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## NICHTLINEARE ANALYSE VON VERBUNDQUERSCHNITTEN - EIN NEUER ALTERNATIVER WEG

• A new approach to the non-linear analysis of cross-sections loaded by normal forces and bending moments is presented in the paper. The mechanical model is based on the LAGRANGE principle of minimum of total potential energy. Deformations, stresses and limit load parameters are obtained by solving a non-linear optimisation problem. The mathematical model is independent of the specifics of material.A new approach to the non-linear analysis of cross-sections loaded by normal forces and bending moments is presented in the paper. The mechanical model is based on the LAGRANGE principle of minimum of total potential energy. Deformations, stresses and limit load parameters are obtained by solving a non-linear optimisation problem. The mathematical model is independent of the specifics of material. In addition to the stress strain relation and the specific strain energy W(ε) two further functions F(ε) and Φ(ε) are introduced to describe the material behaviour. Thus cracks in concrete, non-linearity of material etc. can be taken into account without basic modification of the numerical algorithm. For polygonal cross-sections the GAUSS' integral theorem is used. Numerical solutions of the non-linear optimisation problems can be found by application of standard software. Thus the analysis of reinforced concrete cross-sections or more general composite cross-sections with non-linear behaviour of material is as simple as in the case of linear elasticity. The application of the method is demonstrated for polygonal cross-sections. Pre-stresses or pre-strains can easily be included in the mathematical model.  • Volltext Document Type: Conference Proceeding Erich RaueGND https://doi.org/10.25643/bauhaus-universitaet.3002Cite-Link https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20170327-30027Cite-Link http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html Klaus GürlebeckGND, Carsten KönkeORCiDGND English 2017/03/25 2006/07/14 2017/03/27 Bauhaus-Universität Weimar Bauhaus-Universität Weimar Fakultät Bauingenieurwesen / Professur Massivbau I Fakultät Bauingenieurwesen / Institut für Konstruktiven Ingenieurbau 13 Architektur ; CAD; Computerunterstütztes Verfahren 500 Naturwissenschaften und Mathematik / 510 Mathematik 56 Bauwesen / 56.03 Methoden im Bauingenieurwesen 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, 17. 2006 Creative Commons 4.0 - Namensnennung-Nicht kommerziell (CC BY-NC 4.0)