THE RELATIONSHIP BETWEEN LINEAR ELASTICITY THEORY AND COMPLEX FUNCTION THEORY STUDIED ON THE BASIS OF FINITE DIFFERENCES

  • It is well-known that the solution of the fundamental equations of linear elasticity for a homogeneous isotropic material in plane stress and strain state cases can be equivalently reduced to the solution of a biharmonic equation. The discrete version of the Theorem of Goursat is used to describe the solution of the discrete biharmonic equation by the help of two discrete holomorphic functions. InIt is well-known that the solution of the fundamental equations of linear elasticity for a homogeneous isotropic material in plane stress and strain state cases can be equivalently reduced to the solution of a biharmonic equation. The discrete version of the Theorem of Goursat is used to describe the solution of the discrete biharmonic equation by the help of two discrete holomorphic functions. In order to obtain a Taylor expansion of discrete holomorphic functions we introduce a basis of discrete polynomials which fulfill the so-called Appell property with respect to the discrete adjoint Cauchy-Riemann operator. All these steps are very important in the field of fracture mechanics, where stress and displacement fields in the neighborhood of singularities caused by cracks and notches have to be calculated with high accuracy. Using the sum representation of holomorphic functions it seems possible to reproduce the order of singularity and to determine important mechanical characteristics.show moreshow less

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Metadaten
Document Type:Conference Proceeding
Author: Angela Hommel, Klaus GürlebeckGND
DOI (Cite-Link):https://doi.org/10.25643/bauhaus-universitaet.2801Cite-Link
URN (Cite-Link):https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20170314-28010Cite-Link
ISSN:1611-4086
Parent Title (English):Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar
Editor: Klaus GürlebeckGND, Tom LahmerORCiDGND
Language:English
Date of Publication (online):2017/03/03
Date of first Publication:2015/08/28
Release Date:2017/03/14
Publishing Institution:Bauhaus-Universität Weimar
Creating Corporation:Bauhaus-Universität Weimar
Institutes:Bauhaus-Universität Weimar / In Zusammenarbeit mit der Bauhaus-Universität Weimar
Pagenumber:6
Tag:Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications
GND Keyword:Angewandte Informatik; Angewandte Mathematik; Building Information Modeling; Computerunterstütztes Verfahren
Dewey Decimal Classification:000 Informatik, Informationswissenschaft, allgemeine Werke / 000 Informatik, Wissen, Systeme
500 Naturwissenschaften und Mathematik / 510 Mathematik
BKL-Classification:31 Mathematik / 31.80 Angewandte Mathematik
56 Bauwesen / 56.03 Methoden im Bauingenieurwesen
Collections:Bauhaus-Universität Weimar / Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen, IKM, Weimar / Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen, IKM, Weimar, 20. 2015
Licence (German):License Logo Creative Commons 4.0 - Namensnennung-Nicht kommerziell (CC BY-NC 4.0)