Keywords: delamination, buckling, composite, spring simulation, bend-twist coupling, finite element.

Fiber-reinforced composite materials have been increasingly used over the past few decades in a variety of applications in which a fairly high ratio of stiffness-strength to weight is required. However, these materials are prone to a wide range of defects and damage that can cause significant reductions in stiffness and strength. In particular, when the laminated composites are subjected to compressive loads, delamination becomes a constraint in the design process.

Various methods have been proposed for the analysis of a plate that contains delaminations [1]. Wang et al. [2] have used spring simulation to determine the local buckling load of delaminated beams and plates. In their study, the system is modelled as a beam/plate supported on a continuous elastic foundation by using parallel spring distribution for the delaminated regions as well as for the undelaminated regions. However, in the delaminated regions, some fictitious transverse forces are added at a number of discrete points in order to make the net transverse force at each of these points to vanish.

In the current study the spring simulation technique is developed for determining the buckling loads of plates containing one or two embedded delaminations and the laminates are under uniaxial compression. The laminates are mid-plane symmetry, in which the bend-twist coupling stiffness coefficients are of relatively considerable magnitudes.

It is noted that the adopted technique is different from that implemented by Wang and Chang [2]. This is due to the fact that, in the current model, the spring distribution is used in the undelaminated regions only, while in the method adopted by Wang and Chang, the spring distribution is utilised in the undelaminated regions as well as delaminated regions.

As a result of the presence of bend-twist coupling terms, the differential equation becomes more challenging than the case where the sublaminate is specially orthotropic for which the solution is given in reference [2]. To overcome the difficulty, the Ritz method is implemented in the current study to obtain an approximate solution to the problem. The solution is attempted through the minimization of the total potential energy of the system. The effects of bend-twist coupling stiffness terms are included in the analysis. Also, the FEM analysis is performed to determine the buckling load of delaminated plates and the results are compared with those of spring simulation method.

The good comparison between the results has provided confidence in the validity of the formulation of the developed spring simulation method. Moreover, the ability of the developed method to provide invaluable insight into the buckling behaviour of the delaminated plates has been demonstrated.

1

J.D. Withcomb and K.N. Shivakumar, "Strain energy release rate analysis of plates with postbuckled delaminations", Journal of Composite Materials, Vol. 23, July 1989, PP 714-734. doi:10.1177/002199838902300705

2

J.T.-S. Wang and S.-H. Cheng, "Local buckling of delaminated beams and plates using continuous analysis", Journal of Composite Materials, Vol. 29, No. 10, 1995, PP 1374-1402. doi:10.1177/002199839502901007

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