Isogeometric shape optimization method with patch removal for holed structures

Nonuniform rational B-spline (NURBS) basis function is used as the interpolation function of unknown physical field in isogeometric analysis (IGA) method. The model transformation process is avoided in isogeometric shape optimization, because design, analysis and optimization models can all be represented in the framework of NURBS. Previously, the multiple patches method is often adopted to model topologically complex structures in isogeometric shape optimization. However, it has been found inconvenient for holed structures, especially when multiholes are involved. The reason lies in that the structure needs to be partitioned into many intact patches suitable to structural analysis. Therefore, an isogeometric shape optimization method using patch removal is proposed. The patch partition is achieved on the basis of inner and outer boundaries of holed structures. Moreover, an analytical shape sensitivity approach is developed. By means of classical optimization example of torque arm, it proves that the present method can not only provide a concise modeling approach, but also favor the selection of design variables.