Abstract
The main objective of the work is to present a new formulation of the boundary element method (BEM) for the analysis of dynamically loaded composites reinforced with straight, thin, and perfectly rigid fibers. The matrix is assumed to be homogeneous, isotropic, and linear-elastic. A perfect connection between the fibers and the matrix is assumed. The time-dependent problem is solved using the Laplace transform method. In this original approach, contrary to the finite element method (FEM), only external boundaries of plates and fibers are divided into boundary elements. Because only the boundaries are discretized, it is very easy to modify the length and distribution of the fibers. The proposed method was applied to the analysis of displacements of composites reinforced with carbon nanotubes (CNTs) subjected to impact loads. Three numerical examples of composites with single- and multiple-nanotubes are analyzed. For each plate, two different boundary conditions are imposed. The displacements computed by the BEM and FEM are compared, demonstrating the high accuracy of the method. Analysis of the influence of the number of boundary elements on the accuracy of the solution demonstrates a fast convergence of the method. The examples show the influence of boundary conditions, the influence of load variability in time, the distribution of nanotubes, and their length on displacements. For the assumed reinforcement, a significant reduction in displacements was obtained.