Buckling analysis of symmetric laminated composite plates for various thickness ratios and modes

Abstract

This paper addresses the refined plate theory considering the simplified form of governing differential equations used to solve buckling analysis of laminated composite plates. Such laminated composites are often used in structural applications with recent advancements in material technology. This led to the creation of a new composite with enhanced properties to sustain compressive in-plane loading. Under compressive loads and/or due to thin built-up, laminated composites may be prone to buckle. Hence, it attains attraction to study buckling characteristics of laminated composites and is required filed of research now days. Very few literatures are available on buckling characteristics of laminated composite plate with different boundary conditions. Hence, this study investigates buckling behaviors of laminated composite structures with a cross-ply lamination scheme of plates with such boundary conditions. In addiditon, parametric study is performed for isotropic and such cross ply laminated plates under buckling to study the effect of plate thickness ratios on buckling load. As aspect ratio of laminates gets doubled, buckling loads lower down by 36% for thin to moderately thick plates. As we go from thin to thick plate; buckling loads for laminated plates gets changed by 62% for which details are shown in results part of the present paper. In particular, new results reported in this paper are focused on the significant effects of the buckling for various parameters of laminates, such as boundary condition, aspect ratio, width-to-thickness ratio, and stacking sequences with various modes of buckling.

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References

  1. 1.

    Reissner E (1945) The effect of transverse shear deformations on the bending of elastic plates. J Appl Mech 12:A69–77

    Google Scholar 

  2. 2.

    Mindlin RD (1951) Influence of rotary inertia and shear in flexural motions of isotropic elastic plates. J Appl Mech 18:31–38

    Google Scholar 

  3. 3.

    Reissner E, Stavsky Y (1961) Bending and stretching of certain types of aelotropic elastic plates. J Appl Mech 28:402–408

    Google Scholar 

  4. 4.

    Hardy RL (1971) Multiquadric equations of topography and other irregular surfaces. Geophys Res 176:1905–1915

    Google Scholar 

  5. 5.

    Noor AK (1973) Free vibration of multilayered plates. AIAA J 11:1038–1039

    Google Scholar 

  6. 6.

    Noor AK (1975) Stability of multilayer composite plates. Fiber Sci Technol 8:81–89

    Google Scholar 

  7. 7.

    Dawe DJ, Roufaeil OL (1980) Rayleigh-Ritz vibration analysis of Mindlin plates. J Sound Vib 69(3):345–359

    Google Scholar 

  8. 8.

    Kant T (1982) Numerical analysis of thick plates. Comput Methods Appl Mech Eng 31:1–18

    Google Scholar 

  9. 9.

    Reddy JN (1984) A simple higher-order theory for laminated composite plates. J Appl Mech 51:745–752

    Google Scholar 

  10. 10.

    Reddy JN, Phan ND (1985) Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory. J Sound Vib 98(2):157–170

    Google Scholar 

  11. 11.

    Putcha NS, Reddy JN (1986) Stability and natural vibration analysis of laminated plates by using a mixed element based on a refined plate theory. J Sound Vib 104(2):285–300

    Google Scholar 

  12. 12.

    Putcha NS, Reddy JN (1986) Stability and vibration analysis of laminated plates by using a mixed element based on a refined plate theory. J Sound Vib 104:285–300

    Google Scholar 

  13. 13.

    Owen DRJ, Li ZH (1987) A Refined analysis of laminated plates by finite element displacement methods-II. Vib Stab Comput Struct 26(6):915–923

    Google Scholar 

  14. 14.

    Khdeir AA, Librescu L (1988) Analysis of symmetric cross-ply elastic plates using a higher-order theory. Part ii: buckling and free vibration. Compos Struct 9:259–277

    Google Scholar 

  15. 15.

    Khdeir AA, Librescu L (1988) Analysis of symmetric cross-ply elastic plates using a higher-order theory, part ii: buckling and free vibration. Compos Struct 9:259–277

    Google Scholar 

  16. 16.

    Noor AK, Scott W, Burton W (1989) Stress and free vibration analyses of multilayered composite plates. Compos Struct 11:183–204

    Google Scholar 

  17. 17.

    Madich WR, Nelson SA (1990) Multivariate interpolation and conditionally positive definite functions ii. Math Comput 54(189):211–230

    Google Scholar 

  18. 18.

    Bhimaraddi A (1991) Free vibration analysis of doubly curved shallow shells on rectangular planform using three-dimensional elasticity theory. Int J Solids Struct 27(7):897–913

    Google Scholar 

  19. 19.

    Kitipornchai S, Xiang Y, Wang CM, Liew KM (1993) Buckling of thick skew plates. Int J Numer Methods Eng 36:1299–1310

    Google Scholar 

  20. 20.

    Wang CM, Liew KM, Xiang Y, Kipornchai S (1993) Buckling of rectangular Mindlin plates with internal line supports. Int J Solid Struct 30(1):1–17

    Google Scholar 

  21. 21.

    Liew KM, Han JB, Xiao ZM, Du H (1996) Differential quadrature method for Mindlin plates on winkler foundations. Int J Mech Sci 38:405–421

    Google Scholar 

  22. 22.

    Hon YC, Lu MW, Xue WM, Zhu YM (1997) Multiquadric method for the numerical solution of by phasic mixture model. Appl Math Comput 88:153–175

    Google Scholar 

  23. 23.

    Han JB, Liew KM (1997) Numerical differential quadrature method for Reissner–Mindlin plates on two-parameter foundations. Int J Mech Sci 39:977–989

    Google Scholar 

  24. 24.

    Hinton E (1988) Numerical methods and software for dynamic analysis of plates and shells. Pineridge Press, Swansea

    Google Scholar 

  25. 25.

    Liew KM, Wang CM, Xiang Y, Kitipornchai S (1998) Vibration of Mindlin plates. Elsevier, Amsterdam

    Google Scholar 

  26. 26.

    Shreevastva AK (1999) Effect of aspect ratio on buckling of composite plates. J Compos Sci Technol 59:439–445

    Google Scholar 

  27. 27.

    Buhmann MD (2000) Radial basis functions. Acta Numer 9:1–38

    Google Scholar 

  28. 28.

    Liu GR, Gu YT (2001) A local radial point interpolation method (lrpim) for free vibration analyses of 2-d solids. J Sound Vib 246(1):29–46

    Google Scholar 

  29. 29.

    Yoon J (2001) Spectral approximation orders of radial basis function interpolation on the sobolev space. SIAM J Math Anal 33(4):946–958

    Google Scholar 

  30. 30.

    Wang JG, Liu GR, Lin P (2002) Numerical analysis of biot’s consolidation process by radial point interpolation method. Int J Solids Struct 39(6):1557–1573

    Google Scholar 

  31. 31.

    Liu L, Liu GR, Tan VCB (2002) Element free method for static and free vibration analysis of spatial thin shell structures. Comput Methods Appl Mech Eng 191:5923–5942

    Google Scholar 

  32. 32.

    Liu GR, Wang JG (2002) A point interpolation meshless method based on radial basis functions. Int J Numer Methods Eng 54:1623–1648

    Google Scholar 

  33. 33.

    Liu GR, Chen XL (2002) Buckling of symmetrically laminated composite plates using the element-free Galerkin method. Int J Struct Stab Dyn 2:281–294

    Google Scholar 

  34. 34.

    Wang JG, Liu GR (2002) On the optimal shape parameters of radial basis functions used for 2-d meshless methods. Comput Methods Appl Mech Eng 191:2611–2630

    Google Scholar 

  35. 35.

    Liew KM, Teo TM (2002) Differential cubature method for analysis of shear deformable rectangular plates on pasternak foundations. Int J Mech Sci 44:1179–1194

    Google Scholar 

  36. 36.

    Chen XL, Liu GR, Lim SP (2003) An element free galerkin method for the free vibration analysis of composite laminates of complicated shape. Compos Struct 59:279–289

    Google Scholar 

  37. 37.

    Carrera E (2003) Historical review of zig-zag theories for multilayered plates and shells. Appl Mech Rev 56:287–308

    Google Scholar 

  38. 38.

    Ferreira AJM (2003) A formulation of the multiquadric radial basis function method for the analysis of laminated composite plates. Compos Struct 59:385–392

    Google Scholar 

  39. 39.

    Ferreira AJM (2003) Thick composite beam analysis using a global meshless approximation based on radial basis functions. Mech Adv Mater Struct 10:271–284

    Google Scholar 

  40. 40.

    Ferreira AJM, Roque CMC, Martins PALS (2003) Analysis of composite plates using higher-order shear deformation theory and a finite point formulation based on the multiquadric radial basis function method. Compos Part B 34:627–636

    Google Scholar 

  41. 41.

    Liew KM, Huang YQ (2003) Bending and buckling of thick symmetric rectangular laminates using the moving least-squeares differential quadrature method. Int J Mech Sci 45:95–114

    Google Scholar 

  42. 42.

    Liew KM, Huang YQ, Reddy JN (2003) Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature method. Comput Methods Appl Mech Eng 192(19):2203–2222

    Google Scholar 

  43. 43.

    Liew KM, Huang YQ, Reddy JN (2003) Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature method. Comput Methods Appl Mech Eng 192:2203–2222

    Google Scholar 

  44. 44.

    Dai KY, Liu GR, Lim SP, Chen XL (2004) An element free Galerkin method for static and free vibration analysis of shear-deformable laminated composite plates. J Sound Vib 269:633–652

    Google Scholar 

  45. 45.

    Liew KM, Chen XL, Reddy JN (2004) Mesh-free radial basis function method for buckling analysis of non-uniformity loaded arbitrarily shaped shear deformable plates. Comput Methods Appl Mech Eng 193:205–225

    Google Scholar 

  46. 46.

    Liew KM, Wang J, Ng TY, Tan MJ (2004) Free vibration and buckling analyses of shear deformable plates based on fsdt meshfree method. J Sound Vib 276:997–1017

    Google Scholar 

  47. 47.

    Huang YQ, Li QS (2004) Bending and buckling analysis of antisymmetric laminates using the moving least square differential quadrature method. Comput Methods Appl Mech Eng 193:3471–3492

    Google Scholar 

  48. 48.

    Ferreira AJM, Fasshauer GE (2006) Computation of natural frequencies of shear deformable beams and plates by a rbf-pseudospectral method. Comput Methods Appl Mech Eng 196:134–146

    Google Scholar 

  49. 49.

    Bukect OB, Aysun B (2007) Buckling characteristics of symmetrically and anti-symmetrically laminated composite plates with central cutout. Appl Compos Mater 14:265–276

    Google Scholar 

  50. 50.

    Bajoria KM, Wankhade RL (2012) Free vibration of simply supported piezolaminated composite plates using finite element method. Adv Mater Res 587:52–56

    Google Scholar 

  51. 51.

    Wankhade RL, Bajoria KM (2012) Stability of simply supported smart piezolaminated composite plates using finite element method. In: Proc. int. conf. adv. aeronautical mech. eng,. AME, vol. 1, pp 14–19

  52. 52.

    Wankhade RL, Bajoria KM (2013) Free vibration and stability analysis of piezolaminated plates using finite element method. Smart Mater Struct 22(125040):1–10

    Google Scholar 

  53. 53.

    Wankhade RL, Bajoria KM (2013) Buckling analysis of piezolaminated plates using higher order shear deformation theory. Int J Compos Mater 3:92–99

    Google Scholar 

  54. 54.

    Bajoria KM, Wankhade RL (2015) Vibration of cantilever piezolaminated beam with extension and shear mode piezo actuators. Proc SPIE 9431(943122):1–6

    Google Scholar 

  55. 55.

    Bendine K, Wankhade RL (2016) Vibration control of FGM piezoelectric plate based on lqr genetic search. Open J Civ Eng 6:1–7

    Google Scholar 

  56. 56.

    Wankhade RL, Bajoria KM (2016) Shape control and vibration analysis of piezolaminated plates subjected to electro-mechanical loading. Open J Civ Eng 6:335–345

    Google Scholar 

  57. 57.

    Wankhade RL, Bajoria KM (2017) Numerical optimization of piezolaminated beams under static and dynamic excitations. J Sci Adv Mater Dev 2(2):255–262

    Google Scholar 

  58. 58.

    Bendine K, Wankhade RL (2017) Optimal shape control of piezolaminated beams with different boundary condition and loading using genetic algorithm. Int J Adv Struct Eng 9(4):375–384

    Google Scholar 

  59. 59.

    Wankhade RL, Bajoria KM (2019) Vibration analysis of piezolaminated plates for sensing and actuating applications under dynamic excitation. Int J Struct Stab Dyn 19(10):1950121

    Google Scholar 

  60. 60.

    Morkhade SG, Baswaraj SM, Nayak CB (2019) Comparative study of effect of web openings on the strength capacities of steel beam with trapezoidally corrugated web. Asian J Civ Eng 20(6):1089–1099. https://doi.org/10.1007/s42107-019-00166-6

    Article  Google Scholar 

  61. 61.

    Morkhade SG, Kumthekar FP, Nayak CB (2020) Analytical study of steel I-beam with stepped flanges. Int J Optim Civ Eng 10(2):217–229

    Google Scholar 

  62. 62.

    Nayak CB, Jain M, Walke S (2020) Parametric study of dome with and without opening. J Inst Eng (India) Ser A. https://doi.org/10.1007/s40030-020-00447-3

    Article  Google Scholar 

  63. 63.

    Nayak CB (2020) Experimental and numerical investigation on compressive and flexural behavior of structural steel tubular beams strengthened with AFRP composites. J King Saud Univ Eng Sci. https://doi.org/10.1016/j.jksues.2020.02.001

    Article  Google Scholar 

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Correspondence to Rajan L. Wankhade.

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Wankhade, R.L., Niyogi, S.B. Buckling analysis of symmetric laminated composite plates for various thickness ratios and modes. Innov. Infrastruct. Solut. 5, 65 (2020). https://doi.org/10.1007/s41062-020-00317-8

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Keywords

  • Buckling analysis
  • Mode shapes
  • Laminated composites
  • Orthotropic
  • Eigen values