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Continuum Mechanics and Thermodynamics
Erschienen in: Continuum Mechanics and Thermodynamics 4/2021

07.01.2021 | Original Article

A survey of results on cusped standard and prismatic shells, in particular plates, and bars and on the corresponding singular PDEs

verfasst von: George Jaiani, Natalia Chinchaladze

Erschienen in: Continuum Mechanics and Thermodynamics | Ausgabe 4/2021

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Abstract

An updated comprehensive exploratory survey of the literature on elastic cusped standard and prismatic shells and bars, in particular, cusped plates, and to the corresponding singular partial differential equations and systems is given. The governing systems of equations of statics and dynamics in the cases of compression–tension and bending are derived from I. Vekua’s hierarchical models of the generic Nth-order approximation, in particular, for cusped elastic plates. In the static case, the well-posedness of the basic BVPs for cusped plates is investigated. The BCs at the cusped edge are non-classical, in general, and depend on the kind of thinning. The corresponding criteria are established. In the special cases, the BVPs are solved in the explicit form.
Vorheriger Artikel Constitutive sensitivity to the gradient of plastic deformation in the mechanics of crystalline solids
Nächster Artikel Spherically symmetric state of an elastic micropolar liquid

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Fußnoten
1
\(C({\overline{\omega }})\) denotes a class of functions continuous on \({\overline{\omega }}\); \(C^2(\omega )\) denotes a class of twice continuously differentiable functions with respect to the variables \(x_1\) and \(x_2\) with \((x_1,x_2)\in \omega \).
 
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Metadaten
Titel
A survey of results on cusped standard and prismatic shells, in particular plates, and bars and on the corresponding singular PDEs
verfasst von
George Jaiani
Natalia Chinchaladze
Publikationsdatum
07.01.2021
Verlag
Springer Berlin Heidelberg
Erschienen in
Continuum Mechanics and Thermodynamics / Ausgabe 4/2021
Print ISSN: 0935-1175
Elektronische ISSN: 1432-0959
DOI
https://doi.org/10.1007/s00161-020-00965-2

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