Keywords: topology optimization, multiple load case, plated structures, optimal layout, optimality criteria method, optimal design, robust design.

Research into topology optimization started more than hundred years ago by Maxwell and continued a few years later by Michell. The design was elaborated in elastic or plastic ways and the optimized structures were trusses at this early period although this object was called a frame structure. The classical solutions of the different type of plate or shell problems can be followed by the works of Mroz, Prager, Shield. This presentation will overview these almost forgotten results, more specially the analytical solutions and the non-uniqueness of the optimal solutions. Plated structures are one of the most frequently used engineering structures. The object of this research paper is the optimal design of curved folded plates. There are various solution methods to analyze this type of structure, here the finite strip method is applied. 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 that is represented by the strain energy. For 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 formula, which are formed by the use of the first order optimality condition of the Lagrangian-functions. The application is illustrated by numerical examples.

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