Abstract: The paper presents an example of reliability analysis of shell structures susceptible to stability loss from the condition of node snapping. In the reliability analysis of the structure, uncertain parameters of the task are represented by uncorrelated random variables. The approach used in the paper is an extension of the idea, which assumes the use of Neural Networks (NNs) in Monte Carlo (MC) simulations to analyze the reliability of the structure. For this purpose, it was necessary to build a simple hybrid system formed with the two independent sequentially working Finite Element Method (FEM) and Neural Networks applications.
B I B L I O G R A F I A1.
Carpentier A., Munos R., 2012, Adaptive stratified sampling for Monte-Carlo integration of differentiable functions, Proceedings of the 25th International Conference on Neural Information Processing Systems, 1.
2.
Deng J., Gu D., Li X., Yue Z.Q., 2005, Structural reliability analysis for implicit performance functions using neural networks. Structural Safety, 27, 25–48, DOI: 10.1016/j.strusafe.2004.03.004.
CrossRef
3.
Ditlevsen O., Madsen H., 1996, Structural Reliability Methods, Wiley & Sons.
4.
Dudzik A., 2016, The effectiveness of the FORM method compared to other probabilistic methods in the analysis of bar structures, PHD Disertation (in Polish), Politechnika Świętokrzyska, Kielce.
5.
Dudzik A., 2017, Reliability assessment of steel-aluminium lattice tower, IOP Conference Series: Materials Science and Engineering, 245, 1-9, DOI: 10.1088/1757-899X/245/3/032072.
CrossRef
6.
Dudzik A., Potrzeszcz-Sut B., 2019, The structural reliability analysis using explicit neural state functions, MATEC Web of Conferences, 262, 1, DOI: 10.1051/matecconf/201926210002.
CrossRef
7.
Gwóźdź M., Machowski A., 2011, Selected Tests and Calculations of Building Constructions by Probabilistic Methods (in Polish),Wydawnictwo Politechniki Krakowskiej im. Tadeusza Kościuszki, Krakow.
8.
Hagan M., Menhaj M., 1994, Training feedforward networks with the Marquardt algorithm, IEEE Transactions on Neural Networks, 5, 6, 989-993, DOI: 10.1109/72.329697.
CrossRef
9.
Haykin S., 1999, Neural Networks – A Comprehensive Foundation, Prentice Hall, New York 10. JCSS, 1981, Joint committee on structural safety, general principles on reliability for structural design, IABSE.
10.
JCSS, 1981, Joint committee on structural safety, general principles on reliability for structural design, IABSE.
11.
Jelic A., Baitsch M., Hartmann D., Spitzlei K., Ballnus D., 2004, Distributed computing of failure probabilities for structures in civil engineering, X International Conference on Computing in Civil and Building Engineering, Weimar.
12.
Kaliszuk J., 2011, Hybrid Monte Carlo method in the reliability analysis of structures, Computer Assisted Mechanics and Engineering Sciences, 18, 205-216.
13.
Kaliszuk J., Waszczyszyn Z., 2006, Reliability analysis of a steel girder by the hybrid Monte Carlo method. Progress in steel, composite and aluminium structures, Proceedings of the XIth International Conference on Metal Structures, Rzeszow, 843-847.
14.
Knauff M., 2015, Calculation of Reinforced Concrete Structures According to Eurocode 2 (in Polish), PWN, Warszawa.
15.
Kunstmann H., Kinzelbach W., Siegfried T., 2002, Conditional first-order second-moment method and its application to the quantification of uncertainty in groundwater modeling, Water Resources Reaserch, 38, 4-1035, 6.1-6.14.
CrossRef
16.
Masters T., 1993, Practical Neural Network Recipies in C++, Morgan Kaufmann.
17.
Metropolis N., Ulam S., 1949, The Monte Carlo Method, Journal of the American Statistical Association, 44, 247, 335-341, DOI: 10.1029/2000WR000022.
CrossRef
18.
Olofsson P., Andersson M., 2012, Probability, Statistics, and Stochastic Processes, 2nd ed., Wiley-Interscience, DOI: 10.1002/9781118231296.ch3.
CrossRef
19.
Pabisek E., 2008, Hybrid Systems Integrating FEM and SSN in the Analysis of Selected Problems of Structural Mechanics and Materials (in Polish), Politechnika Krakowska, Krakow.
20.
Pabisek E., Kaliszuk J., Waszczyszyn Z., 2004, Neural and finite element analysis of a plane steel frame reliability by the Classical Monte Carlo method, Artificial Intelligence and Soft Computing – ICAISC 2004, 7th International Conference, Zakopane, 1081-1086.
CrossRef
21.
Papadopoulos V., Giovanis D., Lagaros N., Papadrakakis M., 2012, Accelerated subset simulation with neural networks for reliability analysis, Computer Methods in Applied Mechanics and Engineering, 223-224, 70-80, DOI: 10.1016/j.cma.2012.02.013.
CrossRef
22.
Papadrakakis M., Papadopoulos V., Lagaros N., 1996, Structural reliability analysis of elastic-plastic structures using neural networks and Monte Carlo simulation, Computer Methods in Applied Mechanics and Engineering, 136, 145-163, DOI: 10.1016/0045-7825(96)01011-0.
CrossRef
23.
PN-EN 1990:2004, Basics of structural design (in Polish), PKN, Warszawa.
24.
PN-EN 1993-1-1:2006, Steel structure design – Part 1-1: General rules and rules for buildings (in Polish), PKN, Warszawa.
25.
PN-EN 1993-1-4:2007, Designing of steel structures – Part 1-4: General rules – Supplementary rules for stainless steel structure (in Polish), PKN, Warszawa.
26.
Radoń U., 2012, Application of the FORM Method in the Analysis of Reliability of Truss Structures Susceptible Node Snapping (in Polish), Wydawnictwo Politechniki Świętokrzyskiej, Kielce.
27.
Ramberg W., Osgood W., 1943, Description of stress-strain curves by three parameters, Technical Note No. 902, National Committee for Aeronautics, Washington DC.
28.
Rubinstein R., Kroese D., 2008, Simulation and the Monte Carlo Method, Wiley-Interscience, DOI: 10.1002/9781118631980.
CrossRef
29.
Tsompanakis Y., Lagaros N., Stavroulaki G.E., 2005, Efficient neural network models for structural reliability analysis and identification problems, The Eighth International Conference on the Application of Artificial Intelligence to Civil, Structural and Environmental Engineering, DOI: 10.4203/ccp.82.41.
CrossRef
30.
Waszczyszyn Z., Cichoń C., Radwańska M., 1994, Stability of Structures by Finite Element Methods, Elsevier, Amsterdam. 
Pełny tekst 
DOI