Optimal buckling loads of structures subjected to uncertain loading combinations are obtained. As opposed to the traditional buckling optimization, the applicable loads are not fixed during the optimization search but are assumed to belong to a set of admissible loads. Convex modelling of uncertainty is used to handle the lack of specification in the loads and a reformulation of the optimization problem, the minimax formulation, is considered in order to accommodate the uncertainties of the loads. The optimal designs emerging from the optimization procedures are insensitive and stable to perturbations in the loads within the admissible set; the resulting optimal design is the one obtained under the most unfavourable loading situation.; In order to illustrate the proposed procedure, composite plates and cylindrical shells are optimized for buckling assuming that the loads contain specified and unspecified components. The designs obtained satisfactorily withstand not only one particular loading configuration but a class of loads. The uncertainties considered concern mechanical loads in all cases, and both mechanical and thermal loads in the case of heterogeneous plates.
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