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Extension of the scaled boundary finite element method to plate bending problems
Author(s) -
Dieringer Rolf,
Hebel Jochen,
Becker Wilfried
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110093
Subject(s) - finite element method , ordinary differential equation , extension (predicate logic) , mathematical analysis , bending of plates , bounded function , mathematics , boundary value problem , bending , boundary element method , boundary (topology) , plate theory , bending stiffness , stiffness , differential equation , structural engineering , computer science , engineering , programming language
The scaled boundary finite element method (SBFEM) is extended to the static analysis of thin plates in the framework of Kirchhoff's plate theory. The governing equations are transformed into scaled boundary coordinates. Applying a discrete form of the Kantorovich reduction method results in a set of ordinary differential equations, which can be solved in a closed‐form analytical manner. The element stiffness matrices for bounded and unbounded media can be computed, using appropriate subsets of the analytical solution. Examples show the efficiency of the method, applied to plate bending problems. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)