Operator Calculus Approach to Comparison of Elasticity Models for Modelling of Masonry Structures

  • 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 moreThe 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.show moreshow less

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Metadaten
Document Type:Article
Author:Prof. Dr. Klaus GürlebeckGND, Dr. Dmitrii LegatiukORCiDGND, Kemmar WebberORCiD
DOI (Cite-Link):https://doi.org/10.3390/math10101670Cite-Link
URN (Cite-Link):https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20220721-46726Cite-Link
URL:https://www.mdpi.com/2227-7390/10/10/1670
Parent Title (English):Mathematics
Publisher:MDPI
Place of publication:Basel
Language:English
Date of Publication (online):2022/07/21
Date of first Publication:2022/05/13
Release Date:2022/07/21
Publishing Institution:Bauhaus-Universität Weimar
Institutes and partner institutions:Fakultät Bauingenieurwesen / Professur Komplexe Tragwerke
Volume:2022
Issue:Volume 10, issue 10, article 1670
Pagenumber:22
First Page:1
Last Page:22
Tag:mathematical modelling; micropolar elasticity; model comparison; operator calculus; quaternionic analysis
GND Keyword:Mauerwerk; Elastizitätstheorie; Mathematische Modellierung
Dewey Decimal Classification:600 Technik, Medizin, angewandte Wissenschaften / 620 Ingenieurwissenschaften
BKL-Classification:56 Bauwesen / 56.11 Baukonstruktion
Open Access Publikationsfonds:Open-Access-Publikationsfonds 2022
Licence (German):License Logo Creative Commons 4.0 - Namensnennung (CC BY 4.0)