Issue 51

A. Chikh, Frattura ed Integrità Strutturale, 51 (2020) 115-126; DOI: 10.3221/IGF-ESIS.51.09 126 Detailed mathematical formulations are given and numerical results are established, while the emphasis is set on examining the effect of the several parameters. The results of the actual theory are almost identical to each other and conform well with the existing solutions. R EFERENCES [1] Wang, C. M., Lam, K. Y., and He, X. Q. (1998). Exact Solutions for Timoshenko Beams on Elastic Foundations Using Green’s Functions ∗ . Mechanics of Structures and Machines, 26(1), 101–113. DOI: 10.1080/08905459808945422. [2] Chikh, A., Bakora, A., Heireche, H., Houari, M. S. A., Tounsi, A., and Bedia, E. A. A. (2016). Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory. Structural Engineering and Mechanics, 57(4), 617–639. DOI:10.12989/sem.2016.57.4.617. [3] Akbaş, Ş. D. (2015). Free vibration and bending of functionally graded beams resting on elastic foundation. Research on Engineering Structures and Materials, 1(1), 25–37. DOI:10.17515/resm2015.03st0107 . [4] Chikh, A., Tounsi, A., Hebali, H., and Mahmoud, S. R. (2017). Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT. Smart Structures and Systems, 19(3), 289–297. DOI: 10.12989/sss.2017.19.3.289. [5] Fahsi, A., Tounsi, A., Hebali, H., Chikh, A., Bedia, E. A. A., and Mahmoud, S. R. (2017). A four variable refined nth- order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates. Geomechanics and Engineering, 13(3), 385–410. DOI: 10.12989/gae.2017.13.3.385. [6] Omidi, N., Khorramabadi, M. K., and Niknejad, A. (2009). Dynamic stability of functionally graded beams with piezoelectric layers located on a continuous elastic foundation. Journal of Solid Mechanics, 1(2), 130–136. http://jsm.iau-arak.ac.ir/article_514296.html. [7] Zhong, Z., and Yu, T. (2007). Analytical solution of a cantilever functionally graded beam. Composites Science and Technology, 67(3–4), 481–488. DOI: 10.1016/j.compscitech.2006.08.023. [8] Thai, H.-T., and Vo, T. P. (2012). Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories. International Journal of Mechanical Sciences, 62(1), 57–66. DOI: 10.1016/j.ijmecsci.2012.05.014. [9] Hua Zhu. (2018). Stress performance of embedded carbon fiber reinforced plastics plate consolidated reinforced concrete structure. Frattura ed Integrità Strutturale, 12(46), 361-370. DOI: 10.3221/IGF-ESIS.46.33. [10] Bouchikhi, A. S., Lousdad, A., Yassine, K., Bouida, N. E., Gouasmi, S., and Megueni, A. (2019). Finite Element Analysis of Interactions between two cracks in FGM notched Plate under Mechanical Loading. Frattura ed Integrità Strutturale, 13(48), 174-192. DOI: 10.3221/IGF-ESIS.48.20. [11] Khalfi, Y., Bouchikhi, A. S., and Bellebna, Y. (2019). Mechanical stability investigation of advanced composite plates resting on elastic foundations using a new four-unknown refined theory. Frattura e Integrita Strutturale, (48), 208-221. DOI: 10.3221/IGF-ESIS.48.22. [12] Meftah, K., and Sedira, L. (2019). A nonlinear elasto-plastic analysis of Reissner-Mindlin plates by finite element method. Frattura ed Integrità Strutturale, 13(50), 276-285. DOI: 10.3221/IGF-ESIS.50.23. [13] Saidi, H., and Sahla, M. (2019). Vibration analysis of functionally graded plates with porosity composed of a mixture of Aluminum (Al) and Alumina (Al 2 O 3 ) embedded in an elastic medium. Frattura ed Integrità Strutturale, 13(50), 286-299. DOI: 10.3221/IGF-ESIS.50.24. [14] Chen, W. Q., Lü, C. F., and Bian, Z. G. (2004). A mixed method for bending and free vibration of beams resting on a Pasternak elastic foundation. Applied Mathematical Modelling, 28(10), 877–890. DOI: 10.1016/j.apm.2004.04.001. [15] Ying, J., Lü, C. F., and Chen, W. Q. (2008). Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations. Composite Structures, 84(3), 209–219. DOI: 10.1016/j.compstruct.2007.07.004 [16] Rao, G. V., and Raju, K. K. (2002). Elegant and accurate closed form solutions to predict vibration and buckling behaviour of slender beams on Pasternak foundation. Indian Journal of Engineering & Materials Sciences, 9, 98–102. http://nopr.niscair.res.in/handle/123456789/19729.