Variational Approximate and Mixed-Finite Element Solution for Static Analysis of Laminated Composite Plates


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The main objective of the present study is to give a systematic way for the derivation of laminated composite plates by using the mixed type finite element formulation with a functional. The first order shear deformation plate theory is used. Differential field equations of composite plates are derived from virtual displacement principle. These equations were written in operator form then by using the Gâteaux differential method, a new functional which including the dynamic and geometric boundary conditions is obtained after provide potential conditions. Applying mixed-type finite element based on this new functional, a plate element namely FOPLT32 is derived which have 8 degrees of freedoms on per node, total 32 freedoms. The reliability of the derived FOPLT32 plate elements for static analysis is verified, since the results obtained have been shown to agree well with the existing ones.



Solid State Phenomena (Volume 267)

Edited by:

Regita Bendikienė and Kazimieras Juzėnas




E. Madenci and A. Özütok, "Variational Approximate and Mixed-Finite Element Solution for Static Analysis of Laminated Composite Plates", Solid State Phenomena, Vol. 267, pp. 35-39, 2017

Online since:

October 2017




* - Corresponding Author

[1] J.N. Reddy, Mechanics of laminated composite plates and shells: theory and analysis: CRC press, (2004).

[2] J. Mantari, A. Oktem, C.G. Soares, A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates, Int. J. Solids Struct. 49 (2012) 43-53.


[3] A. Aköz, A. Özütok. A functional for shells of arbitrary geometry and a mixed finite element method for parabolic and circular cylindrical shells, Int. J. Numer. Methods Eng. 47 (2000) 1933-(1981).


[4] A. Aköz, N. Uzcan. The new functional for reissner plates and its application, Computers & Structures, 44 (1992) 1139-1144.


[5] A. Özütok, E. Madenci. Free vibration analysis of cross-ply laminated composite beams by mixed finite element formulation, Int. J. Struct. Stab. Dyn. 13 (2013) 1250056.


[6] J. Belinha, L. Dinis. Analysis of plates and laminates using the element-free Galerkin method, Computers & Structures. 84 (2006) 1547-1559.


[7] N. Ateş, G. Tekin, F. Kadıoğlu. Alternative solution for cross-ply laminated composite thick plates, Građevinar. 68 (2016) 451-460.

[8] J. Xiao, D. Gilhooley, R. Batra, J. Gillespie, M. McCarthy. Analysis of thick composite laminates using a higher-order shear and normal deformable plate theory (HOSNDPT) and a meshless method, Composites Part B: Engineering. 39 (2008) 414-427.