A parametric mapping method for curve shape optimization on 3D panel structures

Three-dimensional (3D) thin-walled panels belong to a kind of lightweight structures that are widely used in aeronautic and aerospace engineering. This paper deals with the shape optimization of curved contours that exist often on this kind of structures. Compared with conventional 2D and 3D shape optimization problems, the particularity and difficulty existing here are how to define design variables properly so that the curve keeps moving on the specific surface of the curved panel during the design process. A new parametric mapping method (PMM) is therefore proposed in this paper. The originality is to manage shape design variables in the 2D intrinsic coordinate system. It is shown that the geometric limitation is satisfied automatically. Moreover, relevant formulations are developed theoretically for design sensitivity analysis. By means of the parametric mapping from 2D intrinsic coordinate system to Cartesian coordinate system, the mesh velocity field related to the finite element model can be easily computed for any unstructured mesh. Finally, a variety of representative examples are presented to illustrate the method.