Methods for estimating the coefficient of variation of the resistance in the design of structures based on nonlinear finite element models

The reliability (safety) of the designed structures is ensured by using the design value of the bearing capacity, taking into account the uncertainty (variability, error) of the bearing capacity. Uncertainty is taken into account by means of a probabilistic model, which is represented as a distribution law with statistical parameters included in it. The most important and frequently used statistical parameters are the mean value and coefficient of variation.

Determining the coefficient of variation for the bearing capacity calculated on the basis of numerical models (computer modeling) is an important task, since existing classical methods cannot be applied. For this reason, the purpose of this article is to develop and study the accuracy of methods for determining the coefficient of variation of the bearing capacity calculated by computer modeling. The proposed method for determining the coefficient of variation is based on the decomposition of the function into a Taylor series, followed by the use of various numerical differentiation schemes. Verification was performed on generalized nonlinear models of load-bearing capacity, for which an exact solution can be obtained using the Monte Carlo method. The practical implementation of the proposed method is demonstrated on finite element models.As the results of the performed research, it is possible to identify the actual methods for determining the coefficient of variation of the bearing capacity calculated by computer modeling, and the values of the coefficients of variation for generalized models of the bearing capacity of thin-walled elements, taking into account the loss of local stability of the web and with the subsequent inclusion of the girder flanges in the work. The value of the coefficient of variation can be most accurately estimated using Taylor series expansion and numerical integration over 3 points, however, this method requires 2N+1 calculations, therefore it can be recommended only for individual verification tasks. As a practical method for estimating the coefficient of variation, Taylor series expansion and numerical integration by 2 points should be used (N+1 calculations are required).

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