A Boundary Element Coupling formulation for three-dimensional reinforced domains

Resumo

This study presents a numerical coupling formulation for the mechanical modelling of reinforced three-
dimensional (3D) structural systems. This formulation is based on the Boundary Element Method (BEM) for the

mechanical analysis of 3D domains with Lagrangian approximation. In this coupling, the material matrix (solid
3D domain) is represented by the usual 3D BEM formulation with Kelvin’s fundamental solutions for isotropic
linear-elastic materials. Numerical integration and singularity subtraction are applied herein. A one-dimensional
approach of the BEM (1DBEM) represents the embedded fibre-reinforcements, which enforce axial mechanical
solicitation. The 1DBEM is based on the 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, which is interpolated by high-order Lagrangian functions. One considers no relative

displacements (perfect bonding). The adherence force is accounted as a body force into the 3D BEM formula-
tion. These aspects characterise the proposed 1DBEM/BEM coupling as an alternative to the usual FEM/BEM

technique, which has been widely applied in the literature. The authors have previously demonstrated in Ro-
drigues Neto and Leonel [1] that the 1DBEM/BEM coupling exhibits superior results when compared against

the usual FEM/BEM approach in 2D applications. This work presents the extension of this formulation for 3D
analyses. The proposed modelling is applied herein in the mechanical analysis of complex 3D applications. The
achieved results are compared against experimental responses available in the literature. The proposed formulation
led to accurate and stable results.