An Isogeometric Boundary Element Formulation for fibre-reinforced 3D domains

Resumo

This study presents an innovative Isogeometric coupling formulation for the mechanical analysis of
3D solids reinforced by fibres. This formulation is based on the coupling of the Isogeometric Boundary Element
Method (IGABEM) and the 1D approach of the Boundary Element Method (1DBEM). The material matrix (solid
3D domain) is modelled by the IGABEM, which uses NURBS and B-Splines functions to represent both geometry
and mechanical fields. These functions allow the exact representation of complex geometries, such as cylinders,
torus and propellers. Besides, a straightforward connection with the geometry design is possible, since most
CAD packages used in engineering projects represent 3D solids through NURBS surfaces at its contours. The
1DBEM is based on the axial fundamental solution for elastic 1D domains. The interaction between the matrix
and fibres is described by an adherence force over the reinforcements’ line, which is interpolated by high-order

polynomial functions. No relative displacements is considered (perfect bonding) and both materials have linear-
elastic behaviour. The proposed coupling formulation is herein named 1DBEM/IGABEM coupling technique. The

mechanical analysis of a numerical application demonstrates the results obtained by the proposed formulation in
comparison with reference results. The proposed formulation requires fewer degrees of freedom than the reference
for the same level of accuracy. Therefore, the Isogeometric coupling presented herein is not only effective for a
large number of complex geometries, but also efficient in the precise representation of mechanical fields.