One-dimensional transient dynamic response of functionally graded spherical layered media
by
Ibrahim Abu-Alsaikh
Fatih-University 34500 Istanbul-Turkey
Coauthors: Mehmet Emir Koksal

In this study, one-dimensional transient dynamic response of functionally graded spherical multilayered media is investigated. The multilayered medium consists of N different layers of functionally graded materials (FGMs), i.e., it is assumed that the stiffness and density of each layer vary continuously in the radial direction, but isotropic and homogeneous in the other two directions. The inner surface of the layered composite is assumed to be subjected to uniform time-dependent normal stresses, while, the outer surface of the composite is assumed free, fixed or subjected to the same load applied at the inner boundary. Furthermore, the composite body is assumed to be initially at rest and the layers of the multilayered medium are assumed perfectly bonded to each other. The method of characteristics is employed to obtain the solutions of this initial-boundary value problem. In this method, the constitutive equations that can be written as a system of first order hyperbolic PDEs are transformed into a system of ODEs each of which is valid along a different family of characteristic lines. These equations, called the canonical equations, are suitable for numerical analysis because the use of the canonical-form makes it possible to obtain the solutions by a step-by-step integration procedure. These solutions are required to satisfy the boundary, quiescent initial and interface conditions. The numerical results are obtained and then displayed in curves denoting the variations of normal stresses with time at different locations and variations of stresses along the radial direction of the spherical composite at different times. These curves clearly reveal the scattering effects caused by the reflections and refractions of waves at the boundaries and interfaces, geometric dispersions, and the effects of non-homogeneity in the wave profiles. Furthermore, they properly predict the sharp variations in the field variable in the neighborhood of the wavefronts. By suitably adjusting the material constants the results for the special case of isotropic, homogenous and linearly elastic multilayered media are obtained and compared with the available solutions in the literature and very good agreement is found. However, the authors have not found suitable one-dimensional solutions through a spherical FGM medium for comparison. Therefore, solutions for a single-spherical-layer made of FGM and for some special multilayered media consists of FGM layer perfectly bonded to linearly, isotropic and homogeneous layer are also obtained by using the method discussed above.

Date received: March 11, 2004

Copyright © 2004 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # canu-34.