Publication: Research - peer-review › Journal article – Annual report year: 2011
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.
|Journal||Computer Methods in Applied Mechanics and Engineering|
|Citations||Web of Science® Times Cited: 12|
- shape optimization, eigenvalues of the Laplace operator, B-spline parametrization, vibrating membrane, Isogeometric analysis