Shape optimization of Dirichlet boundaries based on weighted B-spline finite cell method and level-set function

This paper addresses extended shape optimization problems where structural supports, i.e., Dirichlet boundaries and free boundaries are simultaneously optimized. Unlike traditional FEM, the weighted B-spline finite cell method (FCM) is applied as structural analysis tool and combined with the level-set function (LSF) to take into account Dirichlet boundary condition (DBC) automatically through penalization of the displacement field.The proposed shape optimization method achieves a comprehensive integration of fixed grid, B-spline shape function and level-set function. As both the structure and Dirichlet boundaries are described in the form of LSF, any modification of Dirichlet boundaries can be made in a straightforward way as easily as free boundaries by changing continuous design variables. Meanwhile, the computing accuracy is ensured within the framework of fixed grid owing to the quadtree refinements of boundary cells. Stress related shape optimization problems are finally solved to demonstrate the merit and validity of the proposed optimization method in dealing with shape optimization of Dirichlet boundaries.