Isogeometric Shape Optimization of Vibrating Membranes

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Implementation of regularized isogeometric boundary element methods for gradient‐based shape optimization in two‐dimensional linear elasticity (2016, methodology): “The application of IGA in shape optimization can be found in [47, 48, 49, 50, 51].”
Bounding the influence of domain parameterization and knot spacing on numerical stability in Isogeometric Analysis (2014, methodology): “In [21] and [22] the authors use this technique to optimize the domain of interest for special applications such as vibrating membranes or conducting scatterers.”
On the sensitivities of multiple eigenvalues (2011, background): “This knowledge may be used to, for example, replace potentially non-smooth pair of constraints λ1(t) = ˆ λ1, λ2(t) = ˆ λ2 ,w ith ap air of smooth ones: tr A(t) = ˆ λ1 + ˆ λ2 ,d etA(t) = ˆ λ1 ˆ λ2, see Nguyen et al. (2011) .”
Isogeometric analysis: An overview and computer implementation aspects (2012, background): “IGA has also shown advantages over traditional approaches in the context of optimization problems, [79, 100, 101, 145] where the tight coupling with CAD models offers an extremely attractive approach for industrial applications.”
Shape optimization of continua using NURBS as basis functions (2013, methodology): “Applications of the isogeometric finite element method were presented to vibrating membranes by Manh et al.[28], and to photonic crystals by Qian et al.[42].”