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NURBS mesh of a quarter hemisphere

Non-Uniform Rational B-Splines (NURBS) are a standard tool for describing and modeling curves and surfaces in computer aided design and computer graphics.

B-splines are piecewise polynomial curves composed of linear combinations of B-spline basis functions. The coefficients are points in space, referred to as control points.

For details on NURBS, see:
T.J.R. Hughes, J.A. Cottrell, Y. Bazilevs, Isogeometric analysis: CAD finite elements NURBS exact geometry and mesh refinement, Comput. Meth. Appl. Mech. Engrg. 194 (2005) 4135–4195.

This image is FROM:
D.J. Benson (1), Y. Bazilevs (1), M.C. Hsu (1) and T.J.R. Hughes (2)
(1) Department of Structural Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA
(2) Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th Street, 1 University Station C0200, Austin, TX 78712, USA

“Isogeometric shell analysis: The Reissner–Mindlin shell”, Computer Methods in Applied Mechanics and Engineering, Vol. 199, Nos. 5-8, January 2010, pp. 276-289, Special Issue: Computational Geometry and Analysis, doi:10.1016/j.cma.2009.05.011

ABSTRACT: A Reissner–Mindlin shell formulation based on a degenerated solid is implemented for NURBS-based isogeometric analysis. The performance of the approach is examined on a set of linear elastic and nonlinear elasto-plastic benchmark examples. The analyses were performed with LS-DYNA, an industrial, general-purpose finite element code, for which a user-defined shell element capability was implemented. This new feature, to be reported on in subsequent work, allows for the use of NURBS and other non-standard discretizations in a sophisticated nonlinear analysis framework.

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