A new approach to curvature measures in linear shell theories
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00544897" target="_blank" >RIV/67985840:_____/21:00544897 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1177/1081286520972752" target="_blank" >https://doi.org/10.1177/1081286520972752</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1177/1081286520972752" target="_blank" >10.1177/1081286520972752</a>
Alternative languages
Result language
angličtina
Original language name
A new approach to curvature measures in linear shell theories
Original language description
he paper presents a coordinate-free analysis of deformation measures for shells modeled as 2D surfaces. These measures are represented by second-order tensors. As is well-known, two types are needed in general: the surface strain measure (deformations in tangential directions), and the bending strain measure (warping). Our approach first determines the 3D strain tensor E of a shear deformation of a 3D shell-like body and then linearizes E in two smallness parameters: the displacement and the distance of a point from the middle surface. The linearized expression is an affine function of the signed distance from the middle surface: the absolute term is the surface strain measure and the coefficient of the linear term is the bending strain measure. The main result of the paper determines these two tensors explicitly for general shear deformations and for the subcase of Kirchhoff-Love deformations. The derived surface strain measures are the classical ones: Naghdi’s surface strain measure generally and its well-known particular case for the Kirchhoff-Love deformations. With the bending strain measures comes a surprise: they are different from the traditional ones. For shear deformations our analysis provides a new tensor (Formula presented.), which is different from the widely used Naghdi’s bending strain tensor (Formula presented.). In the particular case of Kirchhoff-Love deformations, the tensor (Formula presented.) reduces to a tensor (Formula presented.) introduced earlier by Anicic and Léger (Formulation bidimensionnelle exacte du modéle de coque 3D de Kirchhoff-Love. C R Acad Sci Paris I 1999: 329: 741-746). Again, (Formula presented.) is different from Koiter’s bending strain tensor (Formula presented.) (frequently used in this context).
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematics and Mechanics of Solids
ISSN
1081-2865
e-ISSN
1741-3028
Volume of the periodical
26
Issue of the periodical within the volume
9
Country of publishing house
GB - UNITED KINGDOM
Number of pages
23
Pages from-to
1241-1263
UT code for WoS article
000682022500001
EID of the result in the Scopus database
2-s2.0-85098250649