Isogeometric Shape Optimization of Vibrating Membranes

Publication: Research - peer-reviewJournal article – Annual report year: 2011

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Isogeometric Shape Optimization of Vibrating Membranes. / Nguyen, Dang Manh; Evgrafov, Anton; Gersborg, Allan Roulund; Gravesen, Jens.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 200, No. 13-16, 2011, p. 1343-1353.

Publication: Research - peer-reviewJournal article – Annual report year: 2011

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Author

Nguyen, Dang Manh; Evgrafov, Anton; Gersborg, Allan Roulund; Gravesen, Jens / Isogeometric Shape Optimization of Vibrating Membranes.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 200, No. 13-16, 2011, p. 1343-1353.

Publication: Research - peer-reviewJournal article – Annual report year: 2011

Bibtex

@article{56f947afc5f44ad29a8aa7f70702eacf,
title = "Isogeometric Shape Optimization of Vibrating Membranes",
keywords = "shape optimization, eigenvalues of the Laplace operator, B-spline parametrization, vibrating membrane, Isogeometric analysis",
publisher = "Elsevier BV",
author = "Nguyen, {Dang Manh} and Anton Evgrafov and Gersborg, {Allan Roulund} and Jens Gravesen",
year = "2011",
doi = "10.1016/j.cma.2010.12.015",
volume = "200",
number = "13-16",
pages = "1343--1353",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",

}

RIS

TY - JOUR

T1 - Isogeometric Shape Optimization of Vibrating Membranes

A1 - Nguyen,Dang Manh

A1 - Evgrafov,Anton

A1 - Gersborg,Allan Roulund

A1 - Gravesen,Jens

AU - Nguyen,Dang Manh

AU - Evgrafov,Anton

AU - Gersborg,Allan Roulund

AU - Gravesen,Jens

PB - Elsevier BV

PY - 2011

Y1 - 2011

N2 - We consider a model problem of isogeometric shape optimization of vibrating membranes whose shapes are allowed to vary freely. The main obstacle we face is the need for robust and inexpensive extension of a B-spline parametrization from the boundary of a domain onto its interior, a task which has to be performed in every optimization iteration. We experiment with two numerical methods (one is based on the idea of constructing a quasi-conformal mapping, whereas the other is based on a spring-based mesh model) for carrying out this task, which turn out to work sufficiently well in the present situation. We perform a number of numerical experiments with our isogeometric shape optimization algorithm and present smooth, optimized membrane shapes. Our conclusion is that isogeometric analysis fits well with shape optimization.

AB - We consider a model problem of isogeometric shape optimization of vibrating membranes whose shapes are allowed to vary freely. The main obstacle we face is the need for robust and inexpensive extension of a B-spline parametrization from the boundary of a domain onto its interior, a task which has to be performed in every optimization iteration. We experiment with two numerical methods (one is based on the idea of constructing a quasi-conformal mapping, whereas the other is based on a spring-based mesh model) for carrying out this task, which turn out to work sufficiently well in the present situation. We perform a number of numerical experiments with our isogeometric shape optimization algorithm and present smooth, optimized membrane shapes. Our conclusion is that isogeometric analysis fits well with shape optimization.

KW - shape optimization

KW - eigenvalues of the Laplace operator

KW - B-spline parametrization

KW - vibrating membrane

KW - Isogeometric analysis

U2 - 10.1016/j.cma.2010.12.015

DO - 10.1016/j.cma.2010.12.015

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

IS - 13-16

VL - 200

SP - 1343

EP - 1353

ER -