Optimization of thin-walled beam structures: Monolithic versus staggered solution schemes

Abstract

This contribution compares the performance of a monolithic and two staggered numerical update schemes for a coupled shape and topology optimization method for thin-walled beam structures. In order to limit the computational time of the optimization method, the thin-walled beam structures are modeled as 2.5D configurations. In this approach, 1D beam elements are used to simulate the beam response in the longitudinal direction, while the cross-sectional properties of the beam elements are calculated from additional 2D finite element method analyses. The sensitivities with respect to the shape and topology design variables are derived in closed form in order to take advantage of a computationally efficient, gradient-based optimization algorithm. The numerical examples concern basic circular and square thin-walled cantilever beam structures, as well as a more complex, non-prismatic thin-walled beam structure representative of a rotor blade used in a horizontal-axis wind turbine. For each numerical example the computational time and the solution computed by the monolithic and staggered update schemes are compared, which provides clear insight into the numerical efficiency of the solution procedure and the uniqueness of the computational result. Although the three different update schemes for the cases examined result in comparable optimized design concepts, the computational efficiency and the specific minimal compliance value found turn out to be rather sensitive to the algorithmic details of the numerical update scheme applied. Since the monolithic update scheme typically navigates a larger design space than the two staggered update schemes, for most cases examined it provides the lowest structural compliance. In the specific case whereby shape optimization (virtually) has no influence on the final, optimized beam configuration, the structural compliance computed by the monolithic scheme may relate to a local minimum that is less optimal compared to the value calculated by a staggered update scheme.