A Note on Averaging of Stiffnesses of Thin Elastic Periodic Plates

The homogenization problem for a nonhornogeneous plate of doubly periodic structure is discussed. lt has been proved that an effective plate with constant effective homogenized stiffnesses is (in a certain meaning) energy equivalent to the considered heterogeneous plate of Y-periodic stiffnesses. M...

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Main Author: T. Lewiński
Format: Article
Language:English
Published: Institute of Fundamental Technological Research 1986-09-01
Series:Engineering Transactions
Online Access:https://et.ippt.pan.pl/index.php/et/article/view/1815
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author T. Lewiński
author_facet T. Lewiński
author_sort T. Lewiński
collection DOAJ
description The homogenization problem for a nonhornogeneous plate of doubly periodic structure is discussed. lt has been proved that an effective plate with constant effective homogenized stiffnesses is (in a certain meaning) energy equivalent to the considered heterogeneous plate of Y-periodic stiffnesses. Moreover, the corrector of the homogenized solution is defined and then its elementary derivation is presented, emphasis being put on the physical clearness of the procedure. In the last section a particular case of a plate with the thickness periodic in one (x1) direction is examined. A comparison is made of two sets of formulas for effective stiffnesses proposed by Duvaut and Kączkowski, respectively. lt is noted that the two formulae for D1212 and D2222 do not coincide.
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id doaj-art-674ca8f6163545a1b8433f85ae3bf033
institution Kabale University
issn 0867-888X
2450-8071
language English
publishDate 1986-09-01
publisher Institute of Fundamental Technological Research
record_format Article
series Engineering Transactions
spelling doaj-art-674ca8f6163545a1b8433f85ae3bf0332025-08-20T03:49:51ZengInstitute of Fundamental Technological ResearchEngineering Transactions0867-888X2450-80711986-09-01343A Note on Averaging of Stiffnesses of Thin Elastic Periodic PlatesT. Lewiński0Technical University of Warszawa, Warszawa The homogenization problem for a nonhornogeneous plate of doubly periodic structure is discussed. lt has been proved that an effective plate with constant effective homogenized stiffnesses is (in a certain meaning) energy equivalent to the considered heterogeneous plate of Y-periodic stiffnesses. Moreover, the corrector of the homogenized solution is defined and then its elementary derivation is presented, emphasis being put on the physical clearness of the procedure. In the last section a particular case of a plate with the thickness periodic in one (x1) direction is examined. A comparison is made of two sets of formulas for effective stiffnesses proposed by Duvaut and Kączkowski, respectively. lt is noted that the two formulae for D1212 and D2222 do not coincide. https://et.ippt.pan.pl/index.php/et/article/view/1815
spellingShingle T. Lewiński
A Note on Averaging of Stiffnesses of Thin Elastic Periodic Plates
Engineering Transactions
title A Note on Averaging of Stiffnesses of Thin Elastic Periodic Plates
title_full A Note on Averaging of Stiffnesses of Thin Elastic Periodic Plates
title_fullStr A Note on Averaging of Stiffnesses of Thin Elastic Periodic Plates
title_full_unstemmed A Note on Averaging of Stiffnesses of Thin Elastic Periodic Plates
title_short A Note on Averaging of Stiffnesses of Thin Elastic Periodic Plates
title_sort note on averaging of stiffnesses of thin elastic periodic plates
url https://et.ippt.pan.pl/index.php/et/article/view/1815
work_keys_str_mv AT tlewinski anoteonaveragingofstiffnessesofthinelasticperiodicplates
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