Optimization of plate supports using a feature mapping approach with techniques to avoid local minima

In this paper, we present a methodology for optimizing the locations of supports in arbitrary plate structures. We adopt a feature mapping approach where the stiffness of the supports is projected onto the finite element mesh using smooth super-Gaussian radial functions. This effectively separates the design space from the analysis model and a compact optimization problem with a continuous design space is obtained. We develop three techniques that improve the obtained minima significantly, namely: continuation of the stiffness projection; control over the initial design; and numerical damping. These techniques make the optimization insensitive to the initial design and much more resilient to convergence to local minima. Furthermore, the proposed method is not sensitive to the finite element mesh density, so coarse meshes may be used to reduce the computational cost. Results show that the optimal locations of supports are not trivial, especially in complex plate geometries, and that asymmetric distributions of supports may be optimal even if the plate is symmetric.