Abstract
The problem of minimizing the maximal stress over an arch structure is studied within linear elastic thin shell theory, the design variable being the shape of the arch. As the maximal stress cost is nondifferentiable, a nonsmooth analysis approach is developed.
The pointwise stress minimization problem is studied. Then, a proof of the subdifferentiability of the maximal stress cost is given, the rapid computation of a subgradient being done by means of an adjoint state method in a very weak sense.
Numerical results are presented. They show that the optimal shape obtained for the L 2-norm of displacements is slightly different from the one obtained for the maximal stress cost.
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Habbal, A. Direct Approach to the Minimization of the Maximal Stress over an Arch Structure. Journal of Optimization Theory and Applications 97, 551–578 (1998). https://doi.org/10.1023/A:1022685908429
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DOI: https://doi.org/10.1023/A:1022685908429