Shape optimal design—A CAD-oriented formulation

In this paper a convenient geometrical representation for shape optimal design is first briefly recalled, as well as the corresponding sensitivity analysis formulation (stress and displacement derivatives). Two-dimensional structures are decomposed into a few design elements described by Bezier or B-splines blending functions. Next, the choice of the optimization algorithm is discussed. It is shown that well-known and efficient methods of structural sizing can be advantageously extended to shape optimal design problems. Experiments are performed with different approximation schemes and a new general optimization algorithm is introduced, which combines mixed approximations and dual methods. Three examples are also treated to demonstrate the generality and the efficiency of the new formulation.