Large Deflection Analysis of Graphene Sheets in the Thermal Environment Using Higher-Order Nonlocal Strain Gradient Principle

[1]   Harik, I.E., 1984. Analytical solution to the orthotropic sector. Journal of Engineering Mechanics, 110 (4), pp.554-568.

[2]   Kumar, R., Kumar, M. & Luthra, G., 2023. Fundamental approaches and applications of nanotechnology: A mini review. Materials Today: Proceedings.

[3]   Farajpour, A., Mohammadi, M., Shahidi, A.R. & Mahzoon, M., 2011. Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model. Physica E: Low-dimensional Systems and Nanostructures, 43 (10), pp.1820-1825.

[4]   Eringen, A.C., 1972. Nonlocal polar elastic continua. International Journal of Engineering Science, 10 (1), pp.1-16.

[5]   Trabelsi, S., Frikha, A., Zghal, S. & Dammak, F., 2018. Thermal post-buckling analysis of functionally graded material structures using a modified fsdt. International Journal of Mechanical Sciences, 144, pp.74-89.

[6]   Trabelsi, S., Frikha, A., Zghal, S. & Dammak, F., 2019. A modified fsdt-based four nodes finite shell element for thermal buckling analysis of functionally graded plates and cylindrical shells. Engineering Structures, 178, pp.444-459.

[7]   Zghal, S., Frikha, A. & Dammak, F., 2020. Large deflection response-based geometrical nonlinearity of nanocomposite structures reinforced with carbon nanotubes. Applied Mathematics and Mechanics, 41 (8), pp.1227-1250.

[8]   Joueid, N., Zghal, S., Chrigui, M. & Dammak, F., 2023. Thermoelastic buckling analysis of plates and shells of temperature and porosity dependent functionally graded materials. Mechanics of Time-Dependent Materials.

[9]   Zghal, S., Joueid, N., Tornabene, F., Dimitri, R., Chrigui, M. & Dammak, F., 2024. Time-dependent deflection responses of fg porous structures subjected to different external pulse loads. Journal of Vibration Engineering & Technologies, 12 (1), pp.857-876.

[10] Trabelsi, S., Zghal, S. & Dammak, F., 2020. Thermo-elastic buckling and post-buckling analysis of functionally graded thin plate and shell structures. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 42 (5), pp.233.

[11] Zghal, S., Frikha, A. & Dammak, F., 2018. Free vibration analysis of carbon nanotube-reinforced functionally graded composite shell structures. Applied Mathematical Modelling, 53, pp.132-155.

[12] Zghal, S. & Dammak, F., 2020. Vibrational behavior of beams made of functionally graded materials by using a mixed formulation. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 234 (18), pp.3650-3666.

[13] Zghal, S., Trabelsi, S. & Dammak, F., 2022. Post-buckling behavior of functionally graded and carbon-nanotubes based structures with different mechanical loadings. Mechanics Based Design of Structures and Machines, 50 (9), pp.2997-3039.

[14] Zghal, S., Frikha, A. & Dammak, F., 2017. Static analysis of functionally graded carbon nanotube-reinforced plate and shell structures. Composite Structures, 176, pp.1107-1123.

[15] Zghal, S., Frikha, A. & Dammak, F., 2018. Mechanical buckling analysis of functionally graded power-based and carbon nanotubes-reinforced composite plates and curved panels. Composites Part B: Engineering, 150, pp.165-183.

[16] Frikha, A., Zghal, S. & Dammak, F., 2018. Dynamic analysis of functionally graded carbon nanotubes-reinforced plate and shell structures using a double directors finite shell element. Aerospace Science and Technology, 78, pp.438-451.

[17] Zghal, S., Frikha, A. & Dammak, F., 2018. Non-linear bending analysis of nanocomposites reinforced by graphene-nanotubes with finite shell element and membrane enhancement. Engineering Structures, 158, pp.95-109.

[18] Mehar, K. & Panda, S.K., 2019. Theoretical deflection analysis of multi-walled carbon nanotube reinforced sandwich panel and experimental verification. Composites Part B: Engineering, 167, pp.317-328.

[19] Mindlin, R.D., 1965. Second gradient of strain and surface-tension in linear elasticity. International Journal of Solids and Structures, 1 (4), pp.417-438.

[20] Aifantis, E.C., 1999. Strain gradient interpretation of size effects. International Journal of Fracture, 95 (1), pp.299-314.

[21] Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J. & Tong, P., 2003. Experiments and theory in strain gradient elasticity. Journal of the Mechanics and Physics of Solids, 51 (8), pp.1477-1508.

[22] Lim, C.W., Zhang, G. & Reddy, J.N., 2015. A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. Journal of the Mechanics and Physics of Solids, 78, pp.298-313.

[23] Gui, Y. & Wu, R., 2023. Buckling analysis of embedded thermo-magneto-electro-elastic nano cylindrical shell subjected to axial load with nonlocal strain gradient theory. Mechanics Research Communications, 128, pp.104043.

[24] Lu, L., Guo, X. & Zhao, J., 2019. A unified size-dependent plate model based on nonlocal strain gradient theory including surface effects. Applied Mathematical Modelling, 68, pp.583-602.

[25] Arefi, M., Kiani, M. & Rabczuk, T., 2019. Application of nonlocal strain gradient theory to size dependent bending analysis of a sandwich porous nanoplate integrated with piezomagnetic face-sheets. Composites Part B: Engineering, 168, pp.320-333.

[26] Farajpour, A., Yazdi, M.R.H., Rastgoo, A. & Mohammadi, M., 2016. A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment. Acta Mechanica, 227 (7), pp.1849-1867.

[27] Nematollahi, M.S. & Mohammadi, H., 2019. Geometrically nonlinear vibration analysis of sandwich nanoplates based on higher-order nonlocal strain gradient theory. International Journal of Mechanical Sciences, 156, pp.31-45.

[28] Thai, C.H., Hung, P.T., Nguyen-Xuan, H. & Phung-Van, P., 2023. A size-dependent meshfree approach for magneto-electro-elastic functionally graded nanoplates based on nonlocal strain gradient theory. Engineering Structures, 292, pp.116521.

[29] Kumar, D., Ali, S.F. & Arockiarajan, A., 2021. Theoretical and experimental studies on large deflection analysis of double corrugated cantilever structures. International Journal of Solids and Structures, 228, pp.111126.

[30] Han, P., Tian, F. & Babaei, H., 2023. Thermally induced large deflection analysis of graphene platelet reinforced nanocomposite cylindrical panels. Structures, 53, pp.1046-1056.

[31] Bertóti, E., 2020. Primal- and dual-mixed finite element models for geometrically nonlinear shear-deformable beams – a comparative study. Computer Assisted Methods in Engineering and Science, 27 (4), pp.285-315.

[32] Liu, L., Zhong, X. & Liao, S., 2023. Accurate solutions of a thin rectangular plate deflection under large uniform loading. Applied Mathematical Modelling, 123, pp.241-258.

[33] Wang, J. & Xiao, J., 2022. Analytical solutions of bending analysis and vibration of rectangular nano laminates with surface effects. Applied Mathematical Modelling, 110, pp.663-673.

[34] Mehar, K., Panda, S.K. & Mahapatra, T.R., 2018. Thermoelastic deflection responses of cnt reinforced sandwich shell structure using finite element method. Scientia Iranica, 25 (5), pp.2722-2737.

[35] Mehar, K., Panda, S.K. & Patle, B.K., 2018. Stress, deflection, and frequency analysis of cnt reinforced graded sandwich plate under uniform and linear thermal environment: A finite element approach. Polymer Composites, 39 (10), pp.3792-3809.

[36] Mehar, K. & Panda Subrata, K., 2017. Nonlinear static behavior of fg-cnt reinforced composite flat panel under thermomechanical load. Journal of Aerospace Engineering, 30 (3), pp.04016100.

[37] Mehar, K. & Panda, S.K., 2018. Elastic bending and stress analysis of carbon nanotube-reinforced composite plate: Experimental, numerical, and simulation. Advances in Polymer Technology, 37 (6), pp.1643-1657.

[38] Mehar, K., Panda, S.K. & Mahapatra, T.R., 2018. Large deformation bending responses of nanotube-reinforced polymer composite panel structure: Numerical and experimental analyses. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 233 (5), pp.1695-1704.

[39] Ambartsumian, S.A., 1960. On the theory of bending of anisotropic plates and shallow shells. Journal of Applied Mathematics and Mechanics, 24 (2), pp.500-514.

[40] Reddy, J.N., 1984. A simple higher-order theory for laminated composite plates. Journal of Applied Mechanics, 51 (4), pp.745-752.

[41] Reissner, E., 1975. On transverse bending of plates, including the effect of transverse shear deformation. International Journal of Solids and Structures, 11 (5), pp.569-573.

[42] Touratier, M., 1991. An efficient standard plate theory. International Journal of Engineering Science, 29 (8), pp.901-916.

[43] Soldatos, K.P., 1992. A transverse shear deformation theory for homogeneous monoclinic plates. Acta Mechanica, 94 (3), pp.195-220.

[44] Aydogdu, M., 2009. A new shear deformation theory for laminated composite plates. Composite Structures, 89 (1), pp.94-101.

[45] Mantari, J.L., Oktem, A.S. & Guedes Soares, C., 2012. A new higher order shear deformation theory for sandwich and composite laminated plates. Composites Part B: Engineering, 43 (3), pp.1489-1499.

[46] Li, Q., Wu, D., Chen, X., Liu, L., Yu, Y. & Gao, W., 2018. Nonlinear vibration and dynamic buckling analyses of sandwich functionally graded porous plate with graphene platelet reinforcement resting on winkler–pasternak elastic foundation. International Journal of Mechanical Sciences, 148, pp.596-610.

[47] Kerr, A.D. & Alexander, H., 1968. An application of the extended kantorovich method to the stress analysis of a clamped rectangular plate. Acta Mechanica, 6 (2), pp.180-196.

[48] Bellman, R. & Casti, J., 1971. Differential quadrature and long-term integration. Journal of Mathematical Analysis and Applications, 34 (2), pp.235-238.

[49] Mousavi, S.M. & Tahani, M., 2012. Analytical solution for bending of moderately thick radially functionally graded sector plates with general boundary conditions using multi-term extended kantorovich method. Composites Part B: Engineering, 43 (3), pp.1405-1416.