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B-spline goal-oriented error estimators for geometrically nonlinear rods

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Abstract

We consider goal-oriented a posteriori error estimators for the evaluation of the errors on quantities of interest associated with the solution of geometrically nonlinear curved elastic rods. For the numerical solution of these nonlinear one-dimensional problems, we adopt a B-spline based Galerkin method, a particular case of the more general isogeometric analysis. We propose error estimators using higher order “enhanced” solutions, which are based on the concept of enrichment of the original B-spline basis by means of the “pure” k-refinement procedure typical of isogeometric analysis. We provide several numerical examples for linear and nonlinear output functionals, corresponding to the rotation, displacements and strain energy of the rod, and we compare the effectiveness of the proposed error estimators.

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Authors and Affiliations

  1. Institute for Computational Engineering and Sciences, The University of Texas at Austin, 1 University Station C0200, Austin, Texas, 78712, USA

    L. Dedè & H. A. F. A. Santos

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  1. L. Dedè
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  2. H. A. F. A. Santos
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Correspondence to L. Dedè.

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Dedè, L., Santos, H.A.F.A. B-spline goal-oriented error estimators for geometrically nonlinear rods. Comput Mech 49, 35–52 (2012). https://doi.org/10.1007/s00466-011-0625-2

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