“…In the context of isogeometric shape optimization, the exact geometric representation enables the computation of the boundary geometric parameters easily and seamlessly, hence, providing a natural platform to implement the continuum adjoint method. This has been intensively studied by Seonho Cho and his co-authors in Cho et al [Cho and Ha (2009)] for general discussions, in Ha et al [Ha, Choi and Cho (2010)] using T-spline based isogeometric method, in Ahn et al [Ahn and Cho (2010)] for level-set-based topology optimization of heat conduction problems, in Koo et al [Koo, Yoon and Cho (2013)] coping with Kronecker delta property, in Yoon et al [Yoon, Ha and Cho (2013); Yoon, Choi and Cho (2015)] for shape design optimization of heat conduction problems, in Choi et al [Choi and Cho (2014)] for stress intensity factors of curved crack problems, in Lee et al [Lee and Cho (2015)] for optimizing built-up structures, in Lee et al [Lee, Lee and Cho (2016)] for ferromagnetic materials in magnetic actuators, in Yoon et al [Yoon and Cho (2016)] for boundary integral equations, in Choi et al [Choi, Yoon and Cho (2016)] for designing curved Kirchhoff beams with finite deformations, in Lee et al [Lee, Yoon and Cho (2017)] for topological shape optimization using dual evolution with boundary integral equation and level sets, in Choi et al [Choi and Cho (2018a)] for designing lattice structures embedded on curve surfaces, in Choi et al [Choi and Cho (2018b)] for using curved beams to design auxetic structures and in Ahn et al [Ahn, Choi and Cho (2018); Ahn, Koo, Kim et al (2018)] for designing nanoscale structures. Wang and his co-authors implemented the continuum adjoint method in Wang et al [Wang and Turteltaub (2015)] for quasi-static problems considering discontinuities in the objective functions, in Wang et al ; Wang and Kumar (2017)] for transient heat conduction problems and in Wang et al [Wang, Poh, Dirrenberger et al (2017)] to design auxetic structures using numerical homogenization method.…”