Isogeometric shape design optimization: exact geometry and enhanced sensitivity

Finite element based shape optimization has some difficulties in the parameterization of design domain. In isogeometric approach, however, the geometric properties of design are embedded into the NURBS basis functions and the control points whose perturbation naturally results in shape changes. Thus, exact geometric models can be used in both response and shape sensitivity analyses, where normal vector and curvature are continuous over the whole design space so that enhanced shape sensitivity can be obtained. In the problems of shape optimal design, refinements and design changes are easily implemented within the isogeometric framework, which maintains exact geometry without subsequent communication with CAD description. The variation of control points results in shape changes and is continuous over the whole design space. Through numerical examples, the developed isogeometric sensitivity is verified to demonstrate excellent agreements with finite difference sensitivity. Also, the proposed method works very well in various shape optimization problems.