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A dedicated Fourier analysis for the simulation of composite pipes with defects
Author(s) -
Baranger E.,
Allix O.,
Blanchard L.
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1945
Subject(s) - truncation (statistics) , conjugate gradient method , matlab , set (abstract data type) , fourier series , computer science , fourier transform , composite number , code (set theory) , truncation error , algorithm , computational science , mechanical engineering , structural engineering , mathematics , engineering , mathematical analysis , programming language , machine learning
Abstract Through the study of a linear problem, this paper introduces some of the ingredients that are needed in order to conduct efficient non‐linear calculations on composite pipes under thermo‐mechanical loading in the presence of defects. Based on the observation that the main degradation scenarios take place at the extremity of a pipe, a refined model is used to describe this end zone while the rest of the pipe is described using a beam model. This study focuses on the efficient resolution of the refined end zone. For that, a dedicated Fourier expansion is used. The initial 3D problem is then transformed in a set of coupled 2D ones. The questions of the expansion truncation and the resolution of the coupled problem are then tackled. The use of a preconditioned conjugate gradient method allows to treat quasi‐industrial problems in a prototype code in Matlab. Copyright © 2006 John Wiley & Sons, Ltd.