@article{GuerlebeckLegatiukWebber,
  author    = {G{\"u}rlebeck, Klaus and Legatiuk, Dmitrii and Webber, Kemmar},
  title     = {Operator Calculus Approach to Comparison of Elasticity Models for Modelling of Masonry Structures},
  series = {Mathematics},
  volume    = {2022},
  journal   = {Mathematics},
  number    = {Volume 10, issue 10, article 1670},
  publisher = {MDPI},
  address   = {Basel},
  doi       = {10.3390/math10101670},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220721-46726},
  pages     = {1 -- 22},
  abstract  = {The solution of any engineering problem starts with a modelling process aimed at formulating a mathematical model, which must describe the problem under consideration with sufficient precision. Because of heterogeneity of modern engineering applications, mathematical modelling scatters nowadays from incredibly precise micro- and even nano-modelling of materials to macro-modelling, which is more appropriate for practical engineering computations. In the field of masonry structures, a macro-model of the material can be constructed based on various elasticity theories, such as classical elasticity, micropolar elasticity and Cosserat elasticity. Evidently, a different macro-behaviour is expected depending on the specific theory used in the background. Although there have been several theoretical studies of different elasticity theories in recent years, there is still a lack of understanding of how modelling assumptions of different elasticity theories influence the modelling results of masonry structures. Therefore, a rigorous approach to comparison of different three-dimensional elasticity models based on quaternionic operator calculus is proposed in this paper. In this way, three elasticity models are described and spatial boundary value problems for these models are discussed. In particular, explicit representation formulae for their solutions are constructed. After that, by using these representation formulae, explicit estimates for the solutions obtained by different elasticity theories are obtained. Finally, several numerical examples are presented, which indicate a practical difference in the solutions.},
  subject      = {Mauerwerk},
  language  = {en}
}
@inproceedings{Schutte2000,
  author    = {Schutte, Gerrit},
  title     = {Zur Ermittlung von Spannungen am Rand eines elastischen Kontinuums},
  doi       = {10.25643/bauhaus-universitaet.613},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-6135},
  year      = {2000},
  abstract  = {F{\"u}r den Entwurf von Ingenieurbauten ist eine zuverl{\"a}ssige Prognose {\"u}ber den Spannungsverlauf im Bauwerk und auf dessen Rand von großer Bedeutung. Eine geschlossene L{\"o}sung der elastischen Bestimmungsgleichungen des Bauwerks ist in der Regel nicht verf{\"u}gbar. Es wird daher unter Verwendung der Methode der gewichteten Reste eine schwache Form der Gleichungen abgeleitet, die zu einem gemischten Arbeitsprinzip f{\"u}hrt. Das zugeh{\"o}rige Finite-Elemente-Modell erlaubt es Spannungen am Rand des Bauwerks zu ermitteln, die im Gleichgewicht zu den angreifenden Lasten stehen.},
  subject      = {Kontinuum},
  language  = {de}
}