Isogeometric Shape Optimization for Design Dependent Loads

This paper presents an isogeometric shape optimization approach for a special class of problems in structural optimization known as design dependent load problems. Isogeometric method has been widely used for structural analysis and shape optimization for its advantages in modeling smooth surfaces, high accuracy, local control, and interfacing with CAD tools. Isogeometric method may be of special advantage for shape optimization problems with design dependent loads as the loads in such class of problems depend on the geometry of the designed surface. The method outlined in this paper is applicable to design dependent load problems where there is a pressure load acting on the boundary of the structure, the direction of the pressure being normal to the profile of the designed structure. In this work minimum compliance optimization subject to volume constraint is considered and isogeometric formulations based on NURBS are presented for such class of problems. The control points of the boundaries of the NURBS geometries are taken as the design variables in the optimization problems. Analytical sensitivity formulations are derived for design dependent load problems and compared with numerically derived sensitivities. A few representative 2D and 3D examples are solved and compared with existing literature to demonstrate the application of the proposed method.