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Stochastic Structural Optimization with Quadratic Loss Functions

In: Stochastic Optimization Methods

Author

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  • Kurt Marti

    (Federal Armed Forces University Munich)

Abstract

Problems from plastic analysis and optimal plastic design are based on the convex, linear or linearized yield/strength condition and the linear equilibrium equation for the stress (state) vector. In practice one has to take into account stochastic variations of several model parameters. Hence, in order to get robust optimal decisions, the structural optimization problem with random parameters must be replaced by an appropriate deterministic substitute problem. A direct approach is proposed based on the primary costs (weight, volume, costs of construction, costs for missing carrying capacity, etc.) and the recourse costs (e.g. costs for repair, compensation for weakness within the structure, damage, failure, etc.). Based on the mechanical survival conditions of plasticity theory, a quadratic error/loss criterion is developed. The minimum recourse costs can be determined then by solving an optimization problem having a quadratic objective function and linear constraints.

Suggested Citation

  • Kurt Marti, 2015. "Stochastic Structural Optimization with Quadratic Loss Functions," Springer Books, in: Stochastic Optimization Methods, edition 3, chapter 0, pages 289-322, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-46214-0_7
    DOI: 10.1007/978-3-662-46214-0_7
    as

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