Bending Problems

  • Sören BartelsEmail author
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 47)


Deforming thin elastic objects within the bending regime is a classical problem in continuum mechanics and efficient mathematical descriptions lead to fourth-order problems. In the case of small displacements, a linear partial differential equation provides accurate approximations, but finite element methods have to be carefully developed to avoid locking phenomena. In the case of large deformations, a pointwise isometry constraint has to be incorporated which can be treated with techniques developed for approximating harmonic maps. Related problems arise in modeling of fluid membranes, but require different numerical methods. Iterative algorithms, together with short implementations, are motivated and analyzed.


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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Abteilung für Angewandte MathematikAlbert-Ludwigs-Universität FreiburgFreiburgGermany

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