A general assessment of a new inverse trigonometric shear deformation theory for laminated composite and sandwich plates using finite element method

Abstract

In this study, a general assessment of inverse trigonometric shear deformation theory, recently developed by the authors, is performed and the structural responses (static, buckling, and free vibration) of laminated-composite and sandwich plates are investigated. The in-plane displacement components are expressed in terms of an inverse cotangent function, which yields the nonlinear shear deformation while the constant transverse displacement is assumed over the thickness of the plate. A computationally efficient finite element model for the implementation of above-mentioned theory is proposed. The continuity requirement of the finite element model is maintained as C⁰ by a suitable choice of nodal field variables. Numerous analysis problems are selected to study the effects of various parameters such as span-to-thickness ratio, lamination sequence, loading conditions, boundary conditions, etc. on the response characteristics of plates. Higher modes are also obtained for the buckling and vibration problems and the ability to investigate higher modes is ensured. The comparison of the present results with the established results in literature indicates the efficiency and range of applicability of the present formulation. Moreover, the formulation is presented in a generalized approach which enables the implementation of all existing seven degree-of-freedom theories in a single computer algorithm thereby making it practically more significant.

Keywords

Laminated composite sandwich plates shear deformation finite element analysis computational mechanics

Get full access to this article

View all access options for this article.

References

Pagano

Hatfield

. Elastic behavior of multilayered bidirectional composites. AIAA J 1972; 10(7): 931–933.

Srinivas

. A refined analysis of composite laminates. J Sound Vib 1973; 30(4): 495–507.

Noor

. Free vibrations of multilayered composite plates. AIAA J 1973; 11(7): 1038–1039.

Noor

. Stability of multilayered composite plates. Fibre Sci Technol 1975; 8(2): 81–89.

Yang

Norris

Stavasky

. Elastic wave propagation in heterogeneous plates. Int J Solids Struct 1966; 2(4): 665–684.

Whitney

. The effect of transverse shear deformation on the bending of laminated plates. J Compos Mater 1969; 3(3): 534–547.

Reissner

. On transverse bending of plates, including the effect of transverse shear deformation. Int J Solids Struct 1975; 11(5): 569–573.

Pai

. A new look at shear correction factors and warping functions of anisotropic laminates. Int J Solids Struct 1995; 32(16): 2295–2313.

Levinson

. An accurate, simple theory of statics and dynamics of elastic plates. Mech Res Commun 1980; 7(6): 343–350.

10.

Christensen

. A higher-order theory of plate deformation. Part 2: Laminated plates. J Appl Mech 1977; 44(4): 669–676.

11.

Reddy

. A simple higher-order theory for laminated composite plates. J Appl Mech 1984; 51(4): 745–752.

12.

Pandya

Kant

. Higher-order shear deformable theories for flexure of sandwich plates—Finite element evaluations. Int J Solids Struct 1988; 24(12): 1267–1286.

13.

Touratier

. An efficient standard plate theory. Int J Eng Sci 1991; 29(8): 901–916.

14.

Soldatos

. A transverse shear deformation theory for homogenous monoclinic plates. Acta Mech 1992; 94(3–4): 195–220.

15.

Karama

Afaq

Mistou

. A new theory for laminated composite plates. Proc IMechE, Part L: J Materials: Design and Applications 2009; 223: 53–62.

16.

Aydogdu

. A new shear deformation theory for laminated composite plates. Compos Struct 2009; 89(1): 94–101.

17.

Meiche

Tounsi

Ziane

. A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate. Int J Mech Sci 2011; 53(4): 237–247.

18.

Mantari

Oktem

Soares

. Static and dynamic analysis of laminated composite and sandwich plates and shells by using a new higher-order shear deformation theory. Compos Struct 2011; 94(1): 37–49.

19.

Mantari

Oktem

Soares

. A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates. Int J Solids Struct 2012; 49(1): 43–53.

20.

Mantari

Oktem

Soares

. A new higher order shear deformation theory for sandwich and composite laminated plates. Compos Part B: Eng 2012; 43(3): 1489–1499.

21.

Grover

Maiti

Singh

. A new inverse hyperbolic shear deformation theory for static and buckling response of laminate composite and sandwich plates. Compos Struct 2013; 95: 667–675.

22.

Grover N, Singh BN and Maiti DK. New non-polynomial shear-deformation theories for structural behavior of laminated-composite and sandwich plates. AIAA J. 2013; 51(8): 1861–1871.

23.

Ferreira

AJM

. Analysis of composite plates using a layerwise shear deformation theory and multiquadrics discretization. Mech Adv Mater Struct 2005; 12(2): 99–112.

24.

Roque

CMC

Ferreira

AJM

Jorge

RMN

. Modelling of composite and sandwich plates by a trigonometric layerwise deformation theory and radial basis functions. Compos Part B: Eng 2005; 36(8): 559–572.

25.

Kulkarni

Kapuria

. Free vibration analysis of composite and sandwich plates using an improved discrete Kirchhoff quadrilateral element based on third-order zigzag theory. Comput Mech 2008; 42(6): 803–824.

26.

Pandit

Singh

Sheikh

. Stochastic perturbation-based finite element for deflection statistics of soft core sandwich plates with random material properties. Int J Mech Sci 2009; 51(5): 363–371.

27.

Thai CH, Ferreira AJM, Carrera E, et al. Isogeometric analysis of laminated composite and sandwich plates using a layerwise deformation theory. Compos Struct. 2013; 104: 196–214.

28.

Carrera

. Theories and finite elements for multilayered, anisotropic, composite plates and shells. Arch Comput Method E 2002; 9(2): 87–140.

29.

Akhras

Cheung

. Finite strip analysis of anisotropic laminated composite plates using higher-order shear deformation theory. Comput Struct 1994; 52(3): 471–477.

30.

Grover

Singh

Maiti

. Analytical and finite element modeling of laminated composite and sandwich plates: An assessment of a new shear deformation theory for free vibration response. Int J Mech Sci 2013; 67: 89–99.

31.

Cook

. Finite element modeling for stress analysis, Singapore: John Wiley & Sons Inc, 1995.

32.

Swaminathan

Patil

. Higher order reﬁned computational model with 12 degrees of freedom for the stress analysis of antisymmetric angle-ply plates – analytical solutions. Compos Struct 2007; 80(4): 595–608.

33.

Ren

Bending, vibration and buckling of laminated plates. In: Cheremisinoff

(eds). Handbook of ceramics and composites, New York: Marcel Dekker, 1990, pp. 413–450.

34.

Xiang

Wang

. Analysis of isotropic, sandwich and laminated plates by a meshless method and various shear deformation theories. Compos Struct 2009; 91(1): 31–37.

35.

Ferriera

AJM

Roque

CMC

Martins

PALS

. 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: Eng 2003; 34(7): 627–636.

36.

Putcha

Reddy

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

37.

Ferreira

AJM

Roque

CMC

Neves

AMA

. Buckling analysis of isotropic and laminated plates by radial basis functions according to a higher-order shear deformation theory. Thin Wall Struct 2011; 49(7): 804–811.