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Follower loads for high order finite elements
Author(s) -
Heisserer Ulrich,
Düster Alexander,
Rank Ernst
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510179
Subject(s) - finite element method , discretization , nonlinear system , polygon mesh , distortion (music) , displacement (psychology) , hydrostatic equilibrium , mathematics , mathematical analysis , geometry , computer science , structural engineering , engineering , physics , psychology , amplifier , computer network , bandwidth (computing) , quantum mechanics , psychotherapist
Finite element modelling of hydrostatic compaction where the applied pressure acts normal to the deformed surface requires a geometric nonlinear formulation and follower load terms [1, 5, 7]. These concepts are applied to high order [6] ( p ‐FEM) elements with hierarchic shape functions. Applying the blending function method allows to precisely describe curved boundaries on coarse meshes. High order elements exhibit good performance even for high aspect ratios and strong distortion and therefore allow an efficient discretization of thin‐walled structures. Since high order finite elements are less prone to locking effects a pure displacement‐based formulation can be chosen. After introducing the basic concept of the p‐version the application of follower loads to geometrically nonlinear high order elements is presented. For the numerical solution the displacement based formulation is linearized yielding the basis for a Newton‐Raphson iteration. The accuracy and performance of the high order finite element scheme is demonstrated by a numerical example. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)