Evaluation of the reliability of structures under creep for stochastic generalized models.

*(Russian. English summary)*Zbl 1326.74133Summary: The nonlinear stochastic model of uniaxial creep and creep rupture strength with three stages of deformation is suggested. The method for the identification of stochastic parameters of model by series of experimental creep curves is developed. The stochastic linearization of model for analytical evaluation of the probability of no-failure for stretchable rod by deformation criterion is obtained. The checking of accordance of the method with the experimental data for the creep of samples made of 12Kh18N10T steel under temperature 850\(^\circ\)C is implemented. The generalization of the approach developed to describe the deformation of structural elements of constructions in terms “generalized load, generalized displacement, time” is obtained. The feature is considered as a unit (specific sample with complex structure). A complete analogy between the curves of uniaxial creep model and generalized creep curves in coordinates “generalized displacement – time” is established for fixed values of the generalized displacement for a feature. Based on the analogy, the generalized stochastic model of rheological deformation of structural elements is proposed. The method for evaluating the reliability of structural elements under creep on parametric failure criteria, implemented in the model example of creep of thick-walled tubes under internal pressure, is developed. The results of the calculations and recommendations for operation life defining are given.

##### MSC:

74S60 | Stochastic and other probabilistic methods applied to problems in solid mechanics |

74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |

60H30 | Applications of stochastic analysis (to PDEs, etc.) |