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

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" kappa-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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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 2011
Accession Number
ADA555331

Entities

People

  • Hugo A. Santos
  • Luca Dede

Organizations

  • University of Texas at Austin

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Convergence
  • Differential Equations
  • Displacement
  • Energy
  • Engineering
  • Equations
  • Errors
  • Estimators
  • Finite Element Analysis
  • Geometry
  • Measurement Transportation Algorithms
  • Notation
  • Optimal Estimators
  • Rotation
  • Test And Evaluation

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Approximation Theory.
  • Structural Dynamics.