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**Robust design of structures using optimization methods.**
*(English)*
Zbl 1067.74554

Summary: The robust design of structures with stochastic parameters is studied using optimization techniques. The first two statistical moments of the stochastic parameters including design variables are considered in conjunction with the second-order perturbation method for the approximation of mean value and variance of the structural response. In this framework, the sensitivities of the mean values and variances of the structural performance function with respect to the design variables are calculated for use in the optimization task. The robust design of structures is formulated as a multi-criteria optimization problem, in which both the expected value and the standard deviation of the objective function are to be minimized. The robustness of the feasibility is also taken into account by involving the variability of the structural response in the constraints. The two-criteria optimization problem is converted into a scalar one and is then solved by a gradient based optimization algorithm. To demonstrate the applicability of the presented method, numerical examples are given, involving static and dynamic response.

### MSC:

74P10 | Optimization of other properties in solid mechanics |

74P05 | Compliance or weight optimization in solid mechanics |

74S05 | Finite element methods applied to problems in solid mechanics |

### Keywords:

Robust design; Structural optimization; Stochastic finite element method; Sensitivity analysis### Software:

CFSQP
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\textit{I. Doltsinis} and \textit{Z. Kang}, Comput. Methods Appl. Mech. Eng. 193, No. 23--26, 2221--2237 (2004; Zbl 1067.74554)

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### References:

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