Meshless structural analyses of complex shape models using implicit surface representations

In this paper, we present a scheme for analyzing structures which have complex shape models. The targets of the structural analysis usually consist of a combination of simple shape models generated using modeling tools such as CAD systems. On the other hand, in the field of computer graphics, there have been proposed a number of techniques that make it possible to create complex shape models from point clouds obtained by three-dimensional (3D) range scanners. One suitable representation for the reconstructed shape is an implicit surface model. One typical advantage of the implicit representation is fast inside/outside distinction. For the analysis of a structure represented as an implicit surface model, we use the Element-Free Galerkin Method (EFGM), which is suitable for the analysis of a structure with an implicit surface representation. For the analysis with the EFGM, internal nodes spread in the object are required and the nodes can be generated easily using the property of fast inside/outside distinction. We also note that the EFGM does not require any information about connectivity between adjoining nodes inside the model. We also present some numerical results of 3D stress problems.