Extension of the scaled boundary finite element method to geometrical and physical nonlinearity

Abstract

AbstractThe 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)