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In this paper an analytical study is presented of the two-dimensional response of an elastic laminated composite plate to an impact load applied to its surface. The surface load is arbitrarily distributed along the extent of the plate surface and varies sharply in time to model the impact loading. Each layer of the laminated plate is of arbitrary (constant) thickness with specified density and orthotropic material properties, with the material axes coincident with the plate axes.
The physical behavior of the plate is exactly represented along the extent of plate in the form of a Fourier series, and its behavior in the thickness direction is modeled by a sufficiently large number of generalized coordinates to capture quantitatively the propagation and dispersion of stress waves due to the surface impact, with emphasis directed to calculating stresses on laminate interfaces. This method of analysis results in a sequence of algebraic eigenvalue problems, the solutions of which are used to decouple the equations of motion into a large number of simple differential equations in time. This procedure is quite straightforward and computationally effective and may be used to study the impact problem for an arbitrarily laminated plate.
An isotropic plate with a specified surface impact loading is presented to indicate both the accuracy of the results obtained and the time domain for which they are valid. A two-layer boron-epoxy plate is examined in detail to indicate the quantity and quality of information which may be generated by this method for composite material structures in impact environments. The results for this problem also reveal potentially harmful effects which develop during impact.
Sufficient information is presented to permit an experimental verification of the results obtained, for regions of time where the magnitudes of the impact stresses are most critical to material integrity.
composite materials, laminates, impact, stress waves, damage, interlayer stresses
Member of Technical Staff, Rockwell International Corp., Los Angeles, Calif.
Associate professor of Engineering and Applied Science, University of California, Los Angeles, Calif.