Abstract
Necessary conditions of optimality for maximizing the buckling load for single or multimodal structures are derived using generalized gradients. The possible design dependence of the pre-buckling displacement is taken into account and implies the appearance of a number of adjoint problems not normally present in, for example, standard vibration problems. The relation to other equivalent forms of the necessary conditions are pointed out and the formulae are demonstrated on simple example problems.
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Rodrigues, H.C., Guedes, J.M. & Bendsøe, M.P. Necessary conditions for optimal design of structures with a nonsmooth eigenvalue based criterion. Structural Optimization 9, 52–56 (1995). https://doi.org/10.1007/BF01742645
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DOI: https://doi.org/10.1007/BF01742645