values of foundation parameters w K and p K . As can be seen, the new results are in excellent concordat with previous ones. Foundation Parameters L/h = 120 L/h = 15 L/h = 5 w K p K Chen et al. [14] Ying et al. [15] Present Chen et al. [14] Ying et al. [15] Present Chen et al. [14] Ying et al. [15] Present 0 0 1.30229 1.30229 1.30416 1.31528 1.31527 1.30416 1.42026 1.42024 1.30416 10 0.64483 0.64483 0.64527 0.64835 0.64830 0.64527 0.67820 0.67451 0.64527 25 0.36611 0.36611 0.36624 0.36742 0.36735 0.36624 0.38170 0.37667 0.36624 10 0 1.18057 1.18057 1.18210 1.19140 1.19134 1.18210 1.28260 1.27731 1.18210 10 0.61333 0.61333 0.61372 0.61656 0.61649 0.61372 0.64639 0.64025 0.61372 25 0.35567 0.35567 0.35579 0.35692 0.35684 0.35579 0.37206 0.36568 0.35579 10 2 0 0.64007 0.64007 0.64051 0.64377 0.64343 0.64051 0.69610 0.66848 0.64051 10 0.42558 0.42558 0.42576 0.42741 0.42716 0.42576 0.45927 0.43881 0.42576 25 0.28285 0.28285 0.28291 0.28380 0.28360 0.28291 0.30516 0.28944 0.28291 Table 1 Comparisons of the mid-span deflection 4 ( / 2)100 ( / 2) c w L E I w L qL  of an isotropic-homogeneous beam on elastic foundations due to a uniform pressure. I