Keywords: laminated composite plate, finite element analysis, large deformation, nonlinear analysis, first order plate theory, first ply failure.

This paper includes an investigation of the behaviour of laminated fibre-reinforced composite plates undergoing large deformations by developing a shell finite element. The flat shell finite element, which was developed for elastic-plastic analysis of homogenous materials in a previous study [1], is adapted for composite materials. The laminates are assumed to be orthotropic and the first order shear deformation theory is applied in the formulation by using triangular shell elements. The virtual work principle and updated Lagrangian method are employed to obtain the governing equations.

To observe the large deformation behaviour of laminated composites, the structures are loaded until the prediction of the first ply failure by using the maximum stress, Hashin's and Tsai-Wu criteria. Several plates constructed of glass-epoxy composite are considered with different fibre angles and three boundary conditions, namely one end clamped, clamped roller and both ends clamped. In the finite element analyses a mesh with 600 three node triangular elements and 341 nodes is used for all cases. The deformed shapes of 2.8 mm thick fourteen-layered symmetric laminates having in-plane dimensions of 300 mm x 100 mm are considered for the five different stacking sequences.

In conclusion; the large displacements obtained to observe the first ply failure for all the cases analysed indicate that nonlinear deformation analysis is necessary for thin plates similar to those that has been considered in this study. The results of the simulations show that the first ply failure loads are found to decrease with increasing ply angles. It is observed that the maximum stress criterion results in the highest first ply failure loads whereas the Tsai-Wu criterion yields the lowest first ply failure loads and the results of the Hashin's criterion lies in between. The displacements at first ply failure decrease with increasing ply angles for the same stacking sequence. The highest and lowest midsurface displacements are obtained, respectively, from the maximum stress criterion and the Tsai Wu criterion, whereas the results obtained using the Hashin's criterion are in between. A comparison for the boundary conditions shows that as the boundary conditions get stiffer the first ply failure loads increase and the deflections experienced decrease.

1

H. Darendeliler, S. Oral, A. Turgut, "A pseudo-layered, elastic- plastic, flat-shell finite element", Computer Methods in Applied Mechanics and Engineering, 174(1-2), 211-218, 1999. doi:10.1016/S0045-7825(98)00315-6

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