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Keyanpour, Mohammad; Nehrani, Ali M.

Optimal thickness of a cylindrical shell subject to stochastic forces. (English) Zbl 1332.74043

J. Optim. Theory Appl. 167, No. 3, 1032-1050 (2015).
Summary: 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.

Cited in 3 Documents

MSC:

74P10 Optimization of other properties in solid mechanics
74K25 Shells
65K10 Numerical optimization and variational techniques
65K15 Numerical methods for variational inequalities and related problems
49M05 Numerical methods based on necessary conditions
49K45 Optimality conditions for problems involving randomness
49K20 Optimality conditions for problems involving partial differential equations

Keywords:

optimal sizing; stochastic partial differential equation; variational formulation; self-adjoint property; stochastic quantification
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References:

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