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CONVERGENCE OF A NEW CONSISTENT FOLDED PLATE THEORY

  • The design of challenging space structures frequently relies on the theory of folded plates. The models are composed of plane facets of which the bending and membrane stiffness are coupled along the folds. In conventional finite element analysis of faceted structures the continuity of the displacement field is enforced exclusively at the nodes. Since approximate solutions for transverse and forThe design of challenging space structures frequently relies on the theory of folded plates. The models are composed of plane facets of which the bending and membrane stiffness are coupled along the folds. In conventional finite element analysis of faceted structures the continuity of the displacement field is enforced exclusively at the nodes. Since approximate solutions for transverse and for in-plane displacements are not members of the same function space, separation occurs in between the common nodes of adjacent elements. It is shown that the kinematic assumptions of Bernoulli are accounted for this incompatibility along the edges in facet models. A general answer to this problem involves substantial modification of plate and membrane theory, but a straight forward formulation can be derived for simply folded plates, structures, whose folds do not intersect. A broad class of faceted structures, including models of various curved shells, belong to this category and can be calculated consistently. The additional requirements to assure continuity concern the mapping of displacement derivatives on the edges. An appropriate finite facet element provides node and edge-oriented degrees of freedom, whose transformation to system degrees of freedom, depends on the geometric configuration at each node. The concept is implemented using conform triangular elements. To evaluate the new approach, the energy norm of representative structures for refined meshes is calculated. The focus is placed on the mathematical convergence towards reliable solutions obtained from finite volume models.show moreshow less

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Metadaten
Document Type:Conference Proceeding
Author: Eva Kasparek
DOI (Cite-Link):https://doi.org/10.25643/bauhaus-universitaet.2972Cite-Link
URN (Cite-Link):https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20170327-29724Cite-Link
URL:http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html
Editor: Klaus GürlebeckGND, Carsten KönkeORCiDGND
Language:English
Date of Publication (online):2017/03/24
Date of first Publication:2006/07/14
Release Date:2017/03/27
Publishing Institution:Bauhaus-Universität Weimar
Creating Corporation:Bauhaus-Universität Weimar
Institutes:Bauhaus-Universität Weimar / In Zusammenarbeit mit der Bauhaus-Universität Weimar
Pagenumber:10
GND Keyword:Architektur <Informatik>; CAD; Computerunterstütztes Verfahren
Dewey Decimal Classification:500 Naturwissenschaften und Mathematik / 510 Mathematik
BKL-Classification: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, 17. 2006
Licence (German):License Logo Creative Commons 4.0 - Namensnennung-Nicht kommerziell (CC BY-NC 4.0)