Two-dimensional solids reinforced by thin bars using the boundary element method

Abstract

In this work, a linear boundary element formulation is presented for analyzing stiffened domains. A particular sub-region technique, in which the equilibrium is preserved along interfaces without traction approximation, is adapted to model fiber immersed in a body. The integral representation is written for a whole body, requiring only the displacement along interfaces. The sub-region is then assumed to be very thin to simulate fibers only when normal forces are taken into account. The thin sub-regions then degenerate so that they can be represented by its skeleton line. The displacement field over the fiber cross-sections is assumed to be constant. In the case of 2D problems, the degrees of freedom are reduced to two components only at each fiber node. Thus, displacement integral representations for collocations defined along the fiber skeleton are needed. The quasi-singular integrals are computed by using closed expressions or employing a numerical scheme with sub-elements. An example is solved to show that the formulation is very accurate for modeling cases of domains stiffened by fibers.