A three-dimensional Boundary Element formulation for boundary conditions on small areas

Resumo

The accurate prediction of the mechanical behaviour of solids and structural systems has fundamen-
tal importance in structural engineering. This task has been handled by numerical methods, such as the Boundary

Element Method (BEM). In this method, integral equations written over the body’s boundaries represent the mecha-
nical behaviour. Then, in three-dimensional analyses, the BEM mesh is composed of two-dimensional elements.

Nevertheless, the mesh construction depends on the position of the distributed loads and displacements over the
boundary. This is a disadvantage when the geometric modelling is performed on Computer Aided Design software,
once the boundary conditions representation leads to additional and inconvenient modifications. To overcome such
drawback, this study presents a BEM formulation which handles distributed boundary conditions non-coincident to
the boundary element mesh. The overlapping element is required, which overlaps the BEM mesh. Both distributed
loads and supports are accounted by the proposed scheme. A numerical application demonstrates the accuracy of
the proposed scheme, in which its responses are compared against numerical data of an equivalent finite element
model. The results demonstrate remarkable accuracy and robustness.