A 1DBEM/BEM COUPLING FORMULATION FOR REINFORCED DOMAINS

Resumo

This work presents a coupled numerical formulation based on the Boundary Element
Method (BEM) for the mechanical analysis of two-dimensional non-homogeneous reinforced
domains. In this technique, the material matrix (two-dimensional domain) is represented by the usual
two-dimensional singular BEM formulation, considering either isotropic or anisotropic behaviors.
Whereas a one-dimensional approach of the BEM, called 1DBEM, is used to represent the
reinforcements, which can be understood as trusses or fibers. The 1DBEM is based on an axial
fundamental solution for elastic 1D domains, which can be easily found in the literature. The
interaction between the matrix and reinforcements is described by an adherence force over the
reinforcements’ line, considering no relative displacements (perfect adherence). These aspects
characterize the 1DBEM/BEM coupling as an alternative to the usual FEM/BEM technique, which has
been widely applied in the literature for modelling this type of problem. Nonhomogeneous reinforced
domains can be correctly represented in this formulation by the sub-region technique in the 2D BEM,
already presented in the literature. In addition, the use of connection fiber-elements enable the crossing
between reinforcements and sub-regions’ interfaces. A one-dimensional approach of elastoplasticity is
supported over to the 1DMEC elements, which can represent the mechanical degradation of the
reinforcement’s material. Numerical applications exhibits equally accurate displacements results and
better stress/force results obtained by the proposed formulation, when compared to the usual
FEM/BEM approach. The 1DBEM/BEM results exhibit minor perturbations in the force results near
discontinuity points, which are usually observed in this type of coupled formulation. Finally, the
numerical applications show accurate and stable results in the modelling of nonhomogeneous
reinforced structures, when compared to the reference results available in the literature, which
demonstrates the robustness of the formulation proposed in this work.