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## NON-LINEAR ANALYSIS OF SHELLS OF REVOLUTION USING MATHEMATICAL OPTIMISATION

• In the paper presented, reinforced concrete shells of revolution are analyzed in both meridional and circumferential directions. Taking into account the physical non-linearity of the material, the internal forces and the deflections of the shell as well as the strain distribution at the cross-sections are calculated. The behavior of concrete under compression is described by linear and non-linearIn the paper presented, reinforced concrete shells of revolution are analyzed in both meridional and circumferential directions. Taking into account the physical non-linearity of the material, the internal forces and the deflections of the shell as well as the strain distribution at the cross-sections are calculated. The behavior of concrete under compression is described by linear and non-linear stress-strain relations. The description of the behavior of concrete under tension must account for tension stiffening effects. A tri-linear function is used to formulate the material law of reinforcement. The problem cannot be solved analytically due to the physical non-linearity. Thus a numerical solution is formulated by means of the LAGRANGE Principle of the minimum of the total potential energy. The kinematically admissible field of deformation is defined by the displacements u in the meridional and w in the radial direction. These displacements must satisfy the equations of compatibility and the kinematical boundary conditions of the shell. The strains are linearly distributed across the wall thickness. The strain energy depends on the specific of the material behavior. Using integral formulations of the material law , the strain energy of each part of the cross-section is defined as a function of the strains at the boundaries of the cross-sections. The shell is discretised in the meridional direction. Various methods of numerical differentiation and numerical integration are applied in order to determine the deformations and the strain energy. The unknown displacements u and w are calculated by a non-restricted extremum problem based on the minimum of the total potential energy. From mathematical point of view, the objective function is a convex function, thus the minimum can be determined without difficulty. The advantage of this formulation is that unlike non-linear methods with path-following algorithms the calculation does not have to account for changing stiffness and load increments. All iterations necessary to find the solution are integrated into the “Solver”. The model presented provides many ways of investigating the influence of various material parameters on the stresses and deformations of the entire shell structure.  ### Download full text files

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Document Type: Conference Proceeding Prof. Dr.-Ing. habil. Erich RaueGND, Hans-Georg Timmler, Hendrik Schröter https://doi.org/10.25643/bauhaus-universitaet.2881Cite-Link https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20170314-28818Cite-Link http://euklid.bauing.uni-weimar.de/ikm2009/paper.html 1611-4086 Klaus GürlebeckGND, Carsten KönkeORCiDGND English 2017/03/14 2010/07/14 2017/03/14 Bauhaus-Universität Weimar Bauhaus-Universität Weimar Fakultät Bauingenieurwesen / Institut für Konstruktiven Ingenieurbau 12 Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing Angewandte Informatik; Angewandte Mathematik; Architektur ; Computerunterstütztes Verfahren 000 Informatik, Informationswissenschaft, allgemeine Werke / 000 Informatik, Wissen, Systeme 500 Naturwissenschaften und Mathematik / 510 Mathematik 31 Mathematik / 31.80 Angewandte 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, 18. 2009 Creative Commons 4.0 - Namensnennung-Nicht kommerziell (CC BY-NC 4.0)