Isogeometric shape optimization of vibrating membranes

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...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2011-03, Vol.200 (13), p.1343-1353
Main Authors: Manh, Nguyen Dang, Evgrafov, Anton, Gersborg, Allan Roulund, Gravesen, Jens
Format: Article
Language:English
Subjects:
Algorithms
B-spline parametrization
Boundaries
Computer simulation
Eigenvalues of the Laplace operator
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Isogeometric analysis
Mathematical models
Membranes
Optimization
Physics
Shape optimization
Solid mechanics
Structural and continuum mechanics
Tasks
Vibrating membrane
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
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Summary: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.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2010.12.015