Modular three-dimensional steel frames, like steel pallet racks or shelving assemblies and scaffoldings are prefabricated structures with slender elements, mostly under compressive forces. The structural analysis includes different non-linearities, e.g. the geometric non-linearities, global and local stability effects, in particular the local buckling of thin-walled elements and the slippage and non-linear behaviour of joints. The optimization of these modular systems requires the most advanced solution techniques but also a systematic preprocessing, sophisticated nonlinear structural analysis and an automated handling of stress- and displacement-constraints and other side-constraints resulting from the underlying code of practice.

Analysis and optimization are based on a fixed set of cross-sections with different wall-thicknesses which are stored in an extendable database. The data related to each cross-section are the elementary sectional properties and the critical stresses for local buckling for different lengths of the elements. For an actual analysis or optimization the critical stress is computed from these data by interpolation.

The objective of the optimization is the minimal cost, which can be approximated by the weighted sum of the volume of the individual elements. The optimization problem involves continuous and discrete variables; it is solved by decomposition into two subproblems. The first one is related to the discrete variables and solved by evolutionary strategies. The second one, the continuous subproblem is solved by using mathematical programming. The decomposition is well suited for parallelization on multi-processor computers.

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