Analytical solution for buckling of embedded laminated plates based on higher order shear deformation plate theory

- Journal title : Steel and Composite Structures
- Volume 21, Issue 4, 2016, pp.883-919
- Publisher : Techno-Press
- DOI : 10.12989/scs.2016.21.4.883

Title & Authors

Analytical solution for buckling of embedded laminated plates based on higher order shear deformation plate theory

Baseri, Vahid; Jafari, Gholamreza Soleimani; Kolahchi, Reza;

Baseri, Vahid; Jafari, Gholamreza Soleimani; Kolahchi, Reza;

Abstract

In this research, buckling analysis of an embedded laminated composite plate is investigated. The elastic medium is simulated with spring constant of Winkler medium and shear layer. With considering higher order shear deformation theory (Reddy), the total potential energy of structure is calculated. Using Principle of Virtual Work, the constitutive equations are obtained. The analytical solution is performed in order to obtain the buckling loads. A detailed parametric study is conducted to elucidate the influences of the layer numbers, orientation angle of layers, geometrical parameters, elastic medium and type of load on the buckling load of the system. Results depict that the highest buckling load is related to the structure with angle-ply orientation type and with increasing the angle up to 45 degrees, the buckling load increases.

Keywords

buckling;laminated composite;Reddy theory;analytical method;elastic medium;

Language

English

Cited by

1.

Buckling analysis of nanocomposite cut out plate using domain decomposition method and orthogonal polynomials,;;;;

1.

2.

3.

4.

5.

6.

7.

References

1.

Alibeigloo, A. and Madoliat, R. (2009), "Static analysis of cross-ply laminated plates with integrated surface piezoelectric layers using differential quadrature", Compos. Struct., 88(3), 342-351.

2.

Chakrabarti, A. and Sheikh, A.H. (2006), "Dynamic instability of laminated sandwich plates using an efficient finite element model", Thin-Wall. Struct., 44(1), 57-68.

3.

Chen, W., Xu, M. and Li, L. (2012), "A model of composite laminated Reddy plate based on new modified couple stress theory", Compos. Struct., 94(7), 2143-2155.

4.

Chow, S.T., Liew, K.M. and Lam, K.Y. (1992), "Transverse vibration of symmetrically laminated rectangular composite plates", Compos. Struct., 20(4), 213-232.

5.

Dawe, D.J. and Yuan, W.X. (2001), "Overal and local buckling of sandwich plates with laminated faceplates, Part I: Analysis", Comput. Methods Appl. Mech. Eng., 190(40-41), 5197-5213.

6.

Ferreira, A.J.M. (2005), "Analysis of composite plates using a layerwise theory and multiquadrics discretization", Mech. Adv. Mater. Struct., 12(2), 99-112.

7.

Ferreira, A.J.M. and Barbosa, J.T. (1970), "Buckling behaviour of composites and sandwich plates", J. Compos. Mater., 4, 20-34.

8.

Ferreira, A.J.M., Roque, C.M.C. and Martins, P.A.L.S. (2003), "Analysis of composite plates using higherorder shear deformation theory and a finite point formulation based on the multiquadric radial basis function method", Compos. B: Eng., 34(7), 627-636.

9.

Ferreira, A.J.M., Fasshauer, G.E., Batra, R.C. and Rodrigues, J.D. (2008), "Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and RBF-PS discretizations with optimal shape parameter", Compos. Struct., 86(4), 328-343.

10.

Ghorbanpour Arani, A., Kolahchi, R. and Vossough, H. (2012), "Buckling analysis and smart control of SLGS using elastically coupled PVDF nanoplate based on the nonlocal Mindlin plate theory", Physica B, 407(22), 4458-4461.

11.

Khdeir, A.A. and Librescu, L. (1988), "Analysis of symmetric cross-ply laminatedelastic plates using a higher-order theory. Part II-Buckling and freevibration", Compos. Struct., 9(4), 259-277.

12.

Luong-Van, H., Nguyen-Thoi, T., Liu, G.R. and Phung-Van, P. (2014), "A cell-based smoothed finite element method using three-node shear-locking free Mindlin plate element (CS-FEM-MIN3) for dynamic response of laminated composite plates on viscoelastic foundation", Eng. Anal. Bound. Elem., 42, 8-19.

13.

Mantari, J.L., Oktem, A.S. and Guedes Soares, C. (2012a), "A new trigonometric layerwise shear deformation theory for the finite element analysis of laminated composite and sandwich plates", Comput. Struct., 94-95, 45-53.

14.

Mantari, J.L., Oktem, A.S. and Guedes Soares, C. (2012b), "A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates", Int. J. Solids Struct., 49(1), 43-53.

15.

Matsunaga, H. (2000), "Vibration and stability of cross-ply laminatedcomposite plates according to a global higher-order plate theory", Compos. Struct., 48(4), 231-244.

16.

Nguyen, T.N., Hui, D., Lee, J. and Nguyen-Xuan, H. (2015), "An efficient computational approach for sizedependent analysis of functionally graded nanoplates", Comput. Meth. Appl. Mech. Eng., 297, 191-218.

17.

Nguyen, T.N., Thai, Ch.H. and 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, 242-255.

18.

Nguyen-Thoi, T., Luong-Van, H., Phung-Van, P., Rabczuk, T. and Tran-Trung, D. (2013), "Dynamic responses of composite plates on the Pasternak foundation subjected to a moving mass by a cell-based smoothed discrete shear gap (CS-FEM-DSG3) method", Int. J. Compos. Mater., 3, 19-27.

19.

Nguyen-Xuan, H., Thai, Ch.H. and Nguyen-Thoi, T. (2013), "Isogeometric finite element analysis of composite sandwich plates using a higher order shear deformation theory", Compos. Part B, 55, 558-574.

20.

Nguyen-Xuan, H., Tran, L.V., Thai, Ch.H., Kulasegaram, S. and Bordas, S.P.A. (2014), "Isogeometric finite element analysis of functionally graded plates using a refined plate theory", Compos. Part B, 64, 222-234.

21.

Pandit, M.K. Singh, B.N. and Sheikh, A.H. (2008a), "Buckling of laminated sandwich plates with soft core based onan improved higher order zigzag theory", Thin-Wall. Struct., 46(11), 1183-1191.

22.

Pandit, M.K., Sheikh, A.H. and Singh, B.N. (2008b), "Vibration characteristic of laminated sandwichplates with soft core based on an improved higher-order zigzag theory", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 222(8), 1443-1152.

23.

Pandit, M.K., Sheikh, A.H. and Singh, B.N. (2009), "Analysis of laminated sandwich plates based on an improved higher order zigzag theory", J. Sandwich Struct. Mat., 24, 235-241.

24.

Pandya, B.N. and Kant, T. (1988), "Higher-order shear deformable theories for flexure of sandwich plates - finite element evaluations", Int. J. Solids Struct., 24(12), 419-451.

25.

Phung-Van, P., Nguyen-Thoi, T., Luong-Van, H., Thai-Hoang, C. and Nguyen-Xuan, H. (2014a), "A cellbased smoothed discrete shear gap method (CS-FEM-DSG3) using layerwise deformation theory for dynamic response of composite plates resting on viscoelastic foundation", Comput. Methods Appl. Mech. Eng., 272, 138-159.

26.

Phung-Van, P., Luong-Van, H., Nguyen-Thoi, T. and Nguyen-Xuan, H. (2014b), "A cell-based smoothed discrete shear gap method (CS-FEM-DSG3) based on the C0-type higher-order shear deformation theory for dynamic responses of Mindlin plates on viscoelastic foundations subjected to a moving sprung vehicle", Int. J. Num. Meth. Eng., 98(13), 988-1014.

27.

Phung-Van, P., Nguyen-Thoi, T. and Nguyen-Xuan H. (2014c), "Geometrically nonlinear analysis of functionally graded plates using a cell-based smoothed three-node plate element (CS-MIN3) based on the C0-HSDT", Comput. Methods Appl. Mech. Eng., 270, 15-36.

28.

Phung-Van, P., Thai, Ch.H., Nguyen-Thoi, T. and Lieu-Xuan, Q. (2014d), "Static and free vibration analyses of composite and sandwich plates by an edge-based smoothed discrete shear gap method (ESDSG3) using triangular elements based on layerwise theory", Compos. Part B: Eng., 60, 227-238.

29.

Phung-Van, P., Nguyen-Thoi, T., Dang-Trung H. and Nguyen-Minh, N. (2014e), "A cell-based smoothed discrete shear gap method (CS-FEM-DSG3) using layerwise theory based on the C0-HSDT for analyses of composite plates", Compos. Struct., 111, 553-565.

30.

Phung-Van, P., Nguyen, L.B., Tran, L.V., Dinh, T.D., Thai, Ch.H., Bordas, S.P.A., Abdel-Wahab, M. and Nguyen-Xuan, H. (2015a), "An efficient computational approach for control of nonlinear transient responses of smart piezoelectric composite plates", Int. J. Nonlin. Mech., 76, 190-202.

31.

Phung-Van, P., Nguyen-Thoi, T., Bui-Xuan, T. and Lieu-Xuan, Q. (2015b), "A cell-based smoothed threenode Mindlin plate element (CS-FEM-MIN3) based on the C0-type higher-order shear deformation for geometrically nonlinear analysis of laminated composite plates", Comput. Mat. Sci., 96, 549-558.

32.

Phung-Van, P., Abdel-Wahab, M., Liew, K.M., Bordas, S.P.A. and Nguyen-Xuan H. (2015c), "Isogeometric analysis of functionally graded carbon nanotube-reinforced composite plates using higher-order shear deformation theory", Compos. Struct., 123, 137-149.

33.

Phung-Van, P., De Lorenzis, L., Chien, H., Thai, M., and Nguyen-Xuan, H. (2015d), "Analysis of laminated composite plates integrated with piezoelectric sensors and actuators using higher-order shear deformation theory and isogeometric finite elements", Comput. Mat. Sci., 96, 495-505.

34.

Putcha, N.S. and Reddy, J.N. (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.

35.

Reddy, J.N. (2010), "Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates", Int. J. Eng. Sci., 48(11), 1507-1512.

36.

Sahoo, R. and Singh, B.N. (2013a), "A new shear deformation theory for the static analysis of laminated composite and sandwich plates", Int. J. Mech. Sci., 75, 324-344.

37.

Sahoo, R. and Singh, B.N. (2013a), "A new inverse hyperbolic zigzag theory for the static analysis of laminated composite and sandwich plates", Compos. Struct., 105, 385-397.

38.

Sahoo, R. and Singh, B.N. (2014), "A new trigonometric zigzag theory for static analysis of laminated composite and sandwich plates", Aero Sci. Tech., 35, 15-27.

39.

Samaei, A.T., Abbasion, S. and Mirsayar, M.M. (2011), "Buckling analysis of a single-layer graphene sheet embedded in an elastic medium based on nonlocal Mindlin plate theory", Mech. Res. Commun., 38(7), 481-485.

40.

Sayyad, A.S. and Ghugal, Y.M. (2014), "A new shear and normal deformation theory for isotropic, transversely isotropic, laminated composite and sandwich plates", Int. J. Mech. Mater. Des., 10(3), 247-255.

41.

42.

Thai, Ch.H., Kulasegaram, S., Tran, L.V. and Nguyen-Xuan, H. (2014), "Generalized shear deformation theory for functionally graded isotropic and sandwich platesbased on isogeometric approach", Comput. Struct., 141, 94-112.