Abstract
In this paper, we extend the Kirchhoff–Love model to thermal buckling and post-buckling analysis of functionally graded structures. The kernel idea of the proposed model consists of the consideration of large displacements and finite rotation to accurately model the thermal effects on buckling and post-buckling behavior of such structures. Both uniform and nonuniform temperature distributions are considered. Material properties of the FG structures are graded in the thickness direction and assumed to obey a power law distribution of the volume fraction of the constituents. The effectiveness and usefulness of the proposed model are highlighted through different numerical examples, and the effects of the volume fraction exponent, thermal loads, length-to-thickness ratio, boundary conditions and geometrical parameters on the buckling and post-buckling behavior of FGM structures are also examined.
Similar content being viewed by others
References
Akbari M, Kiani Y, Eslami M (2015) Thermal buckling of temperature-dependent FGM conical shells with arbitrary edge supports. Acta Mech 226:897–915
Akgos B, Civalek O (2017) Effects of thermal and shear deformation on vibration response of functionally graded thick composite microbeams. Compos B 129:77–87
Anh V, Bich D, Duc N (2015) Nonlinear buckling analysis of thin FGM annular spherical shells on elastic foundations under external pressure and thermal loads. Eur J Mech A/Solids 50:28–38
Arefi M, Mohammadi M, Tabatabaeian A, Dimitri R, Tornabene F (2018) Two-dimensional thermo-elastic analysis of FG-CNTRC cylindrical pressure vessels. Steel Compos Struct 27:525–536
Barati M, Shahverdi H (2018) Nonlinear thermal vibration analysis of refined shear deformable FG nanoplates: two semi-analytical solutions. J Braz Soc Mech Sci Eng 40:64
Batoz J, Dhatt G (1990) Modélisation des structures par éléments finis. Herms-Lavoisier
Bhagat V, Jeyaraj P (2016) Experimental investigation on buckling strength of cylindrical panel: effect of non-uniform temperature field. Procedia Eng 144:474–481
Bhagat V, Jeyaraj P, Murigendrappa S (2016) Buckling and free vibration characteristics of a uniformly heated isotropic cylindrical panel. Procedia Eng 144:474–481
Bouazza M, Tounsi A, Adda-Bedia E, Megueni A (2010) Thermoelastic stability analysis of functionally graded plates: an analytical approach. Comput Mater Sci 49:865–870
Carrera E, Brischetto S, Nali P (2011) Plates and shells for smart structures: classical and advanced theories for modeling and analysis. Wiley, New York
Chan D, Quan T, Kim S, Duc N (2019) Nonlinear dynamic response and vibration of shear deformable piezoelectric functionally graded truncated conical panel in thermal environments. Eur J Mech A/Solids 77:103795
Dammak F, Abid S, Gakwaya A, Dhatt G (2005) A formulation of the non linear discrete Kirchhoff quadrilateral shell element with finite rotations and enhanced strains. Revue Europeenne des Elements Finis 14:7–31
Demir C, Civalek O (2017) A new nonlocal FEM via Hermitian cubic shape functions for thermal vibration of nano beams surrounded by an elastic matrix. Compos Struct 168:872–884
Dhatt G, Touzot G (1981) Une présentation de la méthode des éléments finis . Maloine S.A. Paris et Les Presses de l’Université de Laval Québec
Duc N (2014) Nonlinear static and dynamic stability of functionally graded plates and shells. Vietnam National University Press, Hanoi
Duc N, Cong P (2013) Nonlinear postbuckling of symmetric S-FGM plates resting on elastic foundations using higher order shear deformation plate theory in thermal environments. Compos Struct 100:566–574
Duc N, Quan T (2012) Nonlinear stability analysis of double curved shallow FGM panel on elastic foundation in thermal environments. Mech Compos Mater 48:435–448
Duc N, Tung H (2010) Nonlinear analysis of stability for functionally graded cylindrical shells under axial compression. Comput Mater Sci 49:313–316
Duc N, Tung H (2011) Mechanical and thermal postbuckling of higher order shear deformable functionally graded plates on elastic foundations. Compos Struct 93:2874–2881
Duc N, Cong P, Anh V, Quang V, Tran P, Tuan N, Thinh N (2015a) Mechanical and thermal stability of eccentrically stiffened functionally graded conical shell panels resting on elastic foundations and in thermal environment. Compos Struct 132:597–609
Duc N, Tuan N, Tran P, Dao N, Dat N (2015) Nonlinear dynamic analysis of Sigmoid functionally graded circular cylindrical shells on elastic foundations using the third order shear deformation theory in thermal environments. Int J Mech Sci 101:338–348
Duc N, Kim S, Manh D, Nguyen P (2020a) Effect of eccentrically oblique stiffeners and temperature on the nonlinear static and dynamic response of S-FGM cylindrical panels. Thin Walled Struct 146:106438
Duc N, Kim S, Quan T, Manh D, Cuong N (2020b) Nonlinear buckling of eccentrically stiffened nanocomposite cylindrical panels in thermal environments. Thin Walled Struct 146:106428
Eslami M, Reza M, Jacobs A (2018) Buckling and postbuckling of beams, plates, and shells. Springer, Berlin
Frikha A, Dammak F (2017) Geometrically non-linear static analysis of functionally graded material shells with a discrete double directors shell element. Comput Methods Appl Mech Eng 315:1–24
Farimani M, Mohadeszadeh M (2017) Thermo-elastic bending analysis of FGM rotating plate with axial grading and modified rule of mixture. J Braz Soc Mech Sci Eng 39:299–307
Frikha A, Zghal S, Dammak F (2018a) Dynamic analysis of functionally graded carbon nanotubes-reinforced plate and shell structures using a double directors finite shell element. Aerosp Sci Technol 78:438–451
Frikha A, Zghal S, Dammak F (2018b) Finite rotation three and four nodes shell elements for functionally graded carbon nanotubes-reinforced thin composite shells analysis. Comput Methods Appl Mech Eng 329:289–311
Frikha A, Wali M, Hajlaoui A, Dammak F (2016) Dynamic response of functionally graded material shells with a discrete double directors shell element. Compos Struct 154:385–395
Ganapathi M, Prakash T (2006) Thermal buckling of simply supported functionally graded skew plates. Comput Struct 74:247–50
Ganapathi M, Prakash T, Sundararajan N (2006) Influence of functionally graded material on buckling of skew plates under mechanical loads. J Eng Mech 132:902–905
Gowda RMS, Pandalai KAV (1970) Thermal buckling of orthotropic plates. Stud Struct Mech 9–44
Hajlaoui A, Wali M, Ben Jdidia M, Dammak F (2016) An improved enhanced solid shell element for static and buckling analysis of shell structures. Mech Ind 17:510
Hajlaoui A, Triki E, Frikha A, Wali M, Dammak F (2017) Nonlinear dynamics analysis of FGM shell structures with a higher order shear strain enhanced solid-shell element. Lat Am J Solids Struct 14:72–91
Jaberzadeh E, Azhari M, Boroomand B (2013) Thermal buckling of functionally graded skew and trapezoidal plates with different boundary conditions using the element-free Galerkin method. Eur J Mech A/Solids 42:18–26
Javaheri R, Eslami M (2002a) Buckling of functionally graded plates under in-plane compressive loading. ZAMM 82:277–283
Javaheri R, Eslami M (2002b) Thermal buckling of functionally graded plates. AIAA J 40:162–169
Javaheri R, Eslami M (2002c) Thermal buckling of functionally graded plates based on higher order theory. J Therm Stress 25:603–625
Koizumi M (1993) Functionally gradient materials the concept of FGM. Ceram Trans 34:3–10
Koizumi M (1997) FGM activities in Japan. Compos B 28:1–4
Kandasamy R, Dimitri R, Tornabene F (2016) Numerical study on the free vibration and thermal buckling behavior of moderately thick functionally graded structures in thermal environments. Compos Struct 157:207–221
Kant T, Babu C (2000) Thermal buckling analysis of skew fibre-reinforced composite and sandwich plates using shear deformable finite element models. Compos Struct 49:77–85
Kar V, Panda S, Mahapatra T (2016) Thermal buckling behaviour of shear deformable functionally graded single/doubly curved shell panel with TD and TID properties. Adv Mater Res 5:205–221
Khoa N, Thiem H, Duc N (2019) Nonlinear buckling and postbuckling of imperfect piezoelectric S-FGM circular cylindrical shells with metal–ceramic–metal layers in thermal environment using Reddy’s third-order shear deformation shell theory. Mech Adv Mater Struct 26:248–259
Liew K, Zhao X, Lee Y (2012) Postbuckling responses of functionally graded cylindrical shells under axial compression and thermal loads. Compos B 43:1621–1630
Mars J, Koubaa S, Wali M, Dammak F (2017) Numerical analysis of geometrically non-linear behavior of functionally graded shells. Lat Am J Solids Struct 14:1952–1978
Miyamoto Y, Kaysser W, Rabin B, Kawasaki A, Ford R (1999) Functionally graded materials: design, processing and applications. Springer US
Nejati M, Dimitri R, Tornabene F, Hossein Yas M (2017) Thermal buckling of nanocomposite stiffened cylindrical shells reinforced by functionally graded wavy carbon nanotubes with temperature-dependent properties. Appl Sci 7:1223
Nguyen P, Quang V, Anh V, Duc N (2019) Nonlinear vibration of carbon nanotube reinforced composite truncated conical shells in thermal environment. Int J Struct Stabil Dyn 19:1950158
Panda S, Mahapatra T, Kar V (2017) Nonlinear finite element solution of post-buckling responses of FGM panel structure under elevated thermal load and TD and TID properties. MATEC Web Conf 109:05005
Park J, Kim J (2006) Thermal postbuckling and vibration analyses of functionally graded plates. J Sound Vib 289:77–93
Prabhu M, Durvasula S (1976) Thermal post-buckling characteristics of clamped skew plates. Comput Struct 6:177–185
Prakash T, Singha M, Ganapathi M (2008) Thermal postbuckling analysis of FGM skew plates. Eng Struct 30:22–32
Reddy J (2003) Mechanics of laminated composite plates and shells: theory and analysis. CRC Press, New York
Reddy J, Chin C (1998) Thermomechanical analysis of functionally graded cylinders and plates. J Therm Stress 21:593–626
Shen H (2007) Thermal postbuckling behavior of shear deformable FGM plates with temperature-dependent properties. Int J Mech Sci 49:466–478
Shen H (2014) Nonlinear vibration of nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments. Comput Struct 111:291–300
Simo J, Fox D (1989) On a stress resultants geometrically exact shell model. Part I: formulation and optimal parametrization. Comput Methods Appl Mech Eng 72:267–304
Suresh S, Mortensen A (1997) Functionally graded metals and metalceramiccomposites Part 2. Thermomechanical behavior. Int Mater Rev 42:85–116
Thangaratnam K, Palaninathan A, Ramachandran J (1989) Thermal buckling of composite laminated plates. Comput Struct 32:1117–1124
Tornabene F, Fantuzzi N, Bacciocchi M (2016) Higher-order structural theories for the static analysis of doubly-curved laminated composite panels reinforced by curvilinear fibers. Thin Wall Struct 102:222–245
Tornabene F, Brischetto S, Fantuzzi N, Viola E (2015) Numerical and exact models for free vibration analysis of cylindrical and spherical shell panels. Compos B 81:231–250
Trabelsi S, Frikha A, Zghal S, Dammak F (2018) Thermal post-buckling analysis of functionally graded material structures using a modified FSDT. Int J Mech Sci 144:74–89
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. Eng Struct 178:444–459
Tran L, Thai C, Nguyen-Xuan H (2013) An isogeometric finite element formulation for thermal buckling analysis of functionally graded plates. Finite Elem Anal Des 73:65–76
Van Do V, Lee C (2018) Nonlinear thermal buckling analyses of functionally graded circular plates using higher-order shear deformation theory with a new transverse shear function and an enhanced mesh-free method. Acta Mech 229:3787–3811
Van Do V, Ong T, Lee C (2019) Isogeometric analysis for nonlinear buckling of FGM plates under various types of thermal gradients. Thin Wall Struct 137:448–462
Vuong P, Duc N (2019) Nonlinear vibration of FGM moderately thick toroidal shell segment within the framework of Reddy’s third order-shear deformation shell theory. Int J Mech Mater Des. https://doi.org/10.1007/s10999-019-09473-x
Wali M, Hentati T, Jaraya A, Dammak F (2015) Free vibration analysis of FGM shell structures with a discrete double directors shell element. Compos Struct 125:295–303
Yousefitabar M, Matapouri M (2017) Thermally induced buckling of thin annular FGM plates. J Braz Soc Mech Sci Eng 39:969–980
Zghal S, Frikha A, Dammak F (2017) Static analysis of functionally graded carbon nanotube-reinforced plate and shell structures. Compos Struct 176:1107–1123
Zghal S, Frikha A, Dammak F (2018a) Free vibration analysis of carbon nanotube-reinforced functionally graded composite shell structures. Appl Math Model 53:132–155
Zghal S, Frikha A, Dammak F (2018b) Mechanical buckling analysis of functionally graded power-based and carbon nanotubes-reinforced composite plates and curved panels. Compos B 150:165–183
Zghal S, Frikha A, Dammak F (2018c) Non-linear bending analysis of nanocomposites reinforced by graphene-nanotubes with finite shell element and membrane enhancement. Eng Struct 158:95–109
Zhang D (2017) Thermal post-buckling analysis of functionally graded material elliptical plates based on high-order shear deformation theory. Mech Adv Mater Struct 24:142–148
Zhao X, Liew K (2010) A mesh-free method for analysis of the thermal and mechanical buckling of functionally graded cylindrical shell panels. Comput Mech 45:297–310
Zhao X, Lee Y, Liew K (2009) Mechanical and thermal buckling analysis of functionally graded plates. Compos Struct 90:161–71
Author information
Authors and Affiliations
Corresponding author
Additional information
Technical Editor: Paulo de Tarso Rocha de Mendonça, Ph.D.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Trabelsi, S., Zghal, S. & Dammak, F. Thermo-elastic buckling and post-buckling analysis of functionally graded thin plate and shell structures. J Braz. Soc. Mech. Sci. Eng. 42, 233 (2020). https://doi.org/10.1007/s40430-020-02314-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40430-020-02314-5