Biomedical Engineering Reference
In-Depth Information
Fig. 3.5 a Fixed rectangular shaped influence-domain. b Fixed circular shaped influence-
domain. c Flexible circular shaped influence-domain
same as using triangular or quadrilateral elements in the boundary and high-order
elements in the centre of the solid domain. Fixed and regular shaped influence-
domains can lead to the loss of accuracy in the numerical analysis. Therefore, in
order to maintain a constant connectivity along the solid domain variable influence-
domains are a better solution. To illustrate this idea the number of nodes inside the
influence-domain is established in n = 14 nodes, then performing a radial search,
using the interest point as centre, the n closest nodes are found. In Fig.
3.5
c are
shown the variable influence-domains of two interest points. This technique permits
to avoid the numerical problems identified in Fig.
3.3
b and to construct shape
functions with the same degree of complexity in the complete domain.
3.2.2 Influence-Cells
A new approach to establish the influence-domains in meshless methods was
proposed by Belinha and co-workers in 2007 [
12
]. Instead of using fixed or var-
iable blind influence-domains, the approach proposed by Belinha uses the spatial
colocation of the nodes discretizing the problem domain to determine directly the
influence-domains. This approach uses mathematical concepts such as the Voronoï
diagrams and the Delaunay triangulation, to determine the nodal connectivity of
each node belonging to the global nodal set. Since these influence-domains are
determined based on the geometric and spatial relations between the Voronoï cells
