TY  - JOUR
A1  - Gürlebeck, Klaus
A1  - Legatiuk, Dmitrii
A1  - Webber, Kemmar
T1  - Operator Calculus Approach to Comparison of Elasticity Models for Modelling of Masonry Structures
JF  - Mathematics
N2  - 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.
KW  - Mauerwerk
KW  - Elastizitätstheorie
KW  - Mathematische Modellierung
KW  - quaternionic analysis
KW  - mathematical modelling
KW  - operator calculus
KW  - model comparison
KW  - micropolar elasticity
KW  - OA-Publikationsfonds2022
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20220721-46726
UR  - https://www.mdpi.com/2227-7390/10/10/1670
VL  - 2022
IS  - Volume 10, issue 10, article 1670
SP  - 1
EP  - 22
PB  - MDPI
CY  - Basel
ER  - 
TY  - JOUR
A1  - Rabczuk, Timon
A1  - Zhuang, Xiaoying
A1  - Oterkus, Erkan
T1  - Editorial: Computational modeling based on nonlocal theory
JF  - Engineering with Computers
N2  - Nonlocal theories concern the interaction of objects, which are separated in space. Classical examples are Coulomb’s law or Newton’s law of universal gravitation. They had signficiant impact in physics and engineering. One classical application in mechanics is the failure of quasi-brittle materials. While local models lead to an ill-posed boundary value problem and associated mesh dependent results, nonlocal models guarantee the well-posedness and are furthermore relatively easy to implement into commercial computational software.
KW  - Computersimulation
KW  - Mathematische Modellierung
KW  - computational modeling
KW  - nonlocal theory
Y1  - 2023
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20230517-63658
UR  - https://link.springer.com/article/10.1007/s00366-022-01775-7
VL  - 2023
IS  - Volume 39, issue 3
PB  - Springer
CY  - London
ER  -