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Fast and reliable analysis of free‐edge stress fields in a thermally loaded composite strip by a layerwise laminate theory
Author(s) -
Mittelstedt Christian,
Becker Wilfried
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.1631
Subject(s) - traction (geology) , displacement (psychology) , finite element method , boundary value problem , computation , stress (linguistics) , structural engineering , mathematics , lagrange multiplier , mathematical analysis , enhanced data rates for gsm evolution , plate theory , free energy principle , materials science , engineering , mathematical optimization , algorithm , mechanical engineering , psychology , linguistics , philosophy , telecommunications , psychotherapist , statistics
A layerwise theory for the analysis of free‐edge effects in thermally loaded symmetric laminates with arbitrary layups is developed. The laminate under investigation is decomposed into an arbitrary number of mathematical layers through the thickness. The theory approach employs displacement terms according to Classical Laminate Plate Theory which are upgraded by layerwise displacement functions. The additional layerwise displacement functions consist of unknown inplane functions and linear thickness terms. The principle of minimum potential energy yields the governing Euler–Lagrange equations which allow for a closed‐form analytical solution for the inplane functions, thus characterizing this method as a semi‐analytical one. The underlying boundary conditions of traction free edges are fulfilled in an integral sense. The present results are in excellent agreement with accompanying finite element computations. Copyright © 2006 John Wiley & Sons, Ltd.