Advanced Boundary Element Analysis of Three-Dimensional Elastic Solids with Fiber Reinforcements

Abstract

An advanced boundary element methodology for the analysis of three-dimensional fiber-reinforced elastic solids using the concept of fiber elements has been presented in this paper as an extension of the earlier work of Banerjee and co-workers. The previous simplified formulation was based on the assumption that the Poisson ratios of the matrix and the fiber are equal. However, this may not be a valid assumption for all values of elastic stiffness ratios and fiber to matrix volume ratios. Moreover, such restrictions do not allow for any future extensions to nonlinear analysis. Also, because of limiting computing power available at that time, their implementation was restricted to only a small number of fiber elements in a given analysis. The new algorithm proposed in this work does not make any such assumptions. In this algorithm, the fibers are semianalytically integrated and the resulting equations are back-substituted into the equations for the composite matrix without any further approximation. The present work has been implemented in a general purpose multiregion boundary element computer program and is capable of handling very large numbers of fiber elements in a given analysis. Several numerical examples are presented to validate the proposed method of fiber composite analysis and its applicability is demonstrated via practical engineering problems.