Isogeometric shape optimization of design-dependent structures

Using an isogeometric approach, a continuum-based shape optimization method is developed for elasticity problems. To obtain efficient and precise adjoint shape sensitivity, precise normal and curvature information should be taken into account in shape sensitivity expressions, especially for designdependent problems. In this approach, the basis functions generated from NURBS are directly used to construct a geometrically exact model in response and shape sensitivity analyses. Refinements and design changes are easily implemented within the isogeometric framework. The isogeometric design sensitivity analysis provides more accurate sensitivity of complex geometries including higher order terms. Also, it vastly simplifies the design modification without communicating with the CAD geometry during optimization process. We demonstrate some numerical examples, where the accuracy and efficiency of the isogeometric sensitivity are verified by the comparison with finite difference one. Also, numerical examples for design-dependent design problems are demonstrated to verify the applicability and effectiveness of the proposed method.