Isogeometric Analysis and Shape Optimisation

Publication: Research - peer-reviewConference abstract for conference – Annual report year: 2011

Standard

Isogeometric Analysis and Shape Optimisation. / Gravesen, Jens; Evgrafov, Anton; Gersborg, Allan Roulund; Nguyen, Dang Manh; Nielsen, Peter Nørtoft.

2011. Abstract from US National Congress on Computational Mechanics, Minneapolis and St. Paul, Minnesota, USA, .

Publication: Research - peer-reviewConference abstract for conference – Annual report year: 2011

Harvard

Gravesen, J, Evgrafov, A, Gersborg, AR, Nguyen, DM & Nielsen, PN 2011, 'Isogeometric Analysis and Shape Optimisation' US National Congress on Computational Mechanics, Minneapolis and St. Paul, Minnesota, USA, 01/01/11,

APA

Gravesen, J., Evgrafov, A., Gersborg, A. R., Nguyen, D. M., & Nielsen, P. N. (2011). Isogeometric Analysis and Shape Optimisation. Abstract from US National Congress on Computational Mechanics, Minneapolis and St. Paul, Minnesota, USA, .

CBE

Gravesen J, Evgrafov A, Gersborg AR, Nguyen DM, Nielsen PN. 2011. Isogeometric Analysis and Shape Optimisation. Abstract from US National Congress on Computational Mechanics, Minneapolis and St. Paul, Minnesota, USA, .

MLA

Vancouver

Gravesen J, Evgrafov A, Gersborg AR, Nguyen DM, Nielsen PN. Isogeometric Analysis and Shape Optimisation. 2011. Abstract from US National Congress on Computational Mechanics, Minneapolis and St. Paul, Minnesota, USA, .

Author

Gravesen, Jens; Evgrafov, Anton; Gersborg, Allan Roulund; Nguyen, Dang Manh; Nielsen, Peter Nørtoft / Isogeometric Analysis and Shape Optimisation.

2011. Abstract from US National Congress on Computational Mechanics, Minneapolis and St. Paul, Minnesota, USA, .

Publication: Research - peer-reviewConference abstract for conference – Annual report year: 2011

Bibtex

@misc{20823a89517f4f57bfb661bba42af24a,
title = "Isogeometric Analysis and Shape Optimisation",
author = "Jens Gravesen and Anton Evgrafov and Gersborg, {Allan Roulund} and Nguyen, {Dang Manh} and Nielsen, {Peter Nørtoft}",
year = "2011",
type = "ConferencePaper <importModel: ConferenceImportModel>",

}

RIS

TY - ABST

T1 - Isogeometric Analysis and Shape Optimisation

A1 - Gravesen,Jens

A1 - Evgrafov,Anton

A1 - Gersborg,Allan Roulund

A1 - Nguyen,Dang Manh

A1 - Nielsen,Peter Nørtoft

AU - Gravesen,Jens

AU - Evgrafov,Anton

AU - Gersborg,Allan Roulund

AU - Nguyen,Dang Manh

AU - Nielsen,Peter Nørtoft

PY - 2011

Y1 - 2011

N2 - One of the attractive features of isogeometric analysis is the exact representation of the geometry. The geometry is furthermore given by a relative low number of control points and this makes isogeometric analysis an ideal basis for shape optimisation. I will describe some of the results we have obtained and also some of the problems we have encountered. One of these problems is that the geometry of the shape is given by the boundary alone. And, it is the parametrisation of the boundary which is changed by the optimisation procedure. But isogeometric analysis requires a parametrisation of the whole domain. So in every optimisation cycle we need to extend a parametrisation of the boundary of a domain to the whole domain. It has to be fast in order not to slow the optimisation down but it also has to be robust and give a parametrisation of high quality. These are conflicting requirements so we propose the following approach. During the optimisation a fast linear method is used, but if the parametrisation becomes singular or close to singular then the optimisation is stopped and the parametrisation is improved using a nonlinear method. The optimisation then continues using a linear method. We will explain how the validity of a parametrisation can be checked and we will describe various ways to parametrise a domain. We will in particular study the Winslow functional which turns out to have some desirable properties. Other problems we touch upon is clustering of boundary control points (design variables) and self intersection of the design. The first problem can be solves by a suitable regularisation and the latter by a method that resembles how the validity of the parametrisation is secured.

AB - One of the attractive features of isogeometric analysis is the exact representation of the geometry. The geometry is furthermore given by a relative low number of control points and this makes isogeometric analysis an ideal basis for shape optimisation. I will describe some of the results we have obtained and also some of the problems we have encountered. One of these problems is that the geometry of the shape is given by the boundary alone. And, it is the parametrisation of the boundary which is changed by the optimisation procedure. But isogeometric analysis requires a parametrisation of the whole domain. So in every optimisation cycle we need to extend a parametrisation of the boundary of a domain to the whole domain. It has to be fast in order not to slow the optimisation down but it also has to be robust and give a parametrisation of high quality. These are conflicting requirements so we propose the following approach. During the optimisation a fast linear method is used, but if the parametrisation becomes singular or close to singular then the optimisation is stopped and the parametrisation is improved using a nonlinear method. The optimisation then continues using a linear method. We will explain how the validity of a parametrisation can be checked and we will describe various ways to parametrise a domain. We will in particular study the Winslow functional which turns out to have some desirable properties. Other problems we touch upon is clustering of boundary control points (design variables) and self intersection of the design. The first problem can be solves by a suitable regularisation and the latter by a method that resembles how the validity of the parametrisation is secured.

UR - http://www.usnccm.org/

ER -