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Article information
2018 , Volume 23, ¹ 2, p.88-101
Rogalev A.N., Doronin S.V., Moskvichev V.V.
Estimation of the accuracy of numerical analysis for the deformed state of power structures of technical objects
The solution of applied problems of technogenic safety, survivability, risk and protection is performed for structures which are close to limiting states. These states are characterized by decreasing safety factors down to one. In this case a mistaken estimation for safety factor may cause the situation when the calculated safety factor will be greater than one but the real safety factor will be less than one. Safety factors estimation is performed on the basis of calculation for stress-strain state characteristics. Thus, the issues of accuracy and reliability of determining stresses and deformations are an integral part of the problem of man-made safety. In the numerical analysis of the stress-strain state, the stiffness matrix of the design model is formed, the dimension of which reaches up to tens of millions. A large number of computations for tasks of this dimension is presumably leading to significant rounding errors. Ensuring the grid convergence of results by decreasing the grid spacing is inconsistent with the growth of computational errors due to rounding. For finite element analysis of power structures of technical objects, methods of a posteriori reverse error analysis are proposed that control the effect of rounding errors on the result when solving a solving system of linear algebraic equations. The coefficient matrix of this system is the stiffness matrix of the finite element model. The basic idea is to obtain and solve a system of equations with a known exact solution. Comparison of the results of exact and numerical solutions allows us to estimate the magnitude of the error.
[full text]
Keywords: power structures, finite element models, numerical solution accuracy, reverse error analysis
doi: 10.25743/ICT.2018.23.12802
Author(s):
Rogalev Alexey Nikolaevich
PhD. , Associate Professor
Position: Associate Professor
Office: Institute of Computational Modelling SB RAS
Address: 660036, Russia, Krasnoyarsk, Akademgorodok, 50, p.44
E-mail: rogalyov@icm.krasn.ru
SPIN-code: 7519-8826Doronin Sergey Vladimirovich
PhD. , Associate Professor
Position: Leading research officer
Office: Federal Research Center for Information and Computational Technologies, Krasnoyarsk branch
Address: 660049, Russia, Krasnoyarsk, PO box 25515
Phone Office: (391) 2277296
E-mail: sdoronin@ict.nsc.ru
SPIN-code: 9816-9080Moskvichev Vladimir Viktorovich
Dr. , Professor
Position: Director
Office: Federal Research Center for Information and Computational Technologies,Siberian Federal University
Address: 660049, Russia, Krasnoyarsk, Mira pr., 53
Phone Office: (391) 227-29-12
E-mail: krasn@ict.nsc.ru
SPIN-code: 9332-6468 References:
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Bibliography link:
Rogalev A.N., Doronin S.V., Moskvichev V.V. Estimation of the accuracy of numerical analysis for the deformed state of power structures of technical objects // Computational technologies. 2018. V. 23. ¹ 2. P. 88-101
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