Topology optimization considering multiple loading

Abstract

There is an additional new fact that topology optimization has started its career more than hundred years ago by Maxwell and only a few years later by Michell. The classical solutions of the different type of plate or shell problems can be followed by the works of Mroz, Prager and Shield. This paper overviews these almost forgotten results. In addition to the conspectus of this hidden period, the optimal design of curved folded plates is presented. The finite strip method is used for the analysis. At first, a single load case is considered, but later multiple load cases are used for the design. The base formulation is a minimum volume design with displacement constraint, which is represented by the strain energy. For the multiple loading cases two topology optimization algorithms are elaborated: minimization of the maximum strain energy with respect to a given volume and the minimization of the weighted sum of the compliance of the connected load cases with respect to a given volume. The numerical procedures are based on iterative formulae, which are formed by the use of the first order optimality condition of the Lagrangian-functions. The application is illustrated by numerical examples.