title: On ellipticity of static equations of strain gradient elasticity and infinitesimal stability
metadata.name: dc.contributor.author
metadata.value: Eremeyev, Victor А.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2023-03-14T20:28:56Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2023-03-14T20:28:56Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2023-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Eremeyev V.А. On ellipticity of static equations of strain gradient elasticity and infinitesimal stability. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2023, vol. 10 (68), issue 1, pp. 99–108. https://doi.org/10.21638/spbu01.2023.109 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2023.109
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/39329
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Within the framework of strain gradient elasticity under finite deformations we formulate the strong ellipticity conditions of equilibrium equations. Within the model a strain energy density is a function of the first and second deformation gradients. Ellipticity involves certain constraints on the tangent elastic moduli. It is also closely related to infinitesimal stability which is defined as the positive definiteness of the second variation of the potential energy functional. Here we consider the first boundary-value problem, that is with Dirichlettype boundary conditions. For one-dimensional deformations we determine necessary and sufficient conditions of infinitesimal instability. The latter constitute two inequalities for elastic moduli.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 10 (68); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: strain gradient elasticity
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: strong ellipticity
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: infinitesimal stability
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On ellipticity of static equations of strain gradient elasticity and infinitesimal stability
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 15497-Текст статьи-51848-1-2-20230304.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/39329/1/15497-%d0%a2%d0%b5%d0%ba%d1%81%d1%82%20%d1%81%d1%82%d0%b0%d1%82%d1%8c%d0%b8-51848-1-2-20230304.pdf
resources.format: Adobe PDF
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