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Computational Modelling and Experimental Challenges of Linear and Nonlinear Analysis of Porous Graded Structure: A Comprehensive Review

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Abstract

This research reviewed the functionally graded (FG) structures exposed to mechanical/thermomechanical loading, including the porosity effect. The review focuses on the modelling of FGM via different theoretical approaches adopted in the past and their responses (static, vibration, and transient) without indicating the detailed mathematical implications and the solution methodologies. The present review is majorly divided into three categories of the analysis reported in the published domain of the linear and nonlinear static, vibration, and transient deflection, including the stress parameters. Further, an effort has been made to discuss the articles from the last decade to show the significant improvements made by the different researchers, with a few exceptions. The main findings and subsequent lacunae are summarized to redefine the future course of action in graded structural modelling and the challenges related to the experimentation.

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References

  1. Koizumi M (1997) FGM activities in Japan. Compos Part B 28:1–4. https://doi.org/10.1080/15502287.2016.1231240

    Article  Google Scholar 

  2. Reddy JN, Chin CD (1998) Thermomechanical analysis of functionally graded cylinders and plates. J Therm Stress 21:593–626. https://doi.org/10.1080/01495739808956165

    Article  Google Scholar 

  3. Chi S-H, Chung Y-L (2006) Mechanical behavior of functionally graded material plates under transverse load—part I: analysis. Int J Solids Struct 43:3657–3674. https://doi.org/10.1016/j.ijsolstr.2005.04.011

    Article  MATH  Google Scholar 

  4. Li S, Zheng S, Chen D (2020) Porosity-dependent isogeometric analysis of bi-directional functionally graded plates. Thin-Walled Struct 156:106999. https://doi.org/10.1016/j.tws.2020.106999

    Article  Google Scholar 

  5. Sahmani S, Safaei B (2019) Nonlinear free vibrations of bi-directional functionally graded micro/nano-beams including nonlocal stress and microstructural strain gradient size effects. Thin-Walled Struct 140:342–356. https://doi.org/10.1016/j.tws.2019.03.045

    Article  Google Scholar 

  6. Phung-Van P, Thai CH, Nguyen-Xuan H, Abdel Wahab M (2019) Porosity-dependent nonlinear transient responses of functionally graded nanoplates using isogeometric analysis. Compos Part B Eng 164:215–225. https://doi.org/10.1016/j.compositesb.2018.11.036

    Article  Google Scholar 

  7. Mirjavadi SS, Mohasel Afshari B, Shafiei N et al (2018) Effect of temperature and porosity on the vibration behavior of two-dimensional functionally graded micro-scale Timoshenko beam. JVC/Journal Vib Control 24:4211–4225. https://doi.org/10.1177/1077546317721871

    Article  MathSciNet  Google Scholar 

  8. Amir M, Talha M (2019) Nonlinear vibration characteristics of shear deformable functionally graded curved panels with porosity including temperature effects. Int J Press Vessel Pip 172:28–41. https://doi.org/10.1016/j.ijpvp.2019.03.008

    Article  Google Scholar 

  9. Nguyen NV, Nguyen HX, Lee S, Nguyen-Xuan H (2018) Geometrically nonlinear polygonal finite element analysis of functionally graded porous plates. Adv Eng Softw 126:110–126. https://doi.org/10.1016/j.advengsoft.2018.11.005

    Article  Google Scholar 

  10. Wang YQ, Zu JW (2017) Vibration behaviors of functionally graded rectangular plates with porosities and moving in thermal environment. Aerosp Sci Technol 69:550–562. https://doi.org/10.1016/j.ast.2017.07.023

    Article  Google Scholar 

  11. Bich DH, Dung D, Van, Nam VH (2012) Nonlinear dynamical analysis of eccentrically stiffened functionally graded cylindrical panels. Compos Struct 94:2465–2473. https://doi.org/10.1016/j.compstruct.2012.03.012

    Article  Google Scholar 

  12. Valizadeh N, Natarajan S, Gonzalez-Estrada OA et al (2013) NURBS-based finite element analysis of functionally graded plates: static bending, vibration, buckling and flutter. Compos Struct 99:309–326. https://doi.org/10.1016/j.compstruct.2012.11.008

    Article  Google Scholar 

  13. 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. https://doi.org/10.1016/j.compstruct.2016.08.037

    Article  Google Scholar 

  14. Zhong S, Jin G, Ye T et al (2020) Isogeometric vibration analysis of multi-directional functionally gradient circular, elliptical and sector plates with variable thickness. Compos Struct 250:112470. https://doi.org/10.1016/j.compstruct.2020.112470

    Article  Google Scholar 

  15. Yang J, Huang X-L (2007) Nonlinear transient response of functionally graded plates with general imperfections in thermal environments. Comput Methods Appl Mech Eng 196:2619–2630. https://doi.org/10.1016/j.cma.2007.01.012

    Article  MATH  Google Scholar 

  16. Reddy JN (2004) Mechanics of laminated composite plates and shells: theory and analysis, 2nd edn. CRC Press, Boca Raton, FL

    MATH  Google Scholar 

  17. Reddy JN (2002) Energy principles and variational methods in applied mechanics. John Wiley & Sons, Hoboken

    Google Scholar 

  18. Reddy JN (1984) A simple higher-order theory for laminated composite plates. J Appl Mech Trans ASME 51:745–752. https://doi.org/10.1115/1.3167719

    Article  MATH  Google Scholar 

  19. Kapuria S, Bhattacharyya M, Kumar AN (2008) Bending and free vibration response of layered functionally graded beams: a theoretical model and its experimental validation. Compos Struct 82:390–402. https://doi.org/10.1016/j.compstruct.2007.01.019

    Article  Google Scholar 

  20. Carrera E, Brischetto S, Robaldo A (2008) Variable kinematic model for the analysis of functionally graded material plates. AIAA J 46:194–203. https://doi.org/10.2514/1.32490

    Article  Google Scholar 

  21. Mantari JL, Ramos IA, Carrera E, Petrolo M (2016) Static analysis of functionally graded plates using new non-polynomial displacement fields via carrera unified formulation. Compos Part B Eng 89:127–142. https://doi.org/10.1016/j.compositesb.2015.11.025

    Article  Google Scholar 

  22. Lü CF, Lim CW, Chen WQ (2009) Semi-analytical analysis for multi-directional functionally graded plates: 3-D elasticity solutions. Int J Numer Methods Eng 79:25–44

    Article  MathSciNet  MATH  Google Scholar 

  23. Asemi K, Ashrafi H, Salehi M, Shariyat M (2013) Three-dimensional static and dynamic analysis of functionally graded elliptical plates, employing graded finite elements. Acta Mech 224:1849–1864. https://doi.org/10.1007/s00707-013-0835-0

    Article  MathSciNet  MATH  Google Scholar 

  24. Adineh M, Kadkhodayan M (2017) Three-dimensional thermo-elastic analysis of multi-directional functionally graded rectangular plates on elastic foundation. Acta Mech 228:881–899. https://doi.org/10.1007/s00707-016-1743-x

    Article  MathSciNet  Google Scholar 

  25. Tornabene F, Brischetto S, Fantuzzi N, Bacciocchi M (2016) Boundary conditions in 2D Numerical and 3D exact models for cylindrical bending analysis of functionally graded structures. Shock Vib 2016:1–17. https://doi.org/10.1155/2016/2373862

    Article  Google Scholar 

  26. Niknam H, Fallah A, Aghdam MM (2014) Nonlinear bending of functionally graded tapered beams subjected to thermal and mechanical loading. Int J Non Linear Mech 65:141–147. https://doi.org/10.1016/j.ijnonlinmec.2014.05.011

    Article  Google Scholar 

  27. Li J, Wang G, Guan Y et al (2021) Meshless analysis of bi-directional functionally graded beam structures based on physical neutral surface. Compos Struct 259:113502. https://doi.org/10.1016/j.compstruct.2020.113502

    Article  Google Scholar 

  28. Moradi-Dastjerdi R, Foroutan M, Pourasghar A, Sotoudeh-Bahreini R (2013) Static analysis of functionally graded carbon nanotube-reinforced composite cylinders by a mesh-free method. J Reinf Plast Compos 32:593–601. https://doi.org/10.1177/0731684413476353

    Article  MATH  Google Scholar 

  29. Panda S, Ray MC (2009) Active control of geometrically nonlinear vibrations of functionally graded laminated composite plates using piezoelectric fiber reinforced composites. J Sound Vib 325:186–205. https://doi.org/10.1016/j.jsv.2009.03.016

    Article  Google Scholar 

  30. Genao FY, Kim J, Żur KK (2021) Nonlinear finite element analysis of temperature-dependent functionally graded porous micro-plates under thermal and mechanical loads. Compos Struct 256:112931. https://doi.org/10.1016/j.compstruct.2020.112931

    Article  Google Scholar 

  31. Li M, Zhou L, Liu C (2020) The multi-physical cell-based smoothed finite element method for analyzing transient behavior of functionally grade magneto-electro-elastic thin-walled structures under thermal environment. Thin-Walled Struct 155:106876. https://doi.org/10.1016/j.tws.2020.106876

    Article  Google Scholar 

  32. Liu J, Hao C, Zhou Y, Ye W (2021) Dynamic analysis of functionally graded sandwich beams using a semi-analytic method named scaled boundary finite element method. Eng Anal Bound Elem 130:161–175. https://doi.org/10.1016/j.enganabound.2021.05.010

    Article  MathSciNet  MATH  Google Scholar 

  33. Amir M, Talha M (2018) Thermoelastic vibration of Shear deformable functionally graded curved beams with microstructural defects. Int J Struct Stab Dyn. https://doi.org/10.1142/S0219455418501353

    Article  Google Scholar 

  34. Fazzolari FA, Carrera E (2014) Thermal stability of FGM sandwich plates under various through-the-thickness temperature distributions. J Therm Stress 37:1449–1481. https://doi.org/10.1080/01495739.2014.937251

    Article  Google Scholar 

  35. Javaheri R, Eslami MR (2002) Thermal buckling of functionally graded plates. AIAA J 40:162–169. https://doi.org/10.2514/3.15009

    Article  MATH  Google Scholar 

  36. Duc ND, Quan TQ (2014) Transient responses of functionally graded double curved shallow shells with temperature-dependent material properties in thermal environment. Eur J Mech - A/Solids 47:101–123. https://doi.org/10.1016/j.euromechsol.2014.03.002

    Article  Google Scholar 

  37. Moita JS, Araújo AL, Correia VF et al (2018) Buckling and nonlinear response of functionally graded plates under thermo-mechanical loading. Compos Struct 202:719–730. https://doi.org/10.1016/j.compstruct.2018.03.082

    Article  Google Scholar 

  38. Shen H-S, Chen X, Guo L et al (2015) Nonlinear vibration of FGM doubly curved panels resting on elastic foundations in thermal environments. Aerosp Sci Technol 47:434–446. https://doi.org/10.1016/j.ast.2015.10.011

    Article  Google Scholar 

  39. Fereidoon A, Mohyeddin A, Sheikhi M, Rahmani H (2012) Bending analysis of functionally graded annular sector plates by extended Kantorovich method. Compos Part B Eng 43:2172–2179. https://doi.org/10.1016/j.compositesb.2012.02.019

    Article  Google Scholar 

  40. Oktem AS, Mantari JL, Soares CG (2012) Static response of functionally graded plates and doubly-curved shells based on a higher order shear deformation theory. Eur J Mech A/Solids 36:163–172. https://doi.org/10.1016/j.euromechsol.2012.03.002

    Article  MATH  Google Scholar 

  41. Tornabene F, Viola E (2013) Static analysis of functionally graded doubly-curved shells and panels of revolution. Meccanica 48:901–930. https://doi.org/10.1007/s11012-012-9643-1

    Article  MathSciNet  MATH  Google Scholar 

  42. Tornabene F, Ceruti A (2013) Mixed static and dynamic optimization of four-parameter functionally graded completely doubly curved and degenerate shells and panels using GDQ method. Math Probl Eng 2013:1–33. https://doi.org/10.1155/2013/867079

    Article  MathSciNet  Google Scholar 

  43. Zhang LW, Lei ZX, Liew KM, Yu JL (2014) Static and dynamic of carbon nanotube reinforced functionally graded cylindrical panels. Compos Struct 111:205–212. https://doi.org/10.1016/j.compstruct.2013.12.035

    Article  Google Scholar 

  44. Viola E, Rossetti L, Fantuzzi N, Tornabene F (2014) Static analysis of functionally graded conical shells and panels using the generalized unconstrained third order theory coupled with the stress recovery. Compos Struct 112:44–65. https://doi.org/10.1016/j.compstruct.2014.01.039

    Article  Google Scholar 

  45. Wang A, Chen H, Hao Y, Zhang W (2018) Vibration and bending behavior of functionally graded nanocomposite doubly-curved shallow shells reinforced by graphene nanoplatelets. Results Phys 9:550–559. https://doi.org/10.1016/j.rinp.2018.02.062

    Article  Google Scholar 

  46. Salehipour H, Jamshidi M, Shahsavar A (2020) Considering bending and vibration of homogeneous Nanobeam coated by a FG Layer. J Solid Mech 12:411–437. https://doi.org/10.22034/jsm.2019.1870709.1457

    Article  Google Scholar 

  47. Inada AA, Arman S, Safaei B (2022) A novel review on the efficiency of nanomaterials for solar energy storage systems. J Energy Storage 55:105661. https://doi.org/10.1016/j.est.2022.105661

    Article  Google Scholar 

  48. Sarkon GK, Safaei B, Kenevisi MS et al (2022) State–of–the–art review of machine learning applications in additive manufacturing; from design to manufacturing and property control. Springer Netherlands, Heidelberg

    Book  Google Scholar 

  49. Pydah A, Sabale A (2017) Static analysis of bi-directional functionally graded curved beams. Compos Struct 160:867–876. https://doi.org/10.1016/j.compstruct.2016.10.120

    Article  Google Scholar 

  50. Do T, Van, Nguyen DK, Duc ND et al (2017) Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory. Thin-Walled Struct 119:687–699. https://doi.org/10.1016/j.tws.2017.07.022

    Article  Google Scholar 

  51. Truong TT, Nguyen-Thoi T, Lee J (2019) Isogeometric size optimization of bi-directional functionally graded beams under static loads. Compos Struct 227:111259. https://doi.org/10.1016/j.compstruct.2019.111259

    Article  Google Scholar 

  52. Rachid A, Ouinas D, Lousdad A et al (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

    Article  Google Scholar 

  53. Abdelrahman AA, Ashry M, Alshorbagy AE, Abdallah WS (2021) On the mechanical behavior of two directional symmetrical functionally graded beams under moving load. Int J Mech Mater Des 17:563–586. https://doi.org/10.1007/s10999-021-09547-9

    Article  Google Scholar 

  54. Thang PT, Nguyen-Thoi T, Lee J (2021) Modeling and analysis of bi-directional functionally graded nanobeams based on nonlocal strain gradient theory. Appl Math Comput 407:126303. https://doi.org/10.1016/j.amc.2021.126303

    Article  MathSciNet  MATH  Google Scholar 

  55. Behjat B, Khoshravan MR (2012) Geometrically nonlinear static and free vibration analysis of functionally graded piezoelectric plates. Compos Struct 94:874–882. https://doi.org/10.1016/j.compstruct.2011.08.024

    Article  Google Scholar 

  56. Behjat B, Khoshravan MR (2012) Nonlinear analysis of functionally graded laminates considering piezoelectric effect. J Mech Sci Technol 26:2581–2588. https://doi.org/10.1007/s12206-012-0638-6

    Article  Google Scholar 

  57. Li L, Hu Y (2016) Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material. Int J Eng Sci 107:77–97. https://doi.org/10.1016/j.ijengsci.2016.07.011

    Article  MathSciNet  MATH  Google Scholar 

  58. Yang T, Tang Y, Li Q, Yang X-D (2018) Nonlinear bending, buckling and vibration of bi-directional functionally graded nanobeams. Compos Struct 204:313–319. https://doi.org/10.1016/j.compstruct.2018.07.045

    Article  Google Scholar 

  59. Do VN, Van, Lee C-H (2018) Nonlinear analyses of FGM plates in bending by using a modified radial point interpolation mesh-free method. Appl Math Model 57:1–20. https://doi.org/10.1016/j.apm.2017.12.035

    Article  MathSciNet  MATH  Google Scholar 

  60. Sahmani S, Safaei B (2020) Influence of homogenization models on size-dependent nonlinear bending and postbuckling of bi-directional functionally graded micro/nano-beams. Appl Math Model 82:336–358. https://doi.org/10.1016/j.apm.2020.01.051

    Article  MathSciNet  MATH  Google Scholar 

  61. Chen D, Yang J, Kitipornchai S (2015) Elastic buckling and static bending of shear deformable functionally graded porous beam. Compos Struct 133:54–61. https://doi.org/10.1016/j.compstruct.2015.07.052

    Article  Google Scholar 

  62. Rad AB (2018) Static analysis of non-uniform 2D functionally graded auxetic-porous circular plates interacting with the gradient elastic foundations involving friction force. Aerosp Sci Technol 76:315–339. https://doi.org/10.1016/j.ast.2018.01.036

    Article  Google Scholar 

  63. Chen D, Yang J, Kitipornchai S (2019) Buckling and bending analyses of a novel functionally graded porous plate using Chebyshev-Ritz method. Arch Civ Mech Eng 19:157–170. https://doi.org/10.1016/j.acme.2018.09.004

    Article  Google Scholar 

  64. She G-L, Yuan F-G, Karami B et al (2019) On nonlinear bending behavior of FG porous curved nanotubes. Int J Eng Sci 135:58–74. https://doi.org/10.1016/j.ijengsci.2018.11.005

    Article  MathSciNet  MATH  Google Scholar 

  65. Tran TT, Tran VK, Pham Q-H, Zenkour AM (2021) Extended four-unknown higher-order shear deformation nonlocal theory for bending, buckling and free vibration of functionally graded porous nanoshell resting on elastic foundation. Compos Struct 264:113737. https://doi.org/10.1016/j.compstruct.2021.113737

    Article  Google Scholar 

  66. Pham QH, Nguyen PC, Tran VK, Nguyen-Thoi T (2021) Finite element analysis for functionally graded porous nano-plates resting on elastic foundation. Steel Compos Struct 41:149–166. https://doi.org/10.12989/scs.2021.41.2.149

    Article  Google Scholar 

  67. Nguyen VC, Tran TT, Nguyen-Thoi T, Pham QH (2022) A novel finite element formulation for static bending analysis of functionally graded porous sandwich plates. Front Struct Civ Eng 16:1599–1620. https://doi.org/10.1007/s11709-022-0891-4

    Article  Google Scholar 

  68. Tran TT, Pham QH, Nguyen-Thoi T (2021) Static and free vibration analyses of functionally graded porous variable-thickness plates using an edge-based smoothed finite element method. Def Technol 17:971–986. https://doi.org/10.1016/j.dt.2020.06.001

    Article  Google Scholar 

  69. Liu Z, Yang C, Gao W et al (2019) Nonlinear behaviour and stability of functionally graded porous arches with graphene platelets reinforcements. Int J Eng Sci 137:37–56. https://doi.org/10.1016/j.ijengsci.2018.12.003

    Article  MathSciNet  MATH  Google Scholar 

  70. Chan DQ, Van Hoan P, Trung NT et al (2021) Nonlinear buckling and post-buckling of imperfect FG porous sandwich cylindrical panels subjected to axial loading under various boundary conditions. Acta Mech 232:1163–1179. https://doi.org/10.1007/s00707-020-02882-6

    Article  MathSciNet  MATH  Google Scholar 

  71. Dai H-L, Dai T (2014) Analysis for the thermoelastic bending of a functionally graded material cylindrical shell. Meccanica 49:1069–1081. https://doi.org/10.1007/s11012-013-9853-1

    Article  MathSciNet  MATH  Google Scholar 

  72. Farzam A, Hassani B (2019) Size-dependent analysis of FG microplates with temperature-dependent material properties using modified strain gradient theory and isogeometric approach. Compos Part B Eng 161:150–168. https://doi.org/10.1016/j.compositesb.2018.10.028

    Article  Google Scholar 

  73. Thai S, Nguyen VX, Lieu QX (2022) Bending and free vibration analyses of multi-directional functionally graded plates in thermal environment: a three-dimensional isogeometric analysis approach. Compos Struct 295:115797. https://doi.org/10.1016/j.compstruct.2022.115797

    Article  Google Scholar 

  74. Zou D, Dindarloo MH (2021) Static analysis of the FG with spatial coordinates cylindrical nanoshells in thermal environment. Mech Based Des Struct Mach. https://doi.org/10.1080/15397734.2021.1902349

    Article  Google Scholar 

  75. Zhong S, Zhang J, Jin G et al (2021) Thermal bending and vibration of FGM plates with various cutouts and complex shapes using isogeometric method. Compos Struct 260:113518. https://doi.org/10.1016/j.compstruct.2020.113518

    Article  Google Scholar 

  76. Shen H-S (2015) Nonlinear analysis of functionally graded fiber reinforced composite laminated beams in hygrothermal environments, part I: theory and solutions. Compos Struct 125:698–705. https://doi.org/10.1016/j.compstruct.2014.12.024

    Article  Google Scholar 

  77. Shen H-S, Chen X, Huang X-L (2016) Nonlinear bending and thermal postbuckling of functionally graded fiber reinforced composite laminated beams with piezoelectric fiber reinforced composite actuators. Compos Part B Eng 90:326–335. https://doi.org/10.1016/j.compositesb.2015.12.030

    Article  Google Scholar 

  78. Shen H-S, Xiang Y, Lin F (2017) Nonlinear bending of functionally graded graphene-reinforced composite laminated plates resting on elastic foundations in thermal environments. Compos Struct 170:80–90. https://doi.org/10.1016/j.compstruct.2017.03.001

    Article  Google Scholar 

  79. Babaei H, Kiani Y, Eslami MR (2018) Geometrically nonlinear analysis of functionally graded shallow curved tubes in thermal environment. Thin-Walled Struct 132:48–57. https://doi.org/10.1016/j.tws.2018.08.008

    Article  Google Scholar 

  80. Moita JS, Soares CMM, Soares CAM, Ferreira AJM (2019) Elastoplastic and nonlinear analysis of functionally graded axisymmetric shell structures under thermal environment, using a conical frustum finite element model. Compos Struct 226:111186. https://doi.org/10.1016/j.compstruct.2019.111186

    Article  Google Scholar 

  81. Shenas AG, Ziaee S, Malekzadeh P (2021) Nonlinear deformation of rotating functionally graded trapezoidal microplates in thermal environment. Compos Struct 265:113675. https://doi.org/10.1016/j.compstruct.2021.113675

    Article  Google Scholar 

  82. Akbaş ŞD (2017) Nonlinear static analysis of functionally graded porous beams under thermal effect. Coupled Syst Mech 6:399–415. https://doi.org/10.12989/csm.2017.6.4.399

    Article  Google Scholar 

  83. Gupta A, Talha M (2018) Influence of porosity on the flexural and free vibration responses of functionally graded Plates in Thermal Environment. Int J Struct Stab Dyn 18:1850013. https://doi.org/10.1142/S021945541850013X

    Article  MathSciNet  Google Scholar 

  84. Gong J, Xuan L, Ying B, Wang H (2019) Thermoelastic analysis of functionally graded porous materials with temperature-dependent properties by a staggered finite volume method. Compos Struct 224:111071. https://doi.org/10.1016/j.compstruct.2019.111071

    Article  Google Scholar 

  85. Rezaiee-Pajand M, Masoodi AR (2022) Hygro-thermo-elastic nonlinear analysis of functionally graded porous composite thin and moderately thick shallow panels. Mech Adv Mater Struct 29:594–612. https://doi.org/10.1080/15376494.2020.1780524

    Article  Google Scholar 

  86. Babaei H, Eslami MR (2022) Nonlinear bending analysis of size-dependent FG porous microtubes in thermal environment based on modified couple stress theory. Mech Based Des Struct Mach 50:2714–2735. https://doi.org/10.1080/15397734.2020.1784202

    Article  Google Scholar 

  87. Nikrad SF, Kanellopoulos A, Bodaghi M et al (2021) Large deformation behavior of functionally graded porous curved beams in thermal environment. Arch Appl Mech 91:2255–2278. https://doi.org/10.1007/s00419-021-01882-9

    Article  Google Scholar 

  88. Nam VH, Trung NT, Hoa LK (2019) Buckling and postbuckling of porous cylindrical shells with functionally graded composite coating under torsion in thermal environment. Thin-Walled Struct 144:106253. https://doi.org/10.1016/j.tws.2019.106253

    Article  Google Scholar 

  89. Nam VH, Phuong NT, Dong DT et al (2019) Nonlinear thermo-mechanical buckling of higher-order shear deformable porous functionally graded material plates reinforced by orthogonal and/or oblique stiffeners. Proc Inst Mech Eng Part C J Mech Eng Sci 233:6177–6196. https://doi.org/10.1177/0954406219861658

    Article  Google Scholar 

  90. Liu DY, Wang CY, Chen WQ (2010) Free vibration of FGM plates with in-plane material inhomogeneity. Compos Struct 92:1047–1051. https://doi.org/10.1016/j.compstruct.2009.10.001

    Article  Google Scholar 

  91. Kermani ID, Ghayour M, Mirdamadi HR (2012) Free vibration analysis of multi-directional functionally graded circular and annular plates. J Mech Sci Technol 26:3399–3410. https://doi.org/10.1007/s12206-012-0860-2

    Article  Google Scholar 

  92. Hadi A, Nejad MZ, Hosseini M (2018) Vibrations of three-dimensionally graded nanobeams. Int J Eng Sci 128:12–23. https://doi.org/10.1016/j.ijengsci.2018.03.004

    Article  MathSciNet  MATH  Google Scholar 

  93. Do DTT, Nguyen-Xuan H, Lee J (2020) Material optimization of tri-directional functionally graded plates by using deep neural network and isogeometric multimesh design approach. Appl Math Model 87:501–533. https://doi.org/10.1016/j.apm.2020.06.002

    Article  MathSciNet  MATH  Google Scholar 

  94. Rahmani M, Petrudi AM, Pourdavood MR (2021) Analytical Study of Free Vibrations of Fluid Coupling and structure in collision of turbulent fluid with FGM plate. Int J Heat Technol 39:145–154. https://doi.org/10.18280/ijht.390115

    Article  Google Scholar 

  95. Bakhy SH, Al-Waily M, Al-Shammari MA (2021) Analytical and numerical investigation of the free vibration of functionally graded materials sandwich beams. Arch Mater Sci Eng 110:72–85. https://doi.org/10.5604/01.3001.0015.4314

    Article  Google Scholar 

  96. Cao Y, Khorami M, Baharom S et al (2021) The effects of multi-directional functionally graded materials on the natural frequency of the doubly-curved nanoshells. Compos Struct 258:113403. https://doi.org/10.1016/j.compstruct.2020.113403

    Article  Google Scholar 

  97. Dinh-Cong D, Nguyen-Huynh P, Nguyen SN, Nguyen-Thoi T (2023) Damage identification of functionally graded Beams using Modal Flexibility sensitivity-based damage index. Period Polytech Civ Eng 67:272–281. https://doi.org/10.3311/PPci.21148

    Article  Google Scholar 

  98. Safaei B, Onyibo EC, Goren M et al (2022) Free vibration investigation on RVE of proposed honeycomb sandwich beam and material selection optimization. Facta Univ Ser Mech Eng. https://doi.org/10.22190/FUME220806042S

    Article  Google Scholar 

  99. Qian LF, Batra RC (2005) Design of bidirectional functionally graded plate for optimal natural frequencies. J Sound Vib 280:415–424. https://doi.org/10.1016/j.jsv.2004.01.042

    Article  Google Scholar 

  100. Aragh BS, Hedayati H, Farahani EB, Hedayati M (2011) A novel 2-D six-parameter power-law distribution for free vibration and vibrational displacements of two-dimensional functionally graded fiber-reinforced curved panels. Eur J Mech - A/Solids 30:865–883. https://doi.org/10.1016/j.euromechsol.2011.05.002

    Article  MathSciNet  MATH  Google Scholar 

  101. Şimşek M (2015) Bi-directional functionally graded materials (BDFGMs) for free and forced vibration of Timoshenko beams with various boundary conditions. Compos Struct 133:968–978. https://doi.org/10.1016/j.compstruct.2015.08.021

    Article  Google Scholar 

  102. Thom TT, Kien ND (2018) Free vibration of two-directional FGM beams using a higher-order Timoshenko beam element. Vietnam J Sci Technol 56:380. https://doi.org/10.15625/2525-2518/56/3/10754

    Article  Google Scholar 

  103. Wu C-P, Yu L-T (2019) Free vibration analysis of bi-directional functionally graded annular plates using finite annular prism methods. J Mech Sci Technol 33:2267–2279. https://doi.org/10.1007/s12206-019-0428-5

    Article  Google Scholar 

  104. Viet NV, Zaki W, Wang Q (2020) Free vibration characteristics of sectioned unidirectional/bidirectional functionally graded material cantilever beams based on finite element analysis. Appl Math Mech 41:1787–1804. https://doi.org/10.1007/s10483-020-2664-8

    Article  MathSciNet  MATH  Google Scholar 

  105. Pham Q-H, Nguyen P-C, Tran VK, Nguyen-Thoi T (2021) Isogeometric analysis for free vibration of bidirectional functionally graded plates in the fluid medium. Def Technol. https://doi.org/10.1016/j.dt.2021.09.006

    Article  Google Scholar 

  106. Chen C-S, Chen T-J, Chien R-D (2006) Nonlinear vibration of initially stressed functionally graded plates. Thin-Walled Struct 44:844–851. https://doi.org/10.1016/j.tws.2006.08.007

    Article  Google Scholar 

  107. Strozzi M, Pellicano F (2013) Nonlinear vibrations of functionally graded cylindrical shells. Thin-Walled Struct 67:63–77. https://doi.org/10.1016/j.tws.2013.01.009

    Article  Google Scholar 

  108. Yazdi AA (2013) Homotopy Perturbation Method for Nonlinear Vibration Analysis of functionally graded plate. J Vib Acoust 135:021012. https://doi.org/10.1115/1.4023252

    Article  Google Scholar 

  109. Ghadiri M, Safi M (2017) Nonlinear vibration analysis of functionally graded Nanobeam using Homotopy Perturbation Method. Adv Appl Math Mech 9:144–156. https://doi.org/10.4208/aamm.2015.m899

    Article  MathSciNet  MATH  Google Scholar 

  110. Jafari AA, Khalili SMR, Tavakolian M (2014) Nonlinear vibration of functionally graded cylindrical shells embedded with a piezoelectric layer. Thin-Walled Struct 79:8–15. https://doi.org/10.1016/j.tws.2014.01.030

    Article  Google Scholar 

  111. Tang Y, Lv X, Yang T (2019) Bi-directional functionally graded beams: asymmetric modes and nonlinear free vibration. Compos Part B Eng 156:319–331. https://doi.org/10.1016/j.compositesb.2018.08.140

    Article  Google Scholar 

  112. Chen X, Chen L, Huang S et al (2021) Nonlinear forced vibration of in-plane bi-directional functionally graded materials rectangular plate with global and localized geometrical imperfections. Appl Math Model 93:443–466. https://doi.org/10.1016/j.apm.2020.12.033

    Article  MathSciNet  MATH  Google Scholar 

  113. Mohammadian M (2021) Nonlinear free vibration of damped and undamped bi-directional functionally graded beams using a cubic-quintic nonlinear model. Compos Struct 255:112866. https://doi.org/10.1016/j.compstruct.2020.112866

    Article  Google Scholar 

  114. Sh EL, Kattimani S, Thoi Trung N (2022) Frequency response analysis of edge-cracked magneto-electro-elastic functionally graded plates using extended finite element method. Theor Appl Fract Mech 120:103417. https://doi.org/10.1016/j.tafmec.2022.103417

    Article  Google Scholar 

  115. Chen D, Yang J, Kitipornchai S (2017) Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams. Compos Sci Technol 142:235–245. https://doi.org/10.1016/j.compscitech.2017.02.008

    Article  Google Scholar 

  116. Chen D, Zheng S, Wang Y et al (2020) Nonlinear free vibration analysis of a rotating two-dimensional functionally graded porous micro-beam using isogeometric analysis. Eur J Mech - A/Solids 84:104083. https://doi.org/10.1016/j.euromechsol.2020.104083

    Article  MathSciNet  MATH  Google Scholar 

  117. Babaei M, Hajmohammad MH, Asemi K (2020) Natural frequency and dynamic analyses of functionally graded saturated porous annular sector plate and cylindrical panel based on 3D elasticity. Aerosp Sci Technol 96:105524. https://doi.org/10.1016/j.ast.2019.105524

    Article  Google Scholar 

  118. Keleshteri MM, Jelovica J (2020) Nonlinear vibration behavior of functionally graded porous cylindrical panels. Compos Struct 239:112028. https://doi.org/10.1016/j.compstruct.2020.112028

    Article  Google Scholar 

  119. Chen X, Chen L, Lu Y (2021) Imperfection sensitivity of nonlinear primary resonance behavior in bi-directional functionally graded porous material beam. Compos Struct 271:114142. https://doi.org/10.1016/j.compstruct.2021.114142

    Article  Google Scholar 

  120. Sah SK, Ghosh A (2022) Influence of porosity distribution on free vibration and buckling analysis of multi-directional functionally graded sandwich plates. Compos Struct 279:114795. https://doi.org/10.1016/j.compstruct.2021.114795

    Article  Google Scholar 

  121. Tran TT, Pham Q, Nguyen-Thoi T (2020) An edge-based smoothed finite element for free vibration analysis of functionally graded porous (FGP) plates on Elastic Foundation taking into Mass (EFTIM). Math Probl Eng. https://doi.org/10.1155/2020/8278743

    Article  MathSciNet  Google Scholar 

  122. Hosur Shivaramaiah NK, Kattimani S, Shariati M, Nguyen-Thoi T (2022) Geometrically nonlinear behavior of two-directional functionally graded porous plates with four different materials. Proc Inst Mech Eng Part C J Mech Eng Sci 236:11008–11023. https://doi.org/10.1177/09544062221111038

    Article  Google Scholar 

  123. Kumar HSN, Kattimani S, Marques FD et al (2023) Geometrically nonlinear study of functionally graded saturated porous plates based on refined shear deformation plate theory and Biot’s theory. Int J Struct Stab Dyn. https://doi.org/10.1142/S021945542350013X

    Article  MathSciNet  Google Scholar 

  124. Thang PT, Do DTT, Nguyen TT et al (2022) Free vibration characteristic analysis of functionally graded shells with porosity and neutral surface effects. Ocean Eng 255:111377. https://doi.org/10.1016/j.oceaneng.2022.111377

    Article  Google Scholar 

  125. Nguyen-Thoi T, Ly KD, Truong TT et al (2022) Analysis and optimal control of smart damping for porous functionally graded magneto-electro-elastic plate using smoothed FEM and metaheuristic algorithm. Eng Struct 259:114062. https://doi.org/10.1016/j.engstruct.2022.114062

    Article  Google Scholar 

  126. Pham QH, Thanh Tran T, Ke Tran V et al (2022) Free vibration of functionally graded porous non-uniform thickness annular-nanoplates resting on elastic foundation using ES-MITC3 element. Alexandria Eng J 61:1788–1802. https://doi.org/10.1016/j.aej.2021.06.082

    Article  Google Scholar 

  127. Janghorban M, Zare A (2011) Thermal effect on free vibration analysis of functionally graded arbitrary straight-sided plates with different cutouts. Lat Am J Solids Struct 8:245–257. https://doi.org/10.1590/S1679-78252011000300003

    Article  Google Scholar 

  128. Khalili SMR, Mohammadi Y (2012) Free vibration analysis of sandwich plates with functionally graded face sheets and temperature-dependent material properties: a new approach. Eur J Mech - A/Solids 35:61–74. https://doi.org/10.1016/j.euromechsol.2012.01.003

    Article  MathSciNet  MATH  Google Scholar 

  129. Wang Z, Wang X, Xu G et al (2016) Free vibration of two-directional functionally graded beams. Compos Struct 135:191–198. https://doi.org/10.1016/j.compstruct.2015.09.013

    Article  Google Scholar 

  130. Pandey S, Pradyumna S (2017) A finite element formulation for thermally induced vibrations of functionally graded material sandwich plates and shell panels. Compos Struct 160:877–886. https://doi.org/10.1016/j.compstruct.2016.10.040

    Article  Google Scholar 

  131. Shafiei N, Ghadiri M, Mahinzare M (2019) Flapwise bending vibration analysis of rotary tapered functionally graded nanobeam in thermal environment. Mech Adv Mater Struct 26:139–155. https://doi.org/10.1080/15376494.2017.1365982

    Article  Google Scholar 

  132. Tang Y, Zhong S, Yang T, Ding Q (2019) Interaction between Thermal Field and Two-Dimensional functionally graded materials: a structural mechanical example. Int J Appl Mech 11:1950099. https://doi.org/10.1142/S1758825119500996

    Article  Google Scholar 

  133. Bakhsheshy A, Mahbadi H (2019) The effect of multidimensional temperature distribution on the vibrational characteristics of a size-dependent thick bi-directional functionally graded microplate. Noise Vib Worldw 50:267–290. https://doi.org/10.1177/0957456519883265

    Article  Google Scholar 

  134. Li S-R, Ma H-K (2020) Analysis of free vibration of functionally graded material micro-plates with thermoelastic damping. Arch Appl Mech 90:1285–1304. https://doi.org/10.1007/s00419-020-01664-9

    Article  Google Scholar 

  135. Wang H, Chen C-S, Hsu C-Y, Chen W-R (2022) Vibration and stability of initially stressed functionally graded carbon nanotube-reinforced hybrid composite plates in thermal environments. Mech Based Des Struct Mach 50:1298–1313. https://doi.org/10.1080/15397734.2020.1749070

    Article  Google Scholar 

  136. Alijani F, Amabili M, Bakhtiari-Nejad F (2011) Thermal effects on nonlinear vibrations of functionally graded doubly curved shells using higher order shear deformation theory. Compos Struct 93:2541–2553. https://doi.org/10.1016/j.compstruct.2011.04.016

    Article  MATH  Google Scholar 

  137. Shen H-S, Xiang Y (2012) Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments. Comput Methods Appl Mech Eng 213–216:196–205. https://doi.org/10.1016/j.cma.2011.11.025

    Article  MathSciNet  MATH  Google Scholar 

  138. Shen H-S, Yang D-Q (2015) Nonlinear vibration of functionally graded fiber reinforced composite laminated beams with piezoelectric fiber reinforced composite actuators in thermal environments. Eng Struct 90:183–192. https://doi.org/10.1016/j.engstruct.2015.02.005

    Article  Google Scholar 

  139. Shen H-S, Xiang Y, Lin F (2017) Nonlinear vibration of functionally graded graphene-reinforced composite laminated plates in thermal environments. Comput Methods Appl Mech Eng 319:175–193. https://doi.org/10.1016/j.cma.2017.02.029

    Article  MathSciNet  MATH  Google Scholar 

  140. Quan TQ, Duc ND (2016) Nonlinear vibration and dynamic response of shear deformable imperfect functionally graded double-curved shallow shells resting on elastic foundations in thermal environments. J Therm Stress 39:437–459. https://doi.org/10.1080/01495739.2016.1158601

    Article  Google Scholar 

  141. Duc ND, Hadavinia H, Quan TQ, Khoa ND (2019) Free vibration and nonlinear dynamic response of imperfect nanocomposite FG-CNTRC double curved shallow shells in thermal environment. Eur J Mech - A/Solids 75:355–366. https://doi.org/10.1016/j.euromechsol.2019.01.024

    Article  MathSciNet  MATH  Google Scholar 

  142. Tang Y, Ding Q (2019) Nonlinear vibration analysis of a bi-directional functionally graded beam under hygro-thermal loads. Compos Struct 225:111076. https://doi.org/10.1016/j.compstruct.2019.111076

    Article  Google Scholar 

  143. Zhou K, Huang X, Tian J, Hua H (2018) Vibration and flutter analysis of supersonic porous functionally graded material plates with temperature gradient and resting on elastic foundation. Compos Struct 204:63–79. https://doi.org/10.1016/j.compstruct.2018.07.057

    Article  Google Scholar 

  144. Ibnorachid Z, Boutahar L, Bikri KEL, Benamar R (2019) Buckling temperature and natural frequencies of Thick Porous functionally graded Beams resting on Elastic Foundation in a thermal environment. Adv Acoust Vib 2019:1–17. https://doi.org/10.1155/2019/7986569

    Article  Google Scholar 

  145. Ebrahimi F, Hashemabadi D, Habibi M, Safarpour H (2020) Thermal buckling and forced vibration characteristics of a porous GNP reinforced nanocomposite cylindrical shell. Microsyst Technol 26:461–473. https://doi.org/10.1007/s00542-019-04542-9

    Article  Google Scholar 

  146. Ahmed RA, Khalaf BS, Raheef KM et al (2021) Investigating dynamic response of nonlocal functionally graded porous piezoelectric plates in thermal environment. Steel Compos Struct 40:243–254. https://doi.org/10.12989/scs.2021.40.2.243

    Article  Google Scholar 

  147. Fang J, Yin B, Zhang X (2022) Size-dependent vibrations of porous functionally graded rotating microplates under thermal environment. Eur J Mech - A/Solids 95:104645. https://doi.org/10.1016/j.euromechsol.2022.104645

    Article  MathSciNet  MATH  Google Scholar 

  148. Pham Q-H, Tran TT, Tran VK et al (2022) Bending and hygro-thermo-mechanical vibration analysis of a functionally graded porous sandwich nanoshell resting on elastic foundation. Mech Adv Mater Struct 29:5885–5905. https://doi.org/10.1080/15376494.2021.1968549

    Article  Google Scholar 

  149. Setoodeh AR, Tahani M, Selahi E (2012) Transient dynamic and free vibration analysis of functionally graded truncated conical shells with non-uniform thickness subjected to mechanical shock loading. Compos Part B Eng 43:2161–2171. https://doi.org/10.1016/j.compositesb.2012.02.031

    Article  Google Scholar 

  150. Malekzadeh P, Daraie M (2014) Dynamic analysis of functionally graded truncated conical shells subjected to asymmetric moving loads. Thin-Walled Struct 84:1–13. https://doi.org/10.1016/j.tws.2014.05.007

    Article  Google Scholar 

  151. Liang X, Kou H, Wang L et al (2015) Three-dimensional transient analysis of functionally graded material annular sector plate under various boundary conditions. Compos Struct 132:584–596. https://doi.org/10.1016/j.compstruct.2015.05.066

    Article  Google Scholar 

  152. 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. https://doi.org/10.1016/j.compstruct.2016.07.021

    Article  Google Scholar 

  153. Alavi SH, Eipakchi H (2021) Analytic solution for transient responses of viscoelastic FG plates subjected to various asymmetrically loads. Int J Comput Methods Eng Sci Mech 22:278–296. https://doi.org/10.1080/15502287.2020.1861129

    Article  MathSciNet  Google Scholar 

  154. Vu ANT, Le NAT, Nguyen DK (2021) Dynamic behaviour of bidirectional functionally graded sandwich beams under a moving mass with partial foundation supporting effect. Acta Mech 232:2853–2875. https://doi.org/10.1007/s00707-021-02948-z

    Article  MathSciNet  MATH  Google Scholar 

  155. Duc ND (2013) Nonlinear dynamic response of imperfect eccentrically stiffened FGM double curved shallow shells on elastic foundation. Compos Struct 99:88–96. https://doi.org/10.1016/j.compstruct.2012.11.017

    Article  Google Scholar 

  156. Kurtaran H (2015) Large displacement static and transient analysis of functionally graded deep curved beams with generalized differential quadrature method. Compos Struct 131:821–831. https://doi.org/10.1016/j.compstruct.2015.06.024

    Article  Google Scholar 

  157. Baştürk S, Uyanık H, Kazancı Z (2016) Nonlinear transient response of Basalt/Nickel FGM Composite Plates under Blast load. Procedia Eng 167:30–38. https://doi.org/10.1016/j.proeng.2016.11.666

    Article  Google Scholar 

  158. Hajlaoui A, Triki E, Frikha A et al (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. https://doi.org/10.1590/1679-78253323

    Article  Google Scholar 

  159. Phung-Van P, Ferreira AJM, Nguyen-Xuan H, Wahab MA (2017) An isogeometric approach for size-dependent geometrically nonlinear transient analysis of functionally graded nanoplates. Compos Part B Eng 118:125–134. https://doi.org/10.1016/j.compositesb.2017.03.012

    Article  Google Scholar 

  160. Nazari H, Babaei M, Kiarasi F, Asemi K (2021) Geometrically nonlinear dynamic analysis of functionally graded material plate excited by a moving load applying first-order shear deformation theory via generalized differential quadrature method. SN Appl Sci 3:847. https://doi.org/10.1007/s42452-021-04825-9

    Article  Google Scholar 

  161. Duc ND, Quang VD, Nguyen PD, Chien TM (2018) Nonlinear dynamic response of functionally graded porous plates on elastic foundation subjected to thermal and mechanical loads. J Appl Comput Mech 4:245–259. https://doi.org/10.22055/jacm.2018.23219.1151

    Article  Google Scholar 

  162. Esmaeilzadeh M, Kadkhodayan M (2019) Dynamic analysis of stiffened bi-directional functionally graded plates with porosities under a moving load by dynamic relaxation method with kinetic damping. Aerosp Sci Technol 93:105333. https://doi.org/10.1016/j.ast.2019.105333

    Article  Google Scholar 

  163. Trinh M-C, Nguyen D-D, Kim S-E (2019) Effects of porosity and thermomechanical loading on free vibration and nonlinear dynamic response of functionally graded sandwich shells with double curvature. Aerosp Sci Technol 87:119–132. https://doi.org/10.1016/j.ast.2019.02.010

    Article  Google Scholar 

  164. Kumar HSN, Kattimani S, Nguyen-Thoi T (2021) Influence of porosity distribution on nonlinear free vibration and transient responses of porous functionally graded skew plates. Def Technol 17:1918–1935. https://doi.org/10.1016/j.dt.2021.02.003

    Article  Google Scholar 

  165. Babaei M, Asemi K, Kiarasi F (2021) Dynamic analysis of functionally graded rotating thick truncated cone made of saturated porous materials. Thin-Walled Struct 164:107852. https://doi.org/10.1016/j.tws.2021.107852

    Article  Google Scholar 

  166. Akgün G, Kurtaran H, Kalbaran Ö (2021) Non-linear transient response of porous functionally graded truncated conical panels using GDQ method. Thin-Walled Struct 159:107276. https://doi.org/10.1016/j.tws.2020.107276

    Article  Google Scholar 

  167. Tran TT, Pham Q-H, Nguyen-Thoi T (2020) Dynamic analysis of functionally graded Porous Plates resting on Elastic Foundation taking into Mass subjected to moving loads using an edge-based smoothed finite element Method. Shock Vib 2020:1–19. https://doi.org/10.1155/2020/8853920

    Article  Google Scholar 

  168. Malekzadeh P, Heydarpour Y, Haghighi MRG, Vaghefi M (2012) Transient response of rotating laminated functionally graded cylindrical shells in thermal environment. Int J Press Vessel Pip 98:43–56. https://doi.org/10.1016/j.ijpvp.2012.07.003

    Article  MATH  Google Scholar 

  169. Zhang J-H, Li G-Z, Li S-R (2015) Analysis of transient displacements for a ceramic–metal functionally graded cylindrical shell under dynamic thermal loading. Ceram Int 41:12378–12385. https://doi.org/10.1016/j.ceramint.2015.06.070

    Article  Google Scholar 

  170. Ranjbar J, Alibeigloo A (2016) Response of functionally graded spherical shell to thermo-mechanical shock. Aerosp Sci Technol 51:61–69. https://doi.org/10.1016/j.ast.2016.01.021

    Article  Google Scholar 

  171. Sator L, Sladek V, Sladek J (2019) Coupling effects in transient analysis of FGM plates bending in non-classical thermoelasticity. Compos Part B Eng 165:233–246. https://doi.org/10.1016/j.compositesb.2018.11.093

    Article  MATH  Google Scholar 

  172. Verma KP, Maiti DK (2021) Transient analysis of thermo-mechanically shock loaded four-parameter power law functionally graded shells. Compos Struct 257:113388. https://doi.org/10.1016/j.compstruct.2020.113388

    Article  Google Scholar 

  173. Mojiri HR, Salami SJ (2022) Free vibration and dynamic transient response of functionally graded composite beams reinforced with graphene nanoplatelets (GPLs) resting on elastic foundation in thermal environment. Mech Based Des Struct Mach 50:1872–1892. https://doi.org/10.1080/15397734.2020.1766492

    Article  Google Scholar 

  174. Duc ND, Tran QQ, Khoa ND (2017) New approach to investigate nonlinear dynamic response and vibration of imperfect functionally graded carbon nanotube reinforced composite double curved shallow shells subjected to blast load and temperature. Aerosp Sci Technol 71:360–372. https://doi.org/10.1016/j.ast.2017.09.031

    Article  Google Scholar 

  175. Pradyumna S, Nanda N (2013) Geometrically nonlinear transient response of functionally graded Shell Panels with initial geometric imperfection. Mech Adv Mater Struct 20:217–226. https://doi.org/10.1080/15376494.2011.584148

    Article  Google Scholar 

  176. Alireza Babaee, Jelovica J (2021) Nonlinear transient thermoelastic response of FGM plate under sudden cryogenic cooling. Ocean Eng 226:108875. https://doi.org/10.1016/j.oceaneng.2021.108875

    Article  Google Scholar 

  177. Shariyat M, Lavasani SMH, Khaghani M (2010) Nonlinear transient thermal stress and elastic wave propagation analyses of thick temperature-dependent FGM cylinders, using a second-order point-collocation method. Appl Math Model 34:898–918. https://doi.org/10.1016/j.apm.2009.07.007

    Article  MathSciNet  MATH  Google Scholar 

  178. Shariyat M (2012) Nonlinear transient stress and wave propagation analyses of the FGM thick cylinders, employing a unified generalized thermoelasticity theory. Int J Mech Sci 65:24–37. https://doi.org/10.1016/j.ijmecsci.2012.09.001

    Article  Google Scholar 

  179. Duc ND, Quang VD, Anh VTT (2017) The nonlinear dynamic and vibration of the S-FGM shallow spherical shells resting on an elastic foundations including temperature effects. Int J Mech Sci 123:54–63. https://doi.org/10.1016/j.ijmecsci.2017.01.043

    Article  Google Scholar 

  180. Bich DH, Ninh DG, Kien BH, Hui D (2016) Nonlinear dynamical analyses of eccentrically stiffened functionally graded toroidal shell segments surrounded by elastic foundation in thermal environment. Compos Part B Eng 95:355–373. https://doi.org/10.1016/j.compositesb.2016.04.004

    Article  Google Scholar 

  181. Duc ND (2016) Nonlinear thermal dynamic analysis of eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations using the Reddy’s third-order shear deformation shell theory. Eur J Mech - A/Solids 58:10–30. https://doi.org/10.1016/j.euromechsol.2016.01.004

    Article  MathSciNet  MATH  Google Scholar 

  182. Najibi A, Talebitooti R (2017) Nonlinear transient thermo-elastic analysis of a 2D-FGM thick hollow finite length cylinder. Compos Part B Eng 111:211–227. https://doi.org/10.1016/j.compositesb.2016.11.055

    Article  Google Scholar 

  183. Wang A, Chen H, Zhang W (2019) Nonlinear transient response of doubly curved shallow shells reinforced with graphene nanoplatelets subjected to blast loads considering thermal effects. Compos Struct 225:111063. https://doi.org/10.1016/j.compstruct.2019.111063

    Article  Google Scholar 

  184. Lu Y, Chen X (2020) Nonlinear Parametric Dynamics of bidirectional functionally graded Beams. Shock Vib 2020:1–13. https://doi.org/10.1155/2020/8840833

    Article  Google Scholar 

  185. Abuteir BW, Harkati E, Boutagouga D et al (2021) Thermo-mechanical nonlinear transient dynamic and dynamic-buckling analysis of functionally graded material shell structures using an implicit conservative/decaying time integration scheme. Mech Adv Mater Struct. https://doi.org/10.1080/15376494.2021.1964115

    Article  Google Scholar 

  186. Cong PH, Duc ND (2021) Nonlinear dynamic analysis of porous eccentrically stiffened double curved shallow auxetic shells in thermal environments. Thin-Walled Struct 163:107748. https://doi.org/10.1016/j.tws.2021.107748

    Article  Google Scholar 

  187. Phung-Van P, Thai CH, Ferreira AJM, Rabczuk T (2020) Isogeometric nonlinear transient analysis of porous FGM plates subjected to hygro-thermo-mechanical loads. Thin-Walled Struct 148:106497. https://doi.org/10.1016/j.tws.2019.106497

    Article  Google Scholar 

  188. Chan DQ, Thanh N, Van, Khoa ND, Duc ND (2020) Nonlinear dynamic analysis of piezoelectric functionally graded porous truncated conical panel in thermal environments. Thin-Walled Struct 154:106837. https://doi.org/10.1016/j.tws.2020.106837

    Article  Google Scholar 

  189. Aksoylar C, Ömercikoğlu A, Mecitoğlu Z, Omurtag MH (2012) Nonlinear transient analysis of FGM and FML plates under blast loads by experimental and mixed FE methods. Compos Struct 94:731–744. https://doi.org/10.1016/j.compstruct.2011.09.008

    Article  Google Scholar 

  190. Wattanasakulpong N, Gangadhara Prusty B, Kelly DW, Hoffman M (2012) Free vibration analysis of layered functionally graded beams with experimental validation. Mater Des 36:182–190. https://doi.org/10.1016/j.matdes.2011.10.049

    Article  Google Scholar 

  191. Bajaj K, Shrivastava Y, Dhoke P (2013) Experimental study of functionally graded Beam with fly Ash. J Inst Eng Ser A 94:219–227. https://doi.org/10.1007/s40030-014-0057-z

    Article  Google Scholar 

  192. Sazesh S, Ghassemi A, Ebrahimi R, Khodaei M (2017) Experimental and Numerical Analysis of Titanium/HA FGM for Dental Implantation. Int J Adv Des Manuf Technol 10:57–74

    Google Scholar 

  193. Gheysarian A, Honarpisheh M (2021) Experimental and Numerical Investigation of process parameters on the residual stresses in the Al-Cu FGM materials. Exp Tech 45:601–612. https://doi.org/10.1007/s40799-021-00444-6

    Article  Google Scholar 

  194. Alhijazi M, Safaei B, Zeeshan Q et al (2022) Prediction of elastic properties of thermoplastic composites with natural fibers. J Text Inst. https://doi.org/10.1080/00405000.2022.2131352

    Article  Google Scholar 

  195. Ramteke PM, Panda SK (2023) Nonlinear static and dynamic response prediction of bidirectional doubly-curved porous FG panel and experimental validation. Compos Part A 166:107388. https://doi.org/10.1016/j.compositesa.2022.107388

    Article  Google Scholar 

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Ramteke, P.M., Panda, S.K. Computational Modelling and Experimental Challenges of Linear and Nonlinear Analysis of Porous Graded Structure: A Comprehensive Review. Arch Computat Methods Eng 30, 3437–3452 (2023). https://doi.org/10.1007/s11831-023-09908-x

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  • DOI: https://doi.org/10.1007/s11831-023-09908-x

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