Theoretical Analysis of Wave Propagation in Woven Fabric Composites

Abstract

In a previous paper the authors studied transient elastic wave propagation in woven fabric composites under impact loading. A one-dimensional analysis was developed to predict the elastodynamic and elastostatic behavior. The initial and boundary value problem was formulated and then solved using Laplace transforms. In this paper we examine the same problem using an alternative approach based upon the combination of Laplace transforms and finite Fourier transforms. Using this approach, some of the difficulties caused by the inversion of Laplace transforms encountered in the previous work are overcome. Analytical solutions to dynamic displacements and stresses, including bond shearing stresses, can be obtained for any type of impact loading. The merits as well as the shortcomings of the alternative approach are discussed. It is found that for elastodynamic problems the solution given in this paper are better than those reported in the previous work, since there is no need to perform the numerical inversion of Laplace transforms before superposition of the solutions of the two component problems. On the other hand, for elastostatic problems the solutions given in the previous work are more concise.