Accurate and efficient boundary method for isogeometric shape design sensitivity analysis considering tangential divergence of non-smooth boundary

Abstract

Even though the conventional finite element analysis (FEA)-based boundary method for shape design sensitivity analysis (DSA) has the advantage of low computation costs, the accuracy of computed sensitivity is not satisfactory due to the inaccurate consideration of boundary geometry. To overcome this difficulty, employing an efficient adjoint method, we propose an isogeometric analysis (IGA)-based boundary method for shape DSA that can exactly handle the normal and curvature on a non-smooth boundary. The required computational costs for the boundary method is much less than that of the domain method since the computation is performed only on the boundary. Furthermore, the shape sensitivity of performance measure defined by a boundary functional on the non-smooth boundary can be precisely obtained using the curvature of boundary, the normal component of design velocity, and the tangential divergence of design velocity. Through numerical examples, the accuracy and efficiency of the IGA-based boundary method for DSA are compared with other methods such as FEA-based boundary and domain methods. It is demonstrated that the IGA-based shape design sensitivity of the boundary functional could accurately represent the tangential divergence on the boundary that the linear shape function in the FEA-based one cannot properly represent.