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A new \({\varvec{n}}\)th-order shear deformation theory for isogeometric thermal buckling analysis of FGM plates with temperature-dependent material properties

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Abstract

This study presents an isogeometric analysis (IGA) for investigating the buckling behavior of functionally graded material (FGM) plates in thermal environments. The material properties of the FGM plate are considered to be graded across the thickness, and temperature dependency of the material properties is taken into account. A new nth-order shear deformation theory with the von Kármán type of geometric nonlinearity, in which the optimum order number to best approximate the thermal buckling problem can be chosen, is developed. The principle of virtual work is used to derive the governing equations for the nonlinear thermal buckling analysis. The nth-order shear deformation theory is incorporated into the non-uniform rational B-spline-based IGA which fulfills the \(C^{1}\)-continuity requirement of the proposed higher-order plate theory. The discrete nonlinear system equations are solved by utilizing the modified Newton–Raphson iterative technique. Parametric studies on the buckling behavior of FGM plates subjected to diverse through-thickness temperature variations are performed, and the influence of temperature dependency of the material properties is examined. Results validate the performance accuracy and effectiveness of the proposed IGA based on the nth-order shear deformation theory, and they demonstrate that temperature-dependent material properties should be included in the thermal buckling analysis.

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References

  1. Chareonsuk, J., Vessakosol, P.: Numerical solutions for functionally graded solids under thermal and mechanical loads using a high-order control volume finite element method. Appl. Therm. Eng. 31, 213–227 (2011)

    Google Scholar 

  2. Javaheri, R., Eslami, M.R.: Thermal buckling of functionally graded plates based on higher order theory. J. Therm. Stress. 25, 603–625 (2002)

    Google Scholar 

  3. Javaheri, R., Eslami, M.R.: Thermal buckling of functionally graded plates. AIAA J. 40, 162–169 (2002)

    MATH  Google Scholar 

  4. Wu, L.: Thermal buckling of simply supported moderately thick rectangular FGM plate. Compos. Struct. 64, 211–218 (2004)

    Google Scholar 

  5. Na, K.-S., Kim, J.-H.: Thermal postbuckling investigations of functionally graded plates using 3-D finite element method. Finite Elem. Anal. Des. 42, 749–756 (2006)

    Google Scholar 

  6. Matsunaga, H.: Thermal buckling of functionally graded plates according to a 2D higher-order deformation theory. Compos. Struct. 90, 76–86 (2009)

    Google Scholar 

  7. Tung, H.V., Duc, N.D.: Nonlinear analysis of stability for functionally graded plates under mechanical and thermal loads. Compos. Struct. 92, 1184–1191 (2010)

    Google Scholar 

  8. Duc, N.D., Tung, H.V.: Mechanical and thermal postbuckling of higher order shear deformable functionally graded plates on elastic foundations. Compos. Struct. 93, 2874–2881 (2011)

    Google Scholar 

  9. Khorshidvand, A.R., Eslami, M.R.: A comparison between thermal buckling solutions of power-law, sigmoid, exponential FGM circular plates. Int. J. Eng. Technol. 5, 191–194 (2013)

    Google Scholar 

  10. Ashoori, A.R., Sadough Vanini, S.V.: Thermal buckling of annular microstructure-dependent functionally graded material plates resting on an elastic medium. Compos. Part B Eng. 87, 245–255 (2016)

    MATH  Google Scholar 

  11. Do, V.N.V., Lee, C.H.: Thermal buckling analyses of FGM sandwich plates using the improved radial point interpolation mesh-free method. Compos. Struct. 177, 171–186 (2017)

    Google Scholar 

  12. Do, V.N.V., Lee, C.H.: 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 (2018)

    MathSciNet  Google Scholar 

  13. Do, V.N.V., Lee, C.H.: Quasi-3D higher-order shear deformation theory for thermal buckling analysis of FGM plates based on a meshless method. Aerosp. Sci. Technol. 82–83, 450–465 (2018)

    Google Scholar 

  14. Do, V.N.V., Tran, M.T., Lee, C.H.: Nonlinear thermal buckling analyses of functionally graded plates by a mesh-free radial point interpolation method. Eng. Anal. Bound. Elem. 87, 153–164 (2018)

    MathSciNet  MATH  Google Scholar 

  15. Do, V.N.V., Ong, T.H., Lee, C.H.: Isogeometric analysis for nonlinear buckling of FGM plates under various types of thermal gradients. Thin Walled Struct. 137, 448–462 (2019)

    Google Scholar 

  16. Cong, P.H., Chien, T.M., Khoa, N.D., Duc, N.D.: Nonlinear thermomechanical buckling and post-buckling response of porous FGM plates using Reddy’s HSDT. Aerosp. Sci. Technol. 77, 419–428 (2018)

    Google Scholar 

  17. Na, K.-S., Kim, J.-H.: Three-dimensional thermal buckling analysis of functionally graded materials. Compos. Part B Eng. 35, 429–437 (2004)

    Google Scholar 

  18. Na, K.S., Kim, J.H.: Three-dimensional thermomechanical buckling analysis of functionally graded composite plates. Compos. Struct. 73, 413–422 (2006)

    Google Scholar 

  19. Park, J.S., Kim, J.H.: Thermal postbuckling and vibration analyses of functionally graded plates. J. Sound Vib. 289, 77–93 (2006)

    MATH  Google Scholar 

  20. Shen, H.S.: Thermal postbuckling behavior of shear deformable FGM plates with temperature-dependent properties. Int. J. Mech. Sci. 49, 466–478 (2007)

    Google Scholar 

  21. Lee, Y.Y., Zhao, X., Reddy, J.N.: Postbuckling analysis of functionally graded plates subject to compressive and thermal loads. Comput. Methods Appl. Mech. Eng. 199, 1645–1653 (2010)

    MathSciNet  MATH  Google Scholar 

  22. Zhang, D.G., Zhou, H.M.: Mechanical and thermal post-buckling analysis of FGM rectangular plates with various supported boundaries resting on nonlinear elastic foundations. Thin Walled Struct. 89, 142–151 (2015)

    Google Scholar 

  23. Lee, Y.H., Bae, S.I., Kim, J.H.: Thermal buckling behavior of functionally graded plates based on neutral surface. Compos. Struct. 137, 208–214 (2016)

    Google Scholar 

  24. Taczała, M., Buczkowski, R., Kleiber, M.: Nonlinear buckling and post-buckling response of stiffened FGM plates in thermal environments. Compos. Part B Eng. 109, 238–247 (2017)

    Google Scholar 

  25. Reissner, E.: The effect of transverse shear deformation on the bending of elastic plates. J. Appl. Mech. Trans. ASME 12, 69–77 (1945)

    MathSciNet  MATH  Google Scholar 

  26. Mindlin, R.D.: Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates. J. Appl. Mech. Trans. ASME 18, 31–38 (1951)

    MATH  Google Scholar 

  27. Rabczuk, T., Areias, P.M.A., Belytschko, T.: A meshfree thin shell method for non-linear dynamic fracture. Int. J. Numer. Methods Eng. 72, 524–548 (2007)

    MathSciNet  MATH  Google Scholar 

  28. Rabczuk, T., Gracie, R., Song, J.H., Belytschko, T.: Immersed particle method for fluid-structure interaction. Int. J. Numer. Methods Eng. 81, 48–71 (2010)

    MathSciNet  MATH  Google Scholar 

  29. Fernandez-Mendez, S., Huerta, A.: Imposing essential boundary conditions in mesh-free methods. Comput. Methods Appl. Mech. Eng. 193, 1257–1275 (2004)

    MathSciNet  MATH  Google Scholar 

  30. Xiang, S., Jin, Y.-X., Bi, Z.-Y., Jiang, S.-X., Yang, M.-S.: A \(n\)-order shear deformation theory for free vibration of functionally graded and composite sandwich plates. Compos. Struct. 93, 2826–2832 (2011)

    Google Scholar 

  31. Xiang, S., Kang, G.-W.: A \(n\)th-order shear deformation theory for the bending analysis on the functionally graded plates. Eur. J. Mech. A/Solids 37, 336–343 (2013)

    MathSciNet  MATH  Google Scholar 

  32. Xiang, S., Kang, G.-W., Liu, Y.-Q.: A nth-order shear deformation theory for natural frequency of the functionally graded plates on elastic foundations. Compos. Struct. 111, 224–231 (2014)

    Google Scholar 

  33. Hughes, T.J.R., Cottrell, J.A., Bazilevs, Y.: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Eng. 194, 4135–4195 (2005)

    MathSciNet  MATH  Google Scholar 

  34. Tran, L.V., Thai, C.H., Nguyen-Xuan, H.: An isogeometric finite element formulation for thermal buckling analysis of functionally graded plates. Finite Elem. Anal. Des. 73, 65–76 (2013)

    Google Scholar 

  35. Yin, S., Hale, J.S., Yu, T., Bui, T.Q., Bordas, S.P.A.: Isogeometric locking-free plate element: a simple first order shear deformation theory for functionally graded plates. Compos. Struct. 118, 121–138 (2014)

    Google Scholar 

  36. Nguyen, N.-T., Hui, D., Lee, J., Nguyen-Xuan, H.: An efficient computational approach for size-dependent analysis of functionally graded nanoplates. Comput. Methods Appl. Mech. Eng. 297, 191–218 (2015)

    MathSciNet  MATH  Google Scholar 

  37. Yin, S., Yu, T., Bui, T.Q., Nguyen, M.N.: Geometrically nonlinear analysis of functionally graded plates using isogeometric analysis. Eng. Comput. 32, 519–558 (2015)

    Google Scholar 

  38. Thai, C.H., Zenkour, A.M., Wahab, M.A., Nguyen-Xuan, H.: A simple four-unknown shear and normal deformations theory for FG isotropic and sandwich plates based on isogeometric analysis. Compos. Struct. 139, 77–95 (2016)

    Google Scholar 

  39. Yin, S., Yu, T., Bui, T.Q., Zheng, X., Tanaka, S.: In-plane material inhomogeneity of functionally graded plates: A higher-order shear deformation plate isogeometric analysis. Compos. Part B Eng. 106, 273–284 (2016)

    Google Scholar 

  40. Yu, T., Bui, T.Q., Yin, S., Doan, D.H., Wu, C.T., Do, T.V., Tanaka, S.: On the thermal buckling analysis of functionally graded plates with internal defects using extended isogeometric analysis. Compos. Struct. 136, 684–695 (2016)

    Google Scholar 

  41. Yu, T., Yin, S., Bui, T.Q., Xia, S., Tanaka, S., Hirose, S.: NURBS-based isogeometric analysis of buckling and free vibration problems for laminated composites plates with complicated cutouts using a new simple FSDT theory and level set method. Thin Walled Struct. 101, 141–156 (2016)

    Google Scholar 

  42. Liu, S., Yu, T., Bui, T.Q.: Size effects of functionally graded moderately thick microplates: a novel non-classical simple-FSDT isogeometric analysis. Eur. J. Mech. A/Solids 66, 446–458 (2017)

    MathSciNet  MATH  Google Scholar 

  43. Liu, S., Yu, T., Bui, T.Q., Yin, S., Thai, D.-K., Tanaka, S.: Analysis of functionally graded plates by a simple locking-free quasi-3D hyperbolic plate isogeometric method. Compos. Part B Eng. 120, 182–196 (2017)

    Google Scholar 

  44. Thai, S., Thai, H.-T., Vo, T.P., Reddy, J.N.: Post-buckling of functionally graded microplates under mechanical and thermal loads using isogeomertic analysis. Eng. Struct. 150, 905–917 (2017)

    Google Scholar 

  45. Kiani, Y.: NURBS-based isogeometric thermal postbuckling analysis of temperature dependent graphene reinforced composite laminated plates. Thin Walled Struct. 125, 211–219 (2018)

    Google Scholar 

  46. Lia, K., Wu, D., Chen, X., Cheng, J., Liu, Z., Gao, W., Liu, M.: Isogeometric analysis of functionally graded porous plates reinforced by graphene platelets. Compos. Struct. 204, 114–130 (2018)

    Google Scholar 

  47. Reddy, J.N.: Analysis of functionally graded plates. Int. J. Numer. Methods Eng. 47, 663–684 (2000)

    MATH  Google Scholar 

  48. Zhu, P., Zhang, L.W., Liew, K.M.: Geometrically nonlinear thermomechanical analysis of moderately thick functionally graded plates using a local Petrov–Galerkin approach with moving Kriging interpolation. Compos. Struct. 107, 298–314 (2014)

    Google Scholar 

  49. Reddy, J.N., Chin, C.D.: Thermomechanial analysis of functionally graded cylinders and plates. J. Therm. Stress. 21, 593–626 (1998)

    Google Scholar 

  50. Zenkour, A.M., Sobhy, M.: Thermal buckling of various types of FGM sandwich plates. Compos. Struct. 93, 93–102 (2010)

    Google Scholar 

  51. Fazzolari, F.A., Carrera, E.: Thermal stability of FGM sandwich plates under various through-the-thickness temperature distributions. J. Therm. Stress. 37, 1449–1481 (2014)

    Google Scholar 

  52. Nguyen, V.P., Anitescu, C., Bordas, S.P.A., Rabczuk, T.: Isogeometric analysis: an overview and computer implementation aspects. Math. Comput. Simul. 117, 89–116 (2015)

    MathSciNet  Google Scholar 

  53. Nguyen-Thanh, N., Nguyen-Xuan, H., Bordas, S.P.A., Rabczuk, T.: Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids. Comput. Methods Appl. Mech. Eng. 200, 1892–1908 (2011)

    MathSciNet  MATH  Google Scholar 

  54. Nguyen-Thanh, N., Kiendl, J., Nguyen-Xuan, H., Wüchner, R., Bletzinger, K.U., Bazilevs, Y., Rabczuk, T.: Rotation free isogeometric thin shell analysis using PHT-splines. Comput. Methods Appl. Mech. Eng. 200, 3410–3424 (2011)

    MathSciNet  MATH  Google Scholar 

  55. Nguyen-Thanh, N., Zhou, K., Zhuang, X., Areias, P., Nguyen-Xuan, H., Bazilevs, Y., Rabczuk, T.: Isogeometric analysis of large-deformation thin shells using RHT-splines for multiple-patch coupling. Comput. Methods Appl. Mech. Eng. 316, 1157–1178 (2017)

    MathSciNet  Google Scholar 

  56. Anitescu, C., Hossain, M.N., Rabczuk, T.: Recovery-based error estimation and adaptivity using high-order splines over hierarchical T-meshes. Comput. Methods Appl. Mech. Eng. 328, 638–662 (2018)

    MathSciNet  Google Scholar 

  57. Liew, K.M., Yang, J., Kitipornchai, S.: Thermal post-buckling of laminated plates comprising functionally graded materials with temperature-dependent properties. J. Appl. Mech. Trans. ASME 71, 839–850 (2004)

    MATH  Google Scholar 

  58. Ghiasian, S.E., Kiani, Y., Sadighi, M., Eslami, M.R.: Thermal buckling of shear deformable temperature dependent circular/annular FGM plates. Int. J. Mech. Sci. 81, 137–148 (2014)

    Google Scholar 

  59. Kiani, Y., Eslami, M.R.: An exact solution for thermal buckling of annular FGM plates on an elastic medium. Compos. Part B Eng. 45, 101–110 (2013)

    Google Scholar 

  60. Shen, H.S.: Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments. Compos. Struct. 91, 9–19 (2009)

    Google Scholar 

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Funding

This research was supported by Mid-career Researcher Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (NRF-2015R1A2A2A01006390).

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Authors and Affiliations

  1. Applied Computational Civil and Structural Engineering Research Group, Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Vuong Nguyen Van Do

  2. The Graduate School of Construction Engineering, Chung-Ang University, 84 Heukseok-ro, Dongjak-gu, Seoul, 06974, Republic of Korea

    Chin-Hyung Lee

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  1. Vuong Nguyen Van Do
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Correspondence to Chin-Hyung Lee.

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Do, V.N.V., Lee, CH. A new \({\varvec{n}}\)th-order shear deformation theory for isogeometric thermal buckling analysis of FGM plates with temperature-dependent material properties. Acta Mech 230, 3783–3805 (2019). https://doi.org/10.1007/s00707-019-02480-1

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  • DOI: https://doi.org/10.1007/s00707-019-02480-1

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