Low-velocity impact of laminated composites using a layerwise theory

A layer-wise theory is used to study the low velocity impact response of laminated plates. The forced-vibration analysis is developed by the modal superposition technique. Six different models are introduced for representation of the impact pressure distribution. The first five models, in which the contact area is assumed to be known, result in a nonlinear integral equation similar to the one obtained by Timoshenko in 1913. The resulting nonlinear integral equation is discretised using a time-finite-element scheme. Two different interpolation functions, namely: (i) Lagrangian and (ii) Hermite are used to express the impact force. The Hermitian-polynomials based representation, obviously, more sophisticated, is introduced to verify the Lagrangian based representation. Due to its modular nature the present numerical technique is preferable to the existing numerical methods in the literature. The final loading model, in which the time dependence of the contact area is taken into account according to the Hertzian contact law, resulted in a relatively more complicated but more relalistic, nonlinear integral equation. The analytical developments concerning this model are all new and reported for the first time in this paper. Also a simple, but accurate, numerical technique is developed for solving our new nonlinear integral equation which results in the time-history of the impact force. Our numerical results are first tested with a series of existing example problems. Then a detailed study concerning all the response quantities, including the in-plane and interlaminar stresses, is carried out for cross-ply laminates and important conclusions are reached concerning the usefulness and accuracy of the various plate theories.

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