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Computational Mechanics

, Volume 56, Issue 5, pp 815–827 | Cite as

A posteriori error estimates for continuous/discontinuous Galerkin approximations of the Kirchhoff–Love buckling problem

  • Peter Hansbo
  • Mats G. Larson
Original Paper

Abstract

Second order buckling theory involves a one-way coupled coupled problem where the stress tensor from a plane stress problem appears in an eigenvalue problem for the fourth order Kirchhoff plate. In this paper we present an a posteriori error estimate for the critical buckling load and mode corresponding to the smallest eigenvalue and associated eigenvector. A particular feature of the analysis is that we take the effect of approximate computation of the stress tensor and also provide an error indicator for the plane stress problem. The Kirchhoff plate is discretized using a continuous/discontinuous finite element method based on standard continuous piecewise polynomial finite element spaces. The same finite element spaces can be used to solve the plane stress problem.

Keywords

Discontinuous Galerkin Adaptivity A posteriori error estimate Kirchoff plate Buckling 

Notes

Acknowledgments

This research was supported in part by the Swedish Foundation for Strategic Research Grant No. AM13-0029, the Swedish Research Council Grants Nos. 2011-4992, 2013-4708, and the Swedish strategic research programme eSSENCE.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringJönköping UniversityJönköpingSweden
  2. 2.Department of Mathematics and Mathematical StatisticsUmeå UniversityUmeåSweden

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