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Extension of the scaled boundary finite element method to geometrical and physical nonlinearity
Author(s) -
Behnke Ronny,
Mundil Matthias,
Birk Carolin,
Kaliske Michael
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410119
Subject(s) - finite element method , nonlinear system , extension (predicate logic) , boundary (topology) , mathematical analysis , bounded function , mathematics , plane (geometry) , mixed finite element method , extended finite element method , boundary value problem , geometry , structural engineering , physics , engineering , computer science , quantum mechanics , programming language
The scaled boundary finite element method (SBFEM) has been used in many fields of engineering to solve the governing equations in bounded and unbounded 2D as well as 3D domains. In solid mechanics, the semi‐analytical solution strategy of the SBFE formulation (numerical in circumferential direction, analytical in radial direction) is based on the assumption of linear elastic material behavior and only small geometrical changes. However, a large group of materials (e.g. rubber) shows geometrical and physical nonlinearity at mechanical loading. In this contribution, the extension of the SBFEM to geometrical and physical nonlinearity is examined. A plane finite element is developed which uses the concept of shape functions constructed by the SBFEM in the framework of a nonlinear finite element analysis. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)