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Isogeometric analysis of 2D gradient elasticity

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Abstract

In the present contribution the concept of isogeometric analysis is extended towards the numerical solution of the problem of gradient elasticity in two dimensions. In gradient elasticity the strain energy becomes a function of the strain and its derivative. This assumption results in a governing differential equation which contains fourth order derivatives of the displacements. The numerical solution of this equation with a displacement-based finite element method requires the use of C 1-continuous elements, which are mostly limited to two dimensions and simple geometries. This motivates the implementation of the concept of isogeometric analysis for gradient elasticity. This NURBS based interpolation scheme naturally includes C 1 and higher order continuity of the approximation of the displacements and the geometry. The numerical approach is implemented for two-dimensional problems of linear gradient elasticity and its convergence behavior is studied.

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Authors and Affiliations

  1. Chair of Applied Mechanics, University of Kaiserslautern, Kaiserslautern, Germany

    Markus Klassen & Ralf Müller

  2. Chair of Applied Mechanics, University of Erlangen-Nuremberg, Erlangen, Germany

    Paul Fischer, Julia Mergheim & Paul Steinmann

Authors
  1. Paul Fischer
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  2. Markus Klassen
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  3. Julia Mergheim
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  4. Paul Steinmann
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  5. Ralf Müller
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Correspondence to Markus Klassen.

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Fischer, P., Klassen, M., Mergheim, J. et al. Isogeometric analysis of 2D gradient elasticity. Comput Mech 47, 325–334 (2011). https://doi.org/10.1007/s00466-010-0543-8

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  • DOI: https://doi.org/10.1007/s00466-010-0543-8

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