Isogeometric shape design sensitivity analysis using transformed basis functions for Kronecker delta property

The isogeometric shape design sensitivity analysis (DSA) includes the desirable features; easy design parameterization and accurate shape sensitivity embedding the higher-order geometric information of curvature and normal vector. Due to the non-interpolatory property of NURBS basis, however, the imposition of essential boundary condition is not so straightforward in the isogeometric method. Taking advantages of geometrically exact property, an isogeometric DSA method is developed applying a mixed transformation to handle the boundary condition. A set of control point and NURBS basis function is added using the h-refinement and Newton iterations to precisely locate the control point to impose the boundary condition. In spite of additional transformation, its computation cost is comparable to the original one with penalty approach since the obtained Kronecker delta property enables to reduce the size of system matrix. Through demonstrative numerical examples, the effectiveness, accuracy, and computing cost of the developed DSA method are discussed.