Abstract
The objective of the article involves presenting two approaches to the structure reliability analysis. The primary research method was the First Order Reliability Method (FORM). The Hasofer–Lind reliability index β in conjunction with transformation method in the FORM was adopted as the measure of reliability. The first proposal was combining NUMPRESS software with the non-commercial KRATA program. In this case, the implicit form of the random variables function was created. Limit state function was symbolically given in the standard math notation as a function of the basic random and external variables. The second analysis proposed a hybrid approach enabling the introduction of explicit forms of limit state functions to the reliability program. To create the descriptions of this formula, the neural networks were used and our own original FEM module. The combination of conventional and neural computing can be seen as a hybrid system. The explicit functions were implemented into NUMPRESS software. The values of the reliability index for different descriptions of the mathematical model of the structure were determined. The proposed hybrid approach allowed us to obtain similar results to the results from the reference method.
Highlights
The real engineering objects are not without uncertainty in determining material properties, geometric parameters, boundary conditions, applied loads, etc
The analysis shows how the introduction of random variables affects the value of the Hasofer–Lind reliability index (Figure 7)
For the value of load multiplier μ = 5.73 and description of the mathematical model by variables P and EA, the reliability index assumes the value of β = 1.135, while the introduction of another variable Z reduces the value of the indicator by 74% (β = 0.29)
Summary
The real engineering objects are not without uncertainty in determining material properties, geometric parameters, boundary conditions, applied loads, etc. The randomness of structural parameters is ensured by applying safety factors at the design stage. The most appropriate, is to treat the structure design process as a random event and analyze it with the methods of probability calculus. The most advanced reliability analysis methods are probabilistic methods. These methods are based on the assumption that input variables are of random character. A new very interesting trend has emerged that deals with non-probabilistic or hybrid uncertainties in reliability analysis [1]. The structural reliability theory is already a well-developed research area. The most important literature in this area includes books and monographs presenting the basics of probabilistic theory [2,3,4]
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