INVESTIGADORES
MILLÁN RaÚl Daniel
congresos y reuniones científicas
Título:
Point-set manifold processing: application to thin shell analysis
Autor/es:
DANIEL MILLÁN; ADRIAN ROSOLEN; MARINO ARROYO
Lugar:
Paris
Reunión:
Congreso; IV European Conference on Computational Mechanics (ECCM 2010); 2010
Institución organizadora:
European Community in Computational Methods in Applied Sciences
Resumen:
In spite of techniques developed over the last decade in computer graphics to represent and to manipulate a surface from a cloud of points, meshfree thin-shells analysis is still a challenging task. The fundamental difficulty is that, unlike surface meshes, a cloud of points does not describe well the geometry, nor provides the convenient local parameter spaces given by the reference elements. For this reason, unless a global parameterization of the surface is possible and the meshfree shape functions can be defined on this global 2D parametric domain (this is not the case for a sphere or other surfaces of complex topology), or unless a support mesh is used, there are no methods available. The goal of the present work is to perform calculations on general point-set manifolds (surfaces). We achieve this by approximating the point-set manifold as an overlapping set of smooth local parametric descriptions, which we name patches. Applying weighted Principal Component Analysis (wPCA), we capture the tangent Euclidian structure to the manifold for each patch. We then define local parametrizations of the manifold using smooth meshfree basis functions (here, local maximum entropy approximants) on the plane assigned to a patch. Finally, the local parametrizations are glued together using a partition of unity. Here, we describe the application of these ideas to the Kirchhoff-Love theory of thin shells. The smoothness of the approximants allows us to follow a direct Galerkin approach. For all numerical tests optimal convergence, accurate solutions are achieved.