Free form shape optimization of three dimensional beams using cross section analysis

We introduce an efficient method for shape optimization of three dimensional beams that is based on free-form design of the beam's cross section. The cross section boundary of each beam segment is parameterized by a closed, unclamped B-spline curve, whose control points’ coordinates serve as design variables. The response of the beam is evaluated globally as a one-dimensional entity using 3D beam finite elements, while each cross section is modeled locally using cross section analysis following anisotropic beam theory. A fully consistent analytical sensitivity analysis is derived to account for the relation between the control points and the beam cross-sectional properties and design updates are performed using gradient-based optimization. The proposed method is applied to several test cases, aiming at minimization of compliance or maximization of the fundamental frequency. The numerical results and a comparison to other methods for beam optimization show that the method can generate highly competitive designs. A consistent quantitative comparison to high resolution continuum topology optimization shows that a performance which is only slightly inferior can be achieved, for only a small fraction of the computational effort.