A model problem for a weight optimization
A weight-optimization method for the uniaxial bar under compressive force and self-weight is proposed. The first (initial) step is the shape-finding analysis under the assumption of a uniform stress distribution along the height of the bar. The second step is the weight optimization, i.e. the determination of minimum cross section for the given initial shape, load and material. The weight of the bar is taken as the objective function, the maximum stress in the bar is the state variable, and a Least-Squares algorithm (LSQNONLIN) is the optimization algorithm. We found that a significant mass reduction is achieved with the proposed optimizer and that this method is applicable in the shape optimization when an initial surface is given. We anticipate our method to be a starting point for the optimization of more complex geometries.