References
- Akbas, S,.D. (2017), "Vibration and static analysis of functionally graded porous plates", J. Appl. Comput. Mech., 3(3), 199-207. http://doi.org/10.22055/jacm.2017.21540.1107.
- Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603
- Al-Furjan, M., Habibi, M., Shan, L. and Tounsi, A. (2021), "On the vibrations of the imperfect sandwich higher-order disk with a lactic core using generalize differential quadrature method", Compos. Struct., 257, 113150. https://doi.org/10.1016/j.compstruct.2020.113150.
- Al-Osta, M.A., Saidi, H., Tounsi, A., Al-Dulaijan, S., Al-Zahrani, M., Sharif, A. and Tounsi, A. (2021), "Influence of porosity on the hygro-thermo-mechanical bending response of an AFG ceramic-metal plates using an integral plate model", Smart Struct. Syst., 28(4), 499-513. https://doi.org/10.12989/sss.2021.28.4.499.
- Arshid, E., Khorasani, M., Soleimani-Javid, Z., Amir, S. and Tounsi, A. (2021), "Porosity-dependent vibration analysis of FG microplates embedded by polymeric nanocomposite patches considering hygrothermal effect via an innovative plate theory", Eng. Comput., 1-22. https://doi.org/10.1007/s00366-021-01382-y.
- Attia, A., Berrabah, A. T., Bousahla, A. A., Bourada, F., Tounsi, A. and Mahmoud, S (2021), "Free vibration analysis of FG plates under thermal environment via a simple 4-unknown HSDT", Steel Compos. Struct., 41(6), 899-910. https://doi.org/10.12989/scs.2021.41.6.899.
- Bazilevs, Y., Calo, V.M., Zhang, Y. and Hughes, T.J. (2006), "Isogeometric fluid-structure interaction analysis with applications to arterial blood flow", Comput. Mech., 38(4-5), 310-322. https://doi.org/10.1007/s00466-006-0084-3.
- Bekkaye, T.H.L., Fahsi, B., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H. and Al-Zahrani, M.M. (2020), "Porosity-dependent mechanical behaviors of FG plate using refined trigonometric shear deformation theory", Comput. Concrete, 26(5), 439-450. https://doi.org/10.12989/cac.2020.26.5.439.
- Bellifa, H., Selim, M. M., Chikh, A., Bousahla, A. A., Bourada, F., Tounsi, A. and Tounsi, A. (2021), "Influence of porosity on thermal buckling behavior of functionally graded beams", Smart Struct. Syst., 27(4), 719-728. https://doi.org/10.12989/sss.2021.27.4.719.
- Bakoura, A., Bourada, F., Bousahla, A.A., Tounsi, A., Benrahou, K.H., Tounsi, A. and Mahmoud, S. (2021), "Buckling analysis of functionally graded plates using HSDT in conjunction with the stress function method", Comput. Concrete, 27(1), 73-83. https://doi.org/10.12989/cac.2021.27.1.073.
- Bouafia, K., Selim, M.M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A. and Tounsi, A. (2021), "Bending and free vibration characteristics of various compositions of FG plates on elastic foundation via quasi 3D HSDT model", Steel Compos. Struct., 41(4), 487-503. https://doi.org/10.12989/scs.2021.41.4.487.
- Chami, K., Messafer, T. and Hadji, L. (2020), "Analytical modeling of bending and free vibration of thick advanced composite beams resting on Winkler-Pasternak elastic foundation", Earthq. Struct., 19(2), 91-101. https://doi.org/10.12989/eas.2020.19.2.091.
- Cottrell, J.A., Hughes, T.J. and Bazilevs, Y. (2009), Isogeometric Analysis: Toward Integration of CAD and FEA, John Wiley and Sons, NJ, USA.
- COX, M. (1971), "The numerical evaluation of B-Splines", IMA J. Appl. Math., 10(2), 134-149. https://doi.org/10.1093/imamat/10.2.134.
- De Boor, C. (1972), "On calculating with B-splines", J. Approximation Theory, 6(1), 50-62. https://doi.org/10.1016/0021-9045(72)90080-9
- Guellil, M., Saidi, H., Bourada, F., Bousahla, A.A., Tounsi, A., Al-Zahrani, M.M. and Mahmoud, S. (2021), "Influences of porosity distributions and boundary conditions on mechanical bending response of functionally graded plates resting on Pasternak foundation", Steel Compos. Struct., 38(1), 1-15. https://doi.org/10.12989/scs.2021.38.1.001.
- Ha, L.T. (2022), "Free vibration of a bi-directional imperfect functionally graded sandwich beams", Modern Mechanics and Applications, Springer, Singapore. 100-111. https://doi.org/10.1007/978-981-16-3239-6_8.
- Hadji, L., Bernard, F., Safa, A. and Tounsi, A. (2021), "Bending and free vibration analysis for FGM plates containing various distribution shape of porosity", Adv. Mater. Res., 10(2), 115-135. https://doi.org/10.12989/amr.2021.10.2.115.
- Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011), "A new exact analytical approach for free vibration of Reissner-Mindlin functionally graded rectangular plates", J. Mech. Sci., 53(1), 11-22. https://doi.org/10.1016/j.ijmecsci.2010.10.002.
- Hughes, T.J., Cottrell, J.A. and Bazilevs, Y. (2005), "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement", Comput. Methods Appl. Mech. Eng., 194(39-41), 4135-4195. https://doi.org/10.1016/j.cma.2004.10.008.
- Hachemi, H., Bousahla, A.A., Kaci, A., Bourada, F., Tounsi, A., Benrahou, K.H. and Mahmoud, S. (2021), "Bending analysis of functionally graded plates using a new refined quasi-3D shear deformation theory and the concept of the neutral surface position", Steel Compos. Struct., 39(1), 51-64. https://doi.org/10.12989/scs.2021.39.1.051.
- Hebali, H., Chikh, A., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Hussain, M. and Tounsi, A. (2022), "Effect of the variable visco-Pasternak foundations on the bending and dynamic behaviors of FG plates using integral HSDT model", Arch. Appl. Mech., 83(2), 177-191. https://doi.org/10.12989/gae.2022.28.1.049.
- Keddouri, A., Hadji, L. and Tounsi, A. (2019), "Static analysis of functionally graded sandwich plates with porosities", Adv. Mater. Res., 8(3), 155-177. https://doi.org/10.12989/amr.2019.8.3.155.
- Kaddari, M., Kaci, A., Bousahla, A.A., Tounsi, A., Bourada, F., Bedia, E.A. and Al-Osta, M.A. (2020), "A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: Bending and free vibration analysis", Comput. Concrete, 25(1), 37-57. https://doi.org/10.12989/cac.2020.25.1.037.
- Kumar, Y., Gupta, A. and Tounsi, A. (2021), "Size-dependent vibration response of porous graded nanostructure with FEM and nonlocal continuum model", Adv. Nano Res., 11(1), 1-17. https://doi.org/10.12989/anr.2021.11.1.001.
- Kouider, D., Kaci, A., Selim, M.M., Bousahla, A.A., Bourada, F., Tounsi, A. and Hussain, M. (2021), "An original four-variable quasi-3D shear deformation theory for the static and free vibration analysis of new type of sandwich plates with both FG face sheets and FGM hard core", Steel Compos. Struct., 41(2), 167-191. https://doi.org/10.12989/scs.2021.41.2.167.
- Lei, J., Y. He, Z. Li, S. Guo and D. Liu. (2019), "Postbuckling analysis of bi-directional functionally graded imperfect beams based on a novel third-order shear deformation theory", Compos. Struct., 209, 811-829. https://doi.org/10.1016/j.compstruct.2018.10.106.
- Les, P. and T. Wayne. (1997), The NURBS book, Springer-Verlag, Berlin, Germany.
- Nemat-Alla, M. (2003), "Reduction of thermal stresses by developing two-dimensional functionally graded materials", J. Solids Struct., 40(26), 7339-7356. https://doi.org/10.1016/j.ijsolstr.2003.08.017.
- Nguyen, K.D. and Nguyen-Xuan, H. (2015), "An isogeometric finite element approach for threedimensional static and dynamic analysis of functionally graded material plate structures", Compos. Struct., 132, 423-439. https://doi.org/10.1016/j.compstruct.2015.04.063.
- Menasria, A., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H. and Mahmoud, S. (2020), "A four-unknown refined plate theory for dynamic analysis of FG-sandwich plates under various boundary conditions", Steel Compos. Struct., 36(3), 355-367. https://doi.org/10.12989/scs.2020.36.3.355.
- Merazka, B., Bouhadra, A., Menasria, A., Selim, M.M., Bousahla, A.A., Bourada, F. and Al-Zahrani, M.M. (2021), "Hygrothermo-mechanical bending response of FG plates resting on elastic foundations", Steel Compos. Struct., 39(5), 631-643. https://doi.org/10.12989/scs.2021.39.5.631.
- Mudhaffar, I.M., Tounsi, A., Chikh, A., Al-Osta, M.A., Al-Zahrani, M.M. and Al-Dulaijan, S.U. (2021), "Hygro-thermo-mechanical bending behavior of advanced functionally graded ceramic metal plate resting on a viscoelastic foundation", Structures, 33, 2177-2189. https://doi.org/10.1016/j.istruc.2021.05.090.
- Ramteke, P.M. and Panda, S.K. (2021), "Free vibrational behaviour of multi-directional porous functionally graded structures", Arabian J. Sci. Eng., 46, 7741-7756. https://doi.org/10.1007/s13369-021-05461-6 1-16.
- Rachid, A., Ouinas, D., Lousdad, A., Zaoui, F.Z., Achour, B., Gasmi, H. and Tounsi, A. (2022), "Mechanical behavior and free vibration analysis of FG doubly curved shells on elastic foundation via a new modified displacements field model of 2D and quasi-3D HSDTs", Thin-Walled Struct., 172, 108783. https://doi.org/10.1016/j.tws.2021.108783.
- Saad, M., Hadji, L. and Tounsi, S. (2021), "Effect of porosity on the free vibration analysis of various functionally graded sandwich plates", Adv. Mater. Res., 10(4), 293-311. https://doi.org/10.12989/amr.2021.10.4.293.
- Sah, S.K. and Ghosh, A. (2022), "Influence of porosity distribution on free vibration and buckling analysis of multidirectional functionally graded sandwich plates", Compos. Struct., 279, 114795. https://doi.org/10.1016/j.compstruct.2021.114795.
- Son, T. and Huu-Tai, T. (2019), "Free-vibration analysis of multidirectional functionally graded plates based on 3D isogeometric analysis", J. Sci. Technol. Civil Eng., 13(2), 1-11. https://doi.org/10.31814/stce.nuce2019-13(2)-01.
- Tahir, S. I., Chikh, A., Tounsi, A., Al-Osta, M.A., Al-Dulaijan, S. U. and Al-Zahrani, M.M. (2021), "Wave propagation analysis of a ceramic-metal functionally graded sandwich plate with different porosity distributions in a hygro-thermal environment", Compos. Struct., 269, 114030. https://doi.org/10.1016/j.compstruct.2021.114030.
- Tahir, S. I., Tounsi, A., Chikh, A., Al-Osta, M. A., Al-Dulaijan, S. U. and Al-Zahrani, M.M. (2021), "An integral four-variable hyperbolic HSDT for the wave propagation investigation of a ceramic-metal FGM plate with various porosity distributions resting on a viscoelastic foundation", Waves Random Complex Media, 1-24. https://doi.org/10.1080/17455030.2021.1942310.
- Yin, S., Deng, Y., Yu, T., Gu, S. and Zhang, G. (2021), "Is geometric analysis for non-classical BernoulliEuler beam model incorporating microstructure and surface energy effects", Appl. Math. Modelling, 89, 470-485. http://doi.org/10.1016/j.apm.2020.07.015.
- Yin, S., Deng, Y., Zhang, G., Yu, T. and Gu, S. (2020), "A new isogeometric Timoshenko beam model incorporating microstructures and surface energy effects", Math. Mech. Solids, 25(10), 2005-2022. https://doi.org/10.1177/1081286520917998.
- Yin, S., Xiao, Z., Deng, Y., Zhang, G., Liu, J. and Gu, S. (2021), "Isogeometric analysis of size-dependent Bernoulli-Euler beam based on a reformulated strain gradient elasticity theory", Comput. Struct., 253, 106577. https://doi.org/10.1016/j.compstruc.2021.106577.
- Zaitoun, M. W., Chikh, A., Tounsi, A., Al-Osta, M.A., Sharif, A., Al-Dulaijan, S.U. and Al-Zahrani, M. M. (2022), "Influence of the visco-Pasternak foundation parameters on the buckling behavior of a sandwich functional graded ceramic-metal plate in a hygrothermal environment", Thin-Walled Struct., 170, 108549. https://doi.org/10.1016/j.tws.2021.108549.
- Zine, A., Bousahla, A.A., Bourada, F., Benrahou, K.H., Tounsi, A., Bedia, E.A., Mahmoud, S.R. and Tounsi, A. (2020), "Bending analysis of functionally graded porous plates via a refined shear deformation theory", Comput. Concrete, 26(1), 63-74. https://doi.org/10.12989/cac.2020.26.1.063.