Evolution model of linear micropolar plate
type: Item
instance of: scholarly article
title: Evolution model of linear micropolar plate
zbMATH Open document ID: 1194.74180
author: Josip Tambača
author: Igor Velčić
published in: Annali dell'Università di Ferrara. Sezione VII. Scienze Matematiche
publication date: 2009-12-14T00:00:00Z
review text: First, the authors derive a three-dimensional evolution equation for linearized micropolar thin plate-like bodies, using the thickness of the plate as small parameter. Under suitable assumptions on the asymptotic behavior of the loads and initial conditions, the authors show that a family of approximate solutions converges to a function independent of the cross-sectional variable, that is the unique solution of the three-dimensional problem. Then, to justify mathematically a two-dimensional evolution model of linear micropolar plates, the authors apply the asymptotic analysis, as in classical elasticity. The weak formulation of the limit problem is given in terms of the limit microrotation and limit displacement. Using a correction result for the displacement, the authors interpret the displacement as the translation of the middle plane, and examine the radial stretch and the infinitesimal rotation of the cross-section.
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74A35
Mathematics Subject Classification ID: 74H10
zbMATH DE Number: 5646392
zbMATH Keywords: asymptotic analysis
zbMATH Keywords: weak formulation
zbMATH Keywords: limit microrotation
zbMATH Keywords: limit displacement
reviewed by: Marin I. Marin
MaRDI profile type: Publication
full work available at URL: s11565-007-0020-2
OpenAlex ID: W2029211261
cites work: Derivation and justification of the models of rods and plates from linearized three-dimensional micropolar elasticity
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cites work: Q3051563
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cites work: Microcontinuum Field Theories
cites work: Q4805963
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DOI: 10.1007/S11565-007-0020-2
description: scientific article; zbMATH DE number 5646392