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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2000; 00:16 Prepared using nmeauth.cls [Version: 2002/09/18 v2.02]
 

Summary: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Int. J. Numer. Meth. Engng 2000; 00:1­6 Prepared using nmeauth.cls [Version: 2002/09/18 v2.02]
Thin shell analysis from scattered points with maximum-entropy
approximants
D. Mill´an, A. Rosolen, and M. Arroyo
Laboratori de C`alcul Num`eric (LaC`aN), Departament de Matem`atica Aplicada III (MA3), Universitat
Polit`ecnica de Catalunya (UPC), Campus Nord UPC-C2, E-08034 Barcelona, Spain
SUMMARY
We present a method to process embedded smooth manifolds using sets of points alone. This method
avoids any global parameterization and hence is applicable to surfaces of any genus. It combines
three ingredients: (1) the automatic detection of the local geometric structure of the manifold by
statistical learning methods, (2) the local parameterization of the surface using smooth meshfree
(here maximum-entropy) approximants, and (3) patching together the local representations by means
of a partition of unity. Mesh-based methods can deal with surfaces of complex topology, since they
rely on the element-level parameterizations, but cannot handle high-dimensional manifolds, while
previous meshfree methods for thin shells consider a global parametric domain, which seriously limits
the kinds of surfaces that can be treated. We present the implementation of the method in the context
of Kirchhoff-Love shells, but it is applicable to other calculations on manifolds in any dimension.
With the smooth approximants, this fourth-order partial differential equation is treated directly. We
show the good performance of the method on the basis of the classical obstacle course. Additional

  

Source: Arroyo, Marino - Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya

 

Collections: Engineering; Materials Science