Premium
Coupled multiscale finite element analysis of shell structures
Author(s) -
Hebel Jochen,
Gruttmann Friedrich,
Wagner Werner
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210084
Subject(s) - discretization , finite element method , boundary value problem , stress resultants , quadrilateral , shell (structure) , linear elasticity , mathematics , compatibility (geochemistry) , mathematical analysis , structural engineering , engineering , mechanical engineering , chemical engineering
In this paper, a coupled two‐scale shell model is presented. A variational formulation and associated linearisation for the coupled global‐local boundary value problem is derived. The discretisation of the shell is performed with quadrilaterals, whereas the local boundary value problems at the integration points of the shell are discretised using 8‐noded or 27‐noded brick elements, or solid shell elements. The coupled boundary value problem is simultaneously solved within a Newton iteration scheme. Solutions for small strain problems are computed within the so‐called FE 2 method. In an important test, the correct material matrix for the stress resultants assuming linear elasticity and a homogeneous continuum is verified. Examples show that the developed two‐scale model is able to analyse the global and local mechanical behaviour of heterogeneous shell structures. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)