Optimisation of size-controllable centroidal voronoi tessellation for FEM simulation of micro forming processes

© 2014 The Authors. Published by Elsevier Ltd. Voronoi tessellation has been employed to characterise material features in Finite Element Method (FEM) simulation, however, a poor mesh quality of the voronoi tessellations causes problems in explicit dynamic simulation of forming processes. Although centroidal voronoi tessellation can partly improve the mesh quality by homogenisation of voronoi tessellations, small features, such as short edges and small facets, lead to an inferior mesh quality. Further, centroidal voronoi tessellation cannot represent all real micro structures of materials because of the almost equal tessellation shape and size. In this paper, a density function is applied to control the size and distribution of voronoi tessellations and then a Laplacian operator is employed to optimise the centroidal voronoi tessellations. After optimisation, the small features can be eliminated and the elements are quadrilateral in 2D and hexahedral in 3D cases. Moreover, the mesh quality is significantly higher than that of the mesh generated on the original voronoi or centroidal voronoi tessellation. This work is beneficial for explicit dynamic simulation of forming processes, such as micro deep drawing processes

Non-Uniform Offsetting and its Applications in Laser Path Planning of Sterolithography Machine

Laser path planning is an important step in solid freeform fabrication processes such as Stereolithography (SLA). An important consideration in the laser path planning is to compensate the shape of laser beam. Currently the compensation is divided into two steps, Z-compensation and X-Y compensation, and the shape of laser beam is assumed to be uniform for the whole platform. In this research, we present a sampling based non-uniform offsetting method which accounts for the different shapes of laser beam at various locations. We discuss the related steps and algorithms. We demonstrate its effectiveness by using various test cases. Besides improving the accuracy of SLA machine, non-uniform offsetting can also be applied to address other accuracy issues caused by thermal and structural variationsMechanical Engineerin

Probabilistic and parallel algorithms for centroidal Voronoi tessellations with application to meshless computing and numerical analysis on surfaces

Centroidal Voronoi tessellations (CVT) are Voronoi tessellations of a region such that the generating points of the tessellations are also the centroids of the corresponding Voronoi regions. Such tessellations are of use in very diverse applications, including data compression, clustering analysis, cell biology, territorial behavior of animals, optimal allocation of resources, and grid generation. A detailed review is given in chapter 1. In chapter 2, some probabilistic methods for determining centroidal Voronoi tessellations and their parallel implementation on distributed memory systems are presented. The results of computational experiments performed on a CRAY T3E-600 system are given for each algorithm. These demonstrate the superior sequential and parallel performance of a new algorithm we introduce. Then, new algorithms are presented in chapter 3 for the determination of point sets and associated support regions that can then be used in meshless computing methods. The algorithms are probabilistic in nature so that they are totally meshfree, i.e., they do not require, at any stage, the use of any coarse or fine boundary conforming or superimposed meshes. Computational examples are provided that show, for both uniform and non-uniform point distributions that the algorithms result in high-quality point sets and high-quality support regions. The extensions of centroidal Voronoi tessellations to general spaces and sets are also available. For example, tessellations of surfaces in a Euclidean space may be considered. In chapter 4, a precise definition of such constrained centroidal Voronoi tessellations (CCVT\u27s) is given and a number of their properties are derived, including their characterization as minimizers of a kind of energy. Deterministic and probabilistic algorithms for the construction of CCVT\u27s are presented and some analytical results for one of the algorithms are given. Some computational examples are provided which serve to illustrate the high quality of CCVT point sets. CCVT point sets are also applied to polynomial interpolation and numerical integration on the sphere. Finally, some conclusions are given in chapter 5