Meshfree thin-shells

Meshfree thin-shell analysis avoiding any global parametrization, usually a mesh, persists as a challenging task for slender bodies of nondevelopable middle surfaces. We overcome this problem in the context of the geometrically exact theory of Kirchhoff-Love. We developed a methodology that approximates a point-set surface as an overlapping collection of smooth local parametric descriptions, which we name patches. To performing continuum-based calculus, on the surface, the set of patches is blended by recursing to the partition of unity. We made computations in each parametric space by using smooth local maximum entropy meshfree approximants.

Publications

• Millán D., Rosolen A., and Arroyo M., "Nonlinear manifold learning for meshfree finite deformation thin-shell analysis", International Journal for Numerical Methods in Engineering, Vol. 93, Nro. 7, pp 685-713, 2013. [abstract from publisher, preprint].

• A. Rosolen, D. Millán and M. Arroyo. "Second order convex maximum entropy approximants with applications to high order PDE", International Journal for Numerical Methods in Engineering. Vol. 94, Nr. 2, pp. 150–182, 2013. [abstract from publisher, preprint].

• Millán D., Rosolen A., and Arroyo M., "Thin shell analysis from scattered points with maximum-entropy approximants", International Journal for Numerical Methods in Engineering, Vol. 85, Nro. 6, pp. 723-751, 2011. [abstract from publisher, preprint].