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C1 Discretizations for the Application to Gradient Elasticity

  • Paul Fischer
  • Julia Mergheim
  • Paul Steinmann
Chapter
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 21)

Abstract

For the numerical solution of gradient elasticity, the appearance of strain gradients in the weak form of the equilibrium equation leads to the need for C 1-continuous discretization methods. In the present work, the performances of a variety of C 1-continuous elements as well as the C 1 Natural Element Method are investigated for the application to nonlinear gradient elasticity. In terms of subparametric triangular elements the Argyris, Hsieh–Clough–Tocher and Powell–Sabin split elements are utilized. As an isoparametric quadrilateral element, the Bogner–Fox–Schmidt element is used. All these methods are applied to two different numerical examples and the convergence behavior with respect to the L 2, H 1 and H 2 error norms is examined.

Keywords

Delaunay Triangulation Uniaxial Loading Gradient Elasticity Thick Hollow Cylinder Natural Element Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.University Erlangen-NurembergErlangenGermany

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