Pressurized axisymmetric membrane deforming into a prescribed shape

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F20%3A00341167" target="_blank" >RIV/68407700:21110/20:00341167 - isvavai.cz</a>

Výsledek na webu

<a href="http://hdl.handle.net/10467/93679" target="_blank" >http://hdl.handle.net/10467/93679</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ijsolstr.2020.04.021" target="_blank" >10.1016/j.ijsolstr.2020.04.021</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Pressurized axisymmetric membrane deforming into a prescribed shape

Popis výsledku v původním jazyce

This paper presents a new approach to the optimal design of an axisymmetric membrane with variable thickness, which has potential applications in the development of active optical elements (liquid lenses). The governing equations are based on the Saint Venant-Kirchhoff material law, which postulates a linear relation between the Green-Lagrange strains and the second Piola-Kirchoff stresses, combined with the exact description of geometric nonlinearity, without any simplifying assumptions. It is shown that the membrane thickness can be designed such that the prestressed membrane subjected to a given uniform liquid pressure deforms into a prescribed rotationally symmetric shape, e.g., a spherical or parabolic cap. For the special but important case of a spherical cap, a closed-form solution is derived. A numerical procedure is developed for the general case, and its high accuracy and efficiency is demonstrated by examples. The sensitivity of the optimal design to material parameters and prestressing displacement is assessed.

Název v anglickém jazyce

Pressurized axisymmetric membrane deforming into a prescribed shape

Popis výsledku anglicky

This paper presents a new approach to the optimal design of an axisymmetric membrane with variable thickness, which has potential applications in the development of active optical elements (liquid lenses). The governing equations are based on the Saint Venant-Kirchhoff material law, which postulates a linear relation between the Green-Lagrange strains and the second Piola-Kirchoff stresses, combined with the exact description of geometric nonlinearity, without any simplifying assumptions. It is shown that the membrane thickness can be designed such that the prestressed membrane subjected to a given uniform liquid pressure deforms into a prescribed rotationally symmetric shape, e.g., a spherical or parabolic cap. For the special but important case of a spherical cap, a closed-form solution is derived. A numerical procedure is developed for the general case, and its high accuracy and efficiency is demonstrated by examples. The sensitivity of the optimal design to material parameters and prestressing displacement is assessed.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10306 - Optics (including laser optics and quantum optics)

Projekt

<a href="/cs/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Centrum pokročilých aplikovaných přírodních věd</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

International Journal of Solids and Structures

ISSN

0020-7683

e-ISSN

1879-2146

Svazek periodika

198

Číslo periodika v rámci svazku

August

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

16

Strana od-do

1-16

Kód UT WoS článku

000539430400001

EID výsledku v databázi Scopus

2-s2.0-85084064412