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.

The study deals with stability and dynamic problems in bar structures using a probabilistic approach. Structural design parameters are defined as deterministic values and also as random variables, which are not correlated. The criterion of structural failure is expressed by the condition of non-exceeding the admissible load multiplier and condition of non-exceeding the admissible vertical displacement. The Hasofer-Lind index was used as a reliability measure. The primary research tool is the FORM method. In order to verify the correctness of the calculations Monte Carlo and Importance Sampling methods were used. The sensitivity of the reliability index to the random variables was defined. The limit state function is not an explicit function of random variables. This dependence was determined using a numerical procedure, e.g. the finite element methods. The paper aims to present the communication between the STAND reliability analysis program and the KRATA and MES3D external FE programs.

The indentation test is a popular method for the investigation of the mechanical properties of materials. The technique, which combines traditional indentation tests with mapping the shape of the imprint, provides more data describing the material parameters. In this paper, such methodology is employed for estimating the selected material parameters described by Ramberg–Osgood’s law, i.e., Young’s modulus, the yield point, and the material hardening exponent. Two combined identification methods were used: the P-A procedure, in which the material parameters are identified on the basis of the coordinates of the indentation curves, and the P-C procedure, which uses the coordinates describing the imprint profile. The inverse problem was solved by neural networks. The results of numerical indentation tests—pairs of coordinates describing the indentation curves and imprint profiles—were used as input data for the networks. In order to reduce the size of the input vector, a simple and effective method of approximating the branches of the curves was proposed. In the Results Section, we show the performance of the approximation as a data reduction mechanism on a synthetic dataset. The sparse model generated by the presented approach is also shown to efficiently reconstruct the data while minimizing error in the prediction of the mentioned material parameters. Our approach appeared to consistently provide better performance on the testing datasets with considerably easier computation than the principal component analysis compression results available in the literature.

In the subject of the present study a probabilistic approach to the analysis of steelaluminium lattice tower was used. Structural design parameters are defined as the deterministic values and random variables. Random variables are not correlated. The criterion for structural failure is expressed the limits of functions referring to the serviceability limit state. The description of the limit state of structure implicit forms of the random variables function was used. The study presents a combination of the reliability analysis program with the MES3D external FEM program. The NUMPRESS software, created at the IFTR PAS, was used in the reliability analysis. The Hasofer-Lind reliability index, determined using an iterative procedure of Rackwitz-Fiessler, was used as a reliability measure. The values of reliability index for different cases of the vector of random variables, that is, different descriptions of mathematical model of the structure, were determined. The effect of assumed probability distribution of individual random variables on the value of the reliability index was determined. In the description of random variables, the different types of probability distribution were used and the values of the reliability index for the normal distribution and the distribution chosen according to the kind of a variable were compared. The primary research method is the FORM method. In order to verify the correctness of the calculation Monte Carlo and Importance Sampling methods are used. The relative error of the reliability index was calculated taking the simulation Monte Carlo method as a reference. The effectiveness of the primary research method was performed by comparing the number of calls of the limit state, which is connected with the calculation time. The sensitivity of reliability index to the random variables was defined.

The study presents a probabilistic approach to the problems of static analysis of structural elements. A steel and reinforced concrete elements were analysed. Structural design parameters were defined as deterministic values and random variables. The latter were not correlated. The criterion of structural failure is expressed by limit functions related to the ultimate limit state. In the performed analyses explicit form of the random variables function were used. The Hasofer-Lind index was used as a reliability measure. In the description of random variables were used the different types of probability distribution appropriate to the nature of the variable. Sensitivity of reliability index to the random variables was defined. If the reliability index sensitivity due to the random variable X_i is low when compared with other variables, it can be stated that the impact of this variable on failure probability is small. Therefore, in successive computations it can be treated as a deterministic parameter. Sensitivity analysis leads to simplify the description of the mathematical model, determine the new limit functions and values of the Hasofer-Lind reliability index. Besides the effect of the assumed level of the variation coefficient of selected random variables on value of the reliability index was determined. The primary research method is the FORM method. In order to verify the correctness of the calculation SORM, Monte Carlo and Importance Sampling methods were used. In the examples of reliability analysis the NUMPRESS program was used. In the considered issues the time was not taken into account explicitly.