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Analysis of notches and cracks in circular Kirchhoff plates using the scaled boundary finite element method
Author(s) -
Dieringer Rolf,
Becker Wilfried
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210085
Subject(s) - finite element method , mathematical analysis , bounded function , boundary (topology) , mathematics , singularity , scaling , boundary element method , ordinary differential equation , domain (mathematical analysis) , boundary value problem , partial differential equation , geometry , differential equation , structural engineering , engineering
A new formulation of the scaled boundary finite element method (SBFEM) is presented for the analysis of circular plates in the framework of Kirchhoff's plate theory. Essential for the SBFEM is, that a domain is described by the mapping of its boundary with respect to a scaling centre. The governing partial differential equations are transformed into scaled boundary coordinates and are reduced to a set of ordinary differential equations, which can be solved in a closed‐form analytical manner. If the scaling centre is selected at the root of an existent crack or notch, the SBFEM enables the effective and precise calculation of singularity orders of cracked and notched structures. The element stiffness matrices for bounded and unbounded media are derived. Numerical examples show the performance and efficiency of the method, applied to plate bending problems. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)