Abstract
In this paper, sizing of the thickness of a cylindrical shell subject to a stochastic force is considered. The variational principle of stochastic partial differential equations (PDEs) is applied to derive the necessary optimality conditions. The goal is to determine the optimal thickness of a cylindrical shell such that subject to a stochastic force it does not deform, although, because of the elasticity of a cylindrical shell, occasionally small deformations that do not destroy the structure are allowable. The sizing problem under a stochastic force is considered via a one-dimensional stochastic PDE-constrained optimization problem. Test examples are solved using a self-adjoint gradient algorithm.
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Acknowledgments
Special thanks to the reviewer of this paper for his (her) useful comments. We are grateful to Peter Nestler for providing us with his thesis, which helped us improve our work. We are also grateful to Tomas for his helpful comments on the paper.
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Keyanpour, M., Nehrani, A.M. Optimal Thickness of a Cylindrical Shell Subject to Stochastic Forces. J Optim Theory Appl 167, 1032–1050 (2015). https://doi.org/10.1007/s10957-014-0663-y
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DOI: https://doi.org/10.1007/s10957-014-0663-y
Keywords
- Optimal sizing
- Stochastic partial differential equation
- Variational formulation
- Self-adjoint property
- Stochastic quantification