Civil Engineering Reference
In-Depth Information
way that invalid inverted elements can also be identified in the mesh optimisation. γ-quality
is also cheaper in computation than other shape measures, which is a merit worth consider-
ing in the optimisation of large-scale meshes as element shape qualities have to be computed
repeatedly in the optimisation cycles whether by topological or geometrical means.
Apart from tetrahedral meshes, in three dimensions, optimisation of non-simplicial meshes
by means of topological operations has not yet been formulated. Pure hexahedral meshes are
very often generated by mapping and sweeping methods, which are structures meshed by
nature of their generation, and hence, there is no need to rebuild their topology. As for the
mixed meshes of polyhedral elements, pentahedral and pyramid elements are introduced
mainly for the liaison between the hexahedral and tetrahedral elements. A solution for the
element connections, in general, is difficult enough to leave any room for topological opti-
misation by a change in element types for which other possible solutions would have already
been evaluated right at the spot when the problem first arises. In other words, topological
optimisation of polyhedral meshes might be possible; however, it is unlikely to be cost-
effective as local element swaps can only be applied to very limited locations, if any, even
after time-consuming rigorous analysis.
