Abstract
Natural Structural Shapes are derived for axisymmetrically loaded shells of revolution within the membrane theory of shells. The concept of natural structural shapes is based on the simultaneous minimization of the mass and the strain energy of the loaded structure, a multicriteria optimization problem with Edgeworth-Pareto optimality as the basic optimality concept. The problem is formulated as a multicriteria control problem and necessary conditions for arbitrary loading and boundary are derived. Exact and numerical results are obtained for both the case of uniform pressure and that of a ring load with zero surface loads.
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Stadler, W., Krishnan, V. Natural structural shapes for shells of revolution in the membrane theory of shells. Structural Optimization 1, 19–27 (1989). https://doi.org/10.1007/BF01743806
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DOI: https://doi.org/10.1007/BF01743806