A new approach to curvature measures in linear shell theories

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

A new approach to curvature measures in linear shell theories

Popis výsledku v původním jazyce

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).

Název v anglickém jazyce

A new approach to curvature measures in linear shell theories

Popis výsledku anglicky

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).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematics and Mechanics of Solids

ISSN

1081-2865

e-ISSN

1741-3028

Svazek periodika

26

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

23

Strana od-do

1241-1263

Kód UT WoS článku

000682022500001

EID výsledku v databázi Scopus

2-s2.0-85098250649