Isogeometric structural shape optimization using a fictitious energy regularization

In isogeometric analysis, NURBS basis functions are used as shape functions in an isoparametric finite-element-type discretization. Among other advantageous features, this approach is able to provide exact and smooth representations of a broad class of computational domains with curved boundaries. Therefore, this discretization method seems to be especially convenient for computational shape optimization, where a smooth and CAD-like parametrization of the optimal geometry is desired. Choosing boundary control point coordinates of an isogeometric discretization as design variables, an additional design model can be avoided. However, for a higher number of design variables, typical drawbacks like oscillating boundaries as known from early node-based shape optimization methods appear. To overcome this problem, we propose to use a fictitious energy regularization: the strain energy of a fictitious deformation, which maps the initial to the optimized domain, is employed as a regularizing term in the optimization problem. Moreover, this deformation is used for efficiently moving the dependent nodes within the domain in each step of the optimization process. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)