Manifold processing from scattered points: application to thin shell analysis

DANIEL MILLÁN; ADRIAN ROSOLEN; MARINO ARROYO

Vall de Núria, Barcelona

Workshop; 8th Workshop on Numerical in Applied Science and Engineering 2009; 2009

LaCàN - Universitat Politècnica de Catalunya

A method for point-based (embedded) manifold processing avoiding any kind of mesh or tessellation is presented. In mesh-based processing, the mesh not only provides a geometric description of the surface, but also a support to define a local parametric space and the shape functions. Nevertheless, this approach is seriously hindered in high dimensions due to the absence in general of a single parametric space, and the difficulty of generating high dimensional unstructured meshes. We circumvent this fact by splitting the original manifold into pieces that can be represented as patches, and by gluing them together by using the partition of unity. Numerically, the manifold patches are obtained and joined by combining weighted Principal Component Analysis (wPCA) and Shepard´s shape functions, respectively, and finally local-maximum entropy meshfree approximants (LME) are used for performing calculus on each patch. The properties for the proposed methodology are explored in 3D by computing the elastic energy of solid membranes and the elastic small deformations of thin shells in the context of the Kirchhoff-Love theory.