--

1 (1) 2011

Static and dynanic analysis of composite plate using the C0-type higher-order shear deformation theory


Author - Affiliation:
Tran Vinh Loc - Ton Duc Thang University HCM , Vietnam
Thai Hoang Chien - Ton Duc Thang University HCM , Vietnam
Tran Trung Dung - Open University HCM , Vietnam
Nguyen Xuan Hung - University of Science HCM , Vietnam
Corresponding author: Nguyen Xuan Hung - kim.npt@ou.edu.vn

Abstract
This paper presents a novel numerical procedure based on edge-based smoothed finite element method (ES–FEM) in combination with the C0-type higher-order shear deformation theory (HSDT) for static and dynamic analysis of laminated composite plate. In the present ES–FEM, only the linear approximation is necessary and the discrete shear gap method (DSG) for triangular plate elements is used to avoid the shear locking and spurious zero energy modes. In addition, the stiffness matrices are computed based on smoothing domains associated with the edges of the triangular elements through a strain smoothing technique. Using the C0-type HSDT, the shear correction factors in the original ES-DSG3 can be removed and replaced by two additional degrees of freedom at each node. Several numerical examples are given to show the performance of the proposed method and results obtained are compared to other available ones.

Keywords
Laminated composite plates; finite element method (FEM); edge-based smoothed finite element method (ES-FEM); C0-type higher-order shear deformation theory (HSDT)

Full Text:
PDF

References

A.A. Khdeir, L. Librescu. Analysis of symmetric cross-ply laminated elastic plates using a higher-order theory: part I stress and displacement. Compos Struct 9 (1988) 189-213.


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


N.J. Pagano. Exact solutions for rectangular bidirectional composites and sandwich plates. J Compos Mater 4 (1970) 20–34.


A.K. Noor. Free vibration of multilayered composite plates. AIAA.J 11 (1973) 1038–9.


A.K. Noor. Stability of multilayered composite plates. Fiber Sci Tech 8 (1975) 81-9.


J.N. Reddy. A simple higher-order theory for laminated composite plates. J Appl Mech 51 (1984) 745–52.


Shankara CA, Iyengar NGR. A C0 element for the free vibration analysis of laminated composite plates. Journal of Sound and Vibration 191 (1996) 721-738.


Nguyen-Xuan H, Liu GR, Thai-Hoang C, Nguyen-Thoi T. An edge-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner-Mindlin plates. Comput Methods Appl Mech Eng 199 (2010) 471–89.


Liu GR, Dai KY, Nguyen TT. A smoothed finite element for mechanics problems. Comput Mech 39 (2007) 859–77.


Nguyen-Thanh N, Rabczuk T, Nguyen-Xuan H, Bordas S. A smoothed finite element method for plate analysis. Comput Methods Appl Mech Eng 198 (2008)165–77.


Nguyen-Xuan H, Liu GR, Nguyen-Thoi T, Nguyen Tran C. An edge – based smoothed finite element method (ES-FEM) for analysis of two–dimensional piezoelectric structures. Smart Materials Struct 18 (2009) 065015.


Nguyen-Thoi T, Liu GR, Vu-Do HC, Nguyen-Xuan H. An edge –based smoothed finite element method (ES-FEM) for visco-elastoplastic analyses of 2D solids using triangular mesh. Comput Mech 45 (2009) 23-44.


H. Nguyen-Xuan, Loc V. Tran, T. Nguyen-Thoi, H.C Vu Do, Analysis of functionally graded plates using an edge-based smoothed finite element method, Composite Structures, in press, doi:10.1016/j.compstruct.2011.04.028, 2011.


Chen JS, Wu CT, Yoon S, You Y. A stabilized conforming nodal integration for Galerkin mesh-free methods. Int J Numer Methods Eng 50 (2001) 435–66.


Bletzinger KU, Bischoff M, Ramm E. A unified approach for shear-locking free triangular and rectangular shell finite elements. Comput Struct 75 (2000) 321–34.


J.N. Reddy. Mechanics of laminated composite plates-theory and analysis. NewYork: CRC Press;1997.


Bathe KJ, Dvorkin EN. A four-node plate bending element based on Mindlin/Reissener plate theory and a mixed interpolation. Int J Numer Methods Eng 21 (1985) 367–83.


G. Akhras, M.S. Cheung, W. Li. Finite strip analysis for anisotropic laminated composite plates using higher-order deformation theory. Comput Struct 52 (1994) 471–7


A.J.M. Ferreira, C.M.C. Roque, P.A.L.S. Martins. 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 (2003) 627–36.


J.N. Reddy. Introduction to the finite element method. NewYork:McGrawHill;1993.


A.J.M. Ferreira, Luís M.S. Castro, Silvia Bertoluzza. A high order collocation method for the static and vibration analysis of composite plates using a first-order theory. Composite Structures 34 (2003) 627-636.


K.M. Liew. Solving the vibration of thick symmetric laminates by Reissner/Mindlin plate theory and the p-Ritz method. J. Sound Vib.198 (1996) 343–60.


A.J.M. Ferreira and G.E. Fasshauer. Natural frequencies of shear deformable beams and plates by a RBF-Pseudospectral method. Comput. Methods Appl. Mech. Eng.196 (2006) 134–46.


W. Zhen, C. Wanji. Free vibration of laminated composite and sandwich plates using global-local higher-order theory. J. Sound Vib. 298 (2006) 333–49.


Song Xiang, Shao-xi Jiang, Ze-yang Bi, Yao-xing Jin, Ming-sui Yang. A nth-order meshless generalization of Reddy’s third-order shear deformation theory for the free vibration on laminated composite plates. Compos. Struct.93 (2011) 299–307.



Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.