Geodesic
Formulation of a method of reliability assessment for constructions on the basis of a combination of statistical modeling and numerical methods of stress evaluation
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 70 (2021), pp. 51-63 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, methods for estimating the reliability of constructions are considered. The formulation of a method for estimating the reliability of the design based on a combination of statistical modeling and numerical methods for evaluating stresses is given. The method is based on a “load - bearing capacity” model, which takes into account both stochasticity of mechanical properties of construction materials, randomness of geometric characteristics, and loads of a probabilistic nature. This new method is a system of n nested cycles. The number of governing parameters n depends on the design. The load variation series is calculated in the body of the internal cycle. The load is calculated numerically in terms of stresses using the finite element method. Any commercial solver such as Nastran, Ansys, or Abaqus can be used for this purpose. The probability of failure-free operation (reliability) is calculated involving the variational series of loads and load-carrying ability. For this purpose, the formalized estimation method based on empirical distributions is used. Fundamentals of the latter are available in the monograph “Reliability in Engineering Design” written by Kapur K.C. and Lamberson L.R.. A primary function of the proposed method is to evaluate the probability of failure-free operation of constructions under stationary or quasi-stationary random loads.
Keywords: reliability, load, bearing strength, statistical modeling. 
@article{VTGU_2021_70_a4,
     author = {S. A. Pimenov},
     title = {Formulation of a method of reliability assessment for constructions on the basis of a combination of statistical modeling and numerical methods of stress evaluation},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {51--63},
     year = {2021},
     number = {70},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2021_70_a4/}
}
TY  - JOUR
AU  - S. A. Pimenov
TI  - Formulation of a method of reliability assessment for constructions on the basis of a combination of statistical modeling and numerical methods of stress evaluation
JO  - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
PY  - 2021
SP  - 51
EP  - 63
IS  - 70
UR  - http://geodesic.mathdoc.fr/item/VTGU_2021_70_a4/
LA  - ru
ID  - VTGU_2021_70_a4
ER  - 
%0 Journal Article
%A S. A. Pimenov
%T Formulation of a method of reliability assessment for constructions on the basis of a combination of statistical modeling and numerical methods of stress evaluation
%J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
%D 2021
%P 51-63
%N 70
%U http://geodesic.mathdoc.fr/item/VTGU_2021_70_a4/
%G ru
%F VTGU_2021_70_a4
S. A. Pimenov. Formulation of a method of reliability assessment for constructions on the basis of a combination of statistical modeling and numerical methods of stress evaluation. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 70 (2021), pp. 51-63. http://geodesic.mathdoc.fr/item/VTGU_2021_70_a4/

[1] Volkov V. M., Nadezhnost mashin i tonkostennykh konstruktsii, ucheb. posobie, Izd-vo NGTU, N. Novgorod, 2011, 365 pp.

[2] Kapur K., Lamberson L., Nadezhnost i proektirovanie sistem, Mir, M., 1980, 604 pp.

[3] Pimenov S. A., “Primenenie chislennykh metodov dlya otsenki nadezhnosti konstruktsii”, Novye promyshlennye tekhnologii, 2010, no. 3, 55–57

[4] Pimenov S. A., Palkin I. Yu., “Primenenie rekursivnykh algoritmov pri otsenke nadezhnosti konstruktsii”, Naukoemkie tekhnologii, 2011, no. 4, 39–43

[5] Ostreikovskii V. A., Teoriya nadezhnosti, Vysshaya shkola, M., 2003, 464 pp.

[6] Probabilistic Design Methodology for Composite Aircraft Structures, National Technical Information Service (NTIS), Springfield, Virginia 22161, 1999 http://www.tc.faa.gov/its/worldpac/techrpt/ar99-2.pdf

[7] Zenkevich O. K., Metod konechnykh elementov v tekhnike, Mir, M., 1975, 541 pp.

[8] NX Nastran Numerical Methods User's Guide, UGS, 2005 http://docs.plm.automation.siemens.com/data_services/resources/nxnastran/10/help/en_US/custom/numerical/numerical.pdf

[9] ANSYS Mechanical APDL Basic Analysis Guide, Release 15.0, ANSYS. Inc, November 2013 https://docplayer.net/45466427-Ansys-mechanical-apdl-basic-analysis-guide.html

[10] Abaqus Analysis User's Manual, Release 6.1. Dessault Systems, 2010 https://www.academia.edu/24831145/Abaqus_Analysis_Users_Manual