Engineering with Computers

, Volume 35, Issue 2, pp 467–485 | Cite as

Geometrically nonlinear deflection and stress analysis of skew sandwich shell panel using higher-order theory

  • Pankaj V. Katariya
  • Chetan K. Hirwani
  • Subrata K. PandaEmail author
Original Article


The nonlinear static responses of the skew sandwich flat/curved shell panel including the corresponding stress values are examined in this article under the influence of the unvarying transverse mechanical load. To evaluate the said responses of the sandwich panel, the physical structure model turned to a mathematical form via a higher-order kinematic theory including the stretching term effect in the displacement field variable. The effect of geometrical nonlinearity has been included via Green–Lagrange strain–displacement kinematics. The governing equation has been derived from the variational principle and is solved via direct iterative technique including the finite element procedure. Further, a customized finite element computer code has been developed in MATLAB environment based on the current mathematical model for the computational purpose. To check the comprehensive behavior of the proposed model, the bending responses are obtained for different mesh sizes and compared with the published data (numerical and 3D elasticity solution). Subsequently, a wide range of numerical examples have been solved for the different geometrical configurations (side-to-thickness ratio, curvature ratio, core-to-face thickness ratio, skew angle and support conditions) and the influence of the same on deflection and stress behavior has been shown and discussed in detail.


Bending Equivalent single layer Skew Green–Lagrange HSDT 



  1. 1.
    Ren-huai L (1993) Nonlinear bending of simply supported rectangular sandwich plates. Appl Math Mech 14:217–234CrossRefGoogle Scholar
  2. 2.
    Pilipchuk VN, Berdichevsky VL, Ibrahim RA (2010) Thermo-mechanical coupling in cylindrical bending of sandwich plates. Compos Struct 92:2632–2640CrossRefGoogle Scholar
  3. 3.
    Sturzenbecher R, Hofstetter K (2011) Bending of cross-ply laminated composites: an accurate and efficient plate theory based upon models of Lekhnitskii and Ren. Compos Struct 93:1078–1088CrossRefGoogle Scholar
  4. 4.
    Ferreira AJM, Carrera E, Cinefra M, Roque CMC (2013) Radial basis functions collocation for the bending and free vibration analysis of laminated plates using the Reissner-Mixed Variational Theorem. Eur J Mech A Solids 39:104–112MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Ferreira AJM, Viola E, Tornabene F, Fantuzzi N, Zenkour AM (2013) Analysis of sandwich plates by generalized differential quadrature method. Math Probl Eng. MathSciNetzbMATHGoogle Scholar
  6. 6.
    Nguyen MN, Bui TQ, Truong TT, Tanaka S, Hirose S (2017) Numerical analysis of 3-D solids and composite structures by an enhanced 8-node hexahedral element. Finite Elem Anal Des 131:1–16MathSciNetCrossRefGoogle Scholar
  7. 7.
    Topal U, Uzman U (2008) Strength optimization of laminated composite plates. J Compos Mater 42:1731–1746CrossRefGoogle Scholar
  8. 8.
    Kheirikhah MM, Babaghasabha V (2016) Bending and buckling analysis of corrugated composite sandwich plates. J Braz Soc Mech Sci Eng 38:2571–2588CrossRefGoogle Scholar
  9. 9.
    Reddy BS, Reddy AR, Kumar JS, Reddy KVK (2012) Bending analysis of laminated composite plates using finite element method. Int J Eng Sci Technol 4:177–190Google Scholar
  10. 10.
    Liang-bo D (1989) Bending and vibration of composite laminated plates. Appl Math Mech 10:345–352CrossRefzbMATHGoogle Scholar
  11. 11.
    Kumar A, Singha MK, Tiwari V (2017) Nonlinear bending and vibration analyses of quadrilateral composite plates. Thin Wall Struct 113:170–180CrossRefGoogle Scholar
  12. 12.
    Do TV, Bui TQ, Yu TT, Pham DT, Nguyen CT (2017) Role of material combination and new results of mechanical behaviors for FG sandwich plates in thermal environment. J Comput Sci 21:164–181MathSciNetCrossRefGoogle Scholar
  13. 13.
    Lee LJ, Fan YJ (1996) Bending and vibration analysis of composite sandwich plates. Comput Struct 60:103–112CrossRefzbMATHGoogle Scholar
  14. 14.
    Mehrabian M, Golmakani ME (2015) Nonlinear bending analysis of radial-stiffened annular laminated sector plates with dynamic relaxation method. Comput Math Appl 69:1272–1302MathSciNetCrossRefGoogle Scholar
  15. 15.
    Srinivas S, Rao AK (1970) Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates. Int J Solids Struct 6:1463–1481CrossRefzbMATHGoogle Scholar
  16. 16.
    Butalia TS, Kant T, Dixit VDT (1990) Performance of heterosis element for bending of skew rhombic plates. Comput Struct 34:23–49CrossRefzbMATHGoogle Scholar
  17. 17.
    Cui XY, Liu GR, Li GY (2011) Bending and vibration responses of laminated composite plates using an edge-based smoothing technique. Eng Anal Bound Elem 35:818–826MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Muhammad T, Singh AV (2004) A p-type solution for the bending of rectangular, circular, elliptic and skew plates. Int J Solids Struct 41:3977–3997CrossRefzbMATHGoogle Scholar
  19. 19.
    Heydari MM, Kolahchi R, Heydari M, Abbasi A (2014) Exact solution for transverse bending analysis of embedded laminated Mindlin plate. Struct Eng Mech 49:661–672CrossRefGoogle Scholar
  20. 20.
    Cetkovic M, Vuksanovic Dj (2009) Bending, free vibrations and buckling of laminated composite and sandwich plates using a layerwise displacement model. Compos Struct 88:219–227CrossRefGoogle Scholar
  21. 21.
    Thai ND, D’Ottavio M, Caron JF (2013) Bending analysis of laminated and sandwich plates using a layer-wise stress model. Compos Struct 96:135–142CrossRefGoogle Scholar
  22. 22.
    Cetkovic M (2015) Thermo-mechanical bending of laminated composite and sandwich plates using layerwise displacement model. Compos Struct 125:388–399CrossRefGoogle Scholar
  23. 23.
    Kolahchi R (2017) A comparative study on the bending, vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC, HDQ and DQ methods. Aerosp Sci Technol 66:235–248CrossRefGoogle Scholar
  24. 24.
    Shariyat M (2010) A generalized high-order global-local plate theory for nonlinear bending and buckling analyses of imperfect sandwich plates subjected to thermo-mechanical loads. Compos Struct 92:130–143CrossRefGoogle Scholar
  25. 25.
    Sheikh AH, Chakrabarti A (2003) A new plate bending element based on higher-order shear deformation theory for the analysis of composite plates. Finite Elem Anal Des 39:883–903CrossRefGoogle Scholar
  26. 26.
    Taj G, Chakrabarti A (2013) An Efficient C0 finite element approach for bending analysis of functionally graded ceramic-metal skew shell panels. J Solid Mech 5:47–62Google Scholar
  27. 27.
    Chalak HD, Chakrabarti A, Sheikh AH, Iqbal MA (2014) C0 FE model based on HOZT for the analysis of laminated soft core skew sandwich plates: bending and vibration. Appl Math Modell 38:1211–1223CrossRefzbMATHGoogle Scholar
  28. 28.
    Chakrabarti A, Sheikh AH (2005) Analysis of laminated sandwich plates based on interlaminar shear stress continuous plate theory. J Eng Mech 131:377–384CrossRefGoogle Scholar
  29. 29.
    Mahi A, Adda Bedia EA, Tounsi A (2015) A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates. Appl Math Model 39:2489–2508MathSciNetCrossRefGoogle Scholar
  30. 30.
    Kolahchi R, Bidgoli AMM, Heydari MM (2015) Size-dependent bending analysis of FGM nano-sinusoidal plates resting on orthotropic elastic medium. Struct Eng Mech 55:1001–1014CrossRefGoogle Scholar
  31. 31.
    Zhou Y, Zhu J (2016) Vibration and bending analysis of multiferroic rectangular plates using third-order shear deformation theory. Compos Struct 153:712–723CrossRefGoogle Scholar
  32. 32.
    Sreehari VM, George LJ, Maiti DK (2016) Bending and buckling analysis of smart composite plates with and without internal flaw using an inverse hyperbolic shear deformation theory. Compos Struct 138:64–74CrossRefGoogle Scholar
  33. 33.
    Bui TQ, Do TV, Ton LHT, Doan DH, Tanaka S, Pham DT, Nguyen-Van TA, Yu TT, Hirose S (2016) On the high temperature mechanical behaviors analysis of heated functionally graded plates using FEM and a new third-order shear deformation plate theory. Compos Part B 92:218–241CrossRefGoogle Scholar
  34. 34.
    Do TV, Nguyen DK, Duc ND, Doan DH, Bui TQ (2017) Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory. Thin Walled Struct 119:687–699CrossRefGoogle Scholar
  35. 35.
    Bui TQ, Nguyen MN, Zhang C (2011) An efficient meshfree method for vibration analysis of laminated composite plates. Comput Mech 48:175–193CrossRefzbMATHGoogle Scholar
  36. 36.
    Bui TQ, Khosravifard A, Zhang Ch, Hematiyan MR, Golub MV (2013) Dynamic analysis of sandwich beams with functionally graded core using a truly meshfree radial point interpolation method. Eng Struct 47:90–104CrossRefGoogle Scholar
  37. 37.
    Yin S, Yu TT, Bui TQ, Nguyen MN (2015) Geometrically nonlinear analysis of functionally graded plates using isogeometric analysis. Eng Comput 32:519–558CrossRefGoogle Scholar
  38. 38.
    Yu TT, Yin S, Bui TQ, Hirose S (2015) A simple FSDT-based isogeometric analysis for geometrically nonlinear analysis of functionally graded plates. Finite Elem Anal Des 96:1–10CrossRefGoogle Scholar
  39. 39.
    Walker M, Hamilton R (2007) A technique for optimally designing fibre-reinforced laminated structures for minimum weight with manufacturing uncertainties accounted for. Eng Comput 21:282–288CrossRefGoogle Scholar
  40. 40.
    Upadhyay AK, Shukla KK (2013) Non-linear static and dynamic analysis of skew sandwich plates. Compos Struct 105:141–148CrossRefGoogle Scholar
  41. 41.
    Lal A, Singh BN, Anand S (2011) Nonlinear bending response of laminated composite spherical shell panel with system randomness subjected to hygro-thermo-mechanical loading. Int J Mech Sci 53:855–866CrossRefGoogle Scholar
  42. 42.
    Nguyen TN, Thai CH, Nguyen-Xuan H (2016) On the general framework of high order shear deformation theories for laminated composite plate structures: a novel unified approach. Int J Mech Sci 110:242–255CrossRefGoogle Scholar
  43. 43.
    Nguyena TN, Ngo TD, Nguyen-Xuan H (2017) A novel three-variable shear deformation plate formulation: theory and Isogeometric implementation. Comput Methods Appl Mech Eng 326:376–401MathSciNetCrossRefGoogle Scholar
  44. 44.
    Thai CH, Nguyen TN, Rabczuk T, Nguyen-Xuan H (2016) An improved moving Kriging meshfree method for plate analysis using a refined plate theory. Comput Struct 176:34–49CrossRefGoogle Scholar
  45. 45.
    Thai CH, Ferreira AJM, Nguyen-Xuan H (2017) Naturally stabilized nodal integration meshfree formulations for analysis of laminated composite and sandwich plates. Compos Struct 178:260–276CrossRefGoogle Scholar
  46. 46.
    Nguyen NV, Nguyen HX, Phan DH, Nguyen-Xuan H (2017) A polygonal finite element method for laminated composite plates. Int J Mech Sci 133:863–882CrossRefGoogle Scholar
  47. 47.
    Dash P, Singh BN (2010) Geometrically nonlinear bending analysis of laminated composite plate. Commun Nonlinear Sci Numer Simul 15:3170–3181CrossRefGoogle Scholar
  48. 48.
    Singh VK, Mahapatra TR, Panda SK (2016) Nonlinear flexural analysis of single/doubly curved smart composite shell panels integrated with PFRC actuator. Eur J Mech A Solids A Solids 60:300–314CrossRefGoogle Scholar
  49. 49.
    Mahapatra TR, Kar VS, Panda SK (2016) Large amplitude bending behaviour of laminated composite curved panels. Eng Comput 33:116–138CrossRefGoogle Scholar
  50. 50.
    Jones RM (1999) Mechanics of composite materials. Taylor & Francis, PhiladelphiaGoogle Scholar
  51. 51.
    Cook RD, Malkus DS, Plesha ME, Witt RJ (2003) Concepts and applications of finite element analysis. Willy, SingaporeGoogle Scholar
  52. 52.
    Reddy JN, (2003) Mechanics of laminated composite: plates and shells—theory and analysis. CRC Press, Boca RatonGoogle Scholar
  53. 53.
    Pagano NJ (1970) Exact solutions for rectangular bidirectional composites and sandwich plates. J Comput Math 4:20–34Google Scholar
  54. 54.
    Kant T, Gupta AB, Pendhari SS, Desai YM (2008) Elasticity solution for cross-ply composite and sandwich laminates. Compos Struct 83:13–24CrossRefGoogle Scholar
  55. 55.
    Pagano NJ (1970) Exact solution of rectangular bidirectional composites and sandwich plates. J Compos Mater 4:20–34CrossRefGoogle Scholar
  56. 56.
    Pandya BN, Kant T (1988) Higher-order shear deformation theories for flexure of sandwich plates-finite element evaluations. Int J Solids Struct 24:1267–1286CrossRefzbMATHGoogle Scholar
  57. 57.
    Wu CP, Kuo HC (1993) An interlaminar stress mixed finite element method for the analysis of thick laminated composite plates. Compos Struct 24:29–42CrossRefGoogle Scholar
  58. 58.
    Ramtekkar GS, Desai YM, Shah AH, (2002) Mixed finite element model for thick composite laminated plates. Mech Adv Mater Struct 9:133–156CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  • Pankaj V. Katariya
    • 1
  • Chetan K. Hirwani
    • 1
  • Subrata K. Panda
    • 1
    Email author
  1. 1.Department of Mechanical EngineeringNational Institute of Technology RourkelaRourkelaIndia

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