VORONOI CELL FINITE-ELEMENTS

In this paper, a finite element method has been developed for deformation and stress analysis of domains that have been discretized by Dirichlet tessellation. The discussion is restricted to two-dimensional domains where the generated Voronoi diagram partitions the domain into irregular covex poylgons. This paper forms a sequel to an earlier paper on mesh generation using Dirichlet tessellation techniques by Ghosh and Mukhopadhyay. Two formulations have been developed, considering possible different situations. The first can be easily applicable to the analysis of structured materials that are modeled by a set of isolated material points in a continuum. The second formulation can find use in problems of finite deformation problems, where tessellation may be used as a means of obtaining a natural Lagrangian discretization of a deforming medium to avoid problems associated with mesh distortion.