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 fo r representation of the impact pressure distribution. The first five m odels, in which the contact area is assumed to be known, result in a n onlinear integral equation similar to the one obtained by Timoshenko i n 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, mor e sophisticated, is introduced to verify the Lagrangian based represen tation. Due to its modular nature the present numerical technique is p referable to the existing numerical methods in the literature. The fin al 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 ne w and reported for the first time in this paper. Also a simple, but ac curate, numerical technique is developed for solving our new nonlinear integral equation which results in the time-history of the impact for ce. Our numerical results are first tested with a series of existing e xample problems. Then a detailed study concerning all the response qua ntities, including the in-plane and interlaminar stresses, is carried out for cross-ply laminates and important conclusions are reached conc erning the usefulness and accuracy of the various plate theories.