The radial point interpolation method is employed to analyse the static deflection and damage of thin and thick laminated composite plates using a high order shear deformable theory. The problem domain is represented by regularly distributed nodes. A variational formulation is used to derive the discrete system equations which are based on the third order plate theory suggested by Reddy. The essential boundary conditions are imposed separately, as in the FEM, by means of the penalty method since the RPIM shape functions possess the Kronecker delta function property. The Gauss quadrature scheme is used to perform the integration over the cells and the layers numerically. A Hashin-type failure criterion and a gradual unloading is used with an incremental loading approach for the modelling of damage initiation and evolution. In order to demonstrate the validity and accuracy of the current method, several examples are investigated and the results are compared to those available in the literature. Moreover, side-to-thickness ratios as well as the influence of the number of nodes are discussed.
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References
X.L. Chen, G.R. Liu, S.P. Lim, An element free Galerkin method for the free vibration analysis of composite laminates of complicated shape. Composite Structures 59 (2003) 279–289
Y.Y. Lu, T. Belytschko, L. Gu, A new implementation of the element free Galerkin method. Computational Methods in Applied Mechanics and Engineering 113 (1994) 397–414
S.N. Atluri, T. Zhu, A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Computational Mechanics 22 (1998) 117–127
J. Dolbow, T. Belytschko, An introduction to programming the meshless element-free Galerkin method. Archives of Computational Methods in Engineering 5 (1998) 207–241
T. Belytscko, Y.Y. Lu, L. Gu, Crack propagation by element-free Galerkin methods. Engineering Fracture Mechanics 32 (1995) 2547–2570
P. Krysl, T. Belytscko, Analysis of thin plates by the element-free Galerkin method. Computational Mechanics 17 (1995) 26–35
G.R. Liu, Y.T. Gu, A point interpolation method for two-dimensional solids. International Journal for Numerical Methods in Engineering 50 (2001) 937–951
G.R. Liu, Y.T. Gu, A local radial point interpolation method (LR-PIM) for free vibration analysis of 2-D solids. Journal of Sound and Vibration 246 (2001–1) 29–46
G.R. Liu, Mesh free methods: moving beyond the finite element method, CRC Press, New York, 2002
G.R. Liu, Y.T. Gu, An introduction to meshfree methods and their programming, Springer, New York, 2005
J.N. Reddy, Mechanics of laminated composite plates — theory and analysis, CRC Press, New York, 1997
N.J. Pegano, S.J. Hatfield, Elastic behaviour of multilayered bi-directional composites. American Institute of Aeronautics and Astronautics Journal 10 (1972) 931–933
K.Y. Dai, G.R. Liu, K.M. Lim, X.L. Chen, A mesh-free method for static and free vibration analysis of shear deformable laminated composite plates. Journal of Sound and Vibration 269 (2004) 633–652
J.G. Wang, G.R. Liu, Radial point interpolation method for no-yielding surface models, Proceedings of the first M.I.T. conference on computational fluid and solid mechanics, 12–14 June 2001, 538–540
A.J.M. Ferreira, C.M.C. Roque, R.M.N. Jorge, Static and free vibration analysis of composite shells by radial basis functions. Engineering Analysis with Boundary Elements 30 (2006) 719–733
Z. Hashin, A. Rotem, A fatigue criterion for fiber-reinforced materials. Journal of Composite Materials 7 (1973) 448–464
Z. Hashin, Failure criteria for unidirectional fiber composites. Journal of Applied Mechanics 47 (1980) 329–334
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Djeukou, A., von Estorff, O. (2009). Static and Damage Analyses of Shear Deformable Laminated Composite Plates Using the Radial Point Interpolation Method. In: Ferreira, A.J.M., Kansa, E.J., Fasshauer, G.E., Leitão, V.M.A. (eds) Progress on Meshless Methods. Computational Methods in Applied Sciences, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8821-6_12
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