517:519.6 On the construction of adequate and economical mathematical models in the tasks of continuous monitoring of especially dangerous and technically complex objects

Trutaev S. Y. (АО "Иркутский научно-исследовательский и конструкторский институт химического и нефтяного машиностроения")

STRESS–STRAIN STATE, FINITE ELEMENT METHOD, HAZARDOUS PRODUCTION FACILITY, ESPECIALLY DANGEROUS AND TECHNICALLY COMPLICATED OBJECT, CONTINUOUS MONITORING


doi: 10.18698/2309-3684-2021-1-3148


The possibility of constructing adequate and economical mathematical models of especially dangerous and technically complex objects when solving problems of monitoring their dynamic stress-strain state using the finite element method is discussed. The desired result is achieved on the basis of the application of the developed volumetric finite elements with a mixed degree of interpolation, both geometry and displacements for all edges. At the same time, it is possible to combine both subparametric and isoparametric approaches by varying the degree of interpolating polynomials from one to three within each element. The results of evaluating the effectiveness of the proposed approach are presented on the example of solving a model problem on free oscillations of a pipeline. The proposed family of volumetric finite elements is implemented in the COMPASS finite element package, as well as in the specialized software package MStruct, designed for continuous monitoring of industrial equipment, as well as buildings and structures in real time. An example of the practical application of the developed software for monitoring the dynamic stress-strain state of equipment at a hazardous production facility is presented.


GOST R 22.1.12–2005. Safety in emergencies. Structured system for monitoring and control of building / construction engineering equipment. General requirements. Introduction.2005-09-15. Moscow, Standartinform Publ., 2005, 13 p.
Gradostroitel'nyj kodeks Rossijskoj Federacii [Urban Planning Code of the Russian Federation]: Federal Law of 29 Dec.2004 No.190-FZ: adopted by the State Duma on 22 Dec.2004: Approved by the Federation Council on 24 Dec.2004: [ed.dated July 31, 2020]. Collection of Legislation of the Russian Federation, 2004.
Zenkevich O.K. Metod konechnyh elementov v tekhnike [Finite element method in engineering]. Moscow, Mir Publ., 1975, 541 p.
Bathe K.J. Finite Element Procedures. New Jersey, Prentice Hall Publ., 2014, 1043 p.
Saeed M. Finite Element Analysis: Theory and Application with ANSYS. London, Pearson Publ., 2014, 936 p.
Kohnke P. ANSYS, Inc. Theory. Release 5.7. Canonsburg, ANSYS, Inc., 2001, 1266 p.
Stein E. Error — controlled adaptive finite elements in solid mechanics. Chichester, Wiley Publ., 2003, 410 p.
MSC.Nastran 2004. Reference Manual. USA, MSC.Software Corporation, 2003, 1008 p.
Certificate no.2014619601 Programma strukturnogo monitoringa tekhnologicheskogo oborudovaniya, zdanij i sooruzhenij (MStruct): svidetel'stvo ob ofic.registracii programmy dlya EVM [Program of structural monitoring of technological equipment, buildings and structures (MStruct)]: certificate of ofic.registration of a computer program / S.Y. Trutaev, V.V. Trutaeva; applicant and copyright holder: JSC “IrkutskNIIhimmash” — no.2014617158; application 20.07.2004; registered in the register of computer programs 20.10.2004 — [1].
GOST R 55431–2013. Piping systems. Calculated and experimental method for estimating the dynamic stress–strain state. Introduction.2013-12-01. Moscow, Standartinform Publ., 2014, 14 p.
Pat.2626391 Russian Federation, IPC G01M 7/00 (2006.01). Sposob monitoringa napryazhenno–deformirovannogo sostoyaniya ob"ektov povyshennoj opasnosti [A method for monitoring the stress–strain state of high–risk objects] / S.Y. Trutaev, K.A. Kuznetsov. — no.2016135360; application 30.08.2016; publ.26.07.2017, Bul.no.21— 7 p.
Bate K., Wilson E. Numerical Methods in Finite Element Analysis. New Jersey, Prentice Hall, 1976, 544 p.
Graupe D. Identification of system. New York, Krieger Publ., 1976, 276 p.
Jill Ph., Murray W., Wright M. Practical optimization. London, Academic Press, 1981, 418 p.
Trutaeva V.V., Pogodin V.K., Bezdelev V.V. Primenenie programmnoj sistemy COMPASS dlya rascheta mashinostroitel'nyh detalej i konstrukcij [Application of the COMPASS software system for calculating machine-building parts and structures]. Materialy III mezhdunarodnoj konferencii «Problemy mekhaniki sovremennyh mashin» [Proceedings of the III International Conference "Problems of Mechanics of modern machines"], Ulan-Ude, 2006, vol.3, pp.82–86.
Bezdelev V.V., Buklemishev A.V. Programmnaya sistema COMPASS: Rukovodstvo pol'zovatelya: uchebnoe posobie dlya studentov, obuchayushchihsya po napravleniyu «Stroitel'stvo» [COMPASS software system: User's Guide: a textbook for students studying in the direction of «Construction»]. Irkutsk, ISU Publ., 2000, 120 p.
Prezhenceva V.V. Ierarhiya ob"emnyh konechnyh elementov s peremennym chislom uzlov na rebrah [Hierarchy of volumetric finite elements with a variable number of nodes on the edges] Proceedings of Irkutsk State Technical University, 2004, no.4 (20), pp.179–180.
Bezdelev V.V., Prezhentseva V.V. Funkcii formy tetraedral'nogo konechnogo elementa s peremennym chislom promezhutochnyh uzlov na rebrah [Shape functions of a tetrahedral finite element with a variable number of intermediate nodes on the edges].Proceedings of Irkutsk State Technical University, 2007, no.2–1 (30), pp.91–98.
Prezhentseva V.V., Bezdelev V.V. Ierarhiya dvumernyh i trekhmernyh konechnyh elementov s peremennym chislom uzlov v programmnoj sisteme COMPASS [Hierarchy of two-dimensional and three-dimensional finite elements with a variable number of nodes in the COMPASS software system]. Vestnik NGASU [Bulletin of NGASU], 2005, vol.8, no.2, pp.71–78.
Prezhentseva V.V., Bezdelev V.V. Dokazatel'stvo sovmestimosti konechnyh elementov razlichnyh topologicheskih tipov [Proof of compatibility of finite elements of various topological types]. Novye tekhnologii v investicionno–stroitel'noj sfere i ZHKKH [New technologies in the investment and construction sector and housing], 2005, vol.1, no.2, pp.15–19.
Trutaeva V.V., Bezdelev V.V. Topologicheskaya sovmestimost' ob"emnyh konechnyh elementov s peremennym chislom uzlov na rebrah [Topological compatibility of volumetric finite elements with a variable number of nodes on edges]. Materialy III mezhdunarodnoj konferencii «Problemy mekhaniki sovremennyh mashin» [Proceedings of the III International Conference "Problems of Mechanics of modern machines"], Ulan-Ude, 2006, vol.1, pp.246–249.
Trutaev S.Yu., Trutaeva V.V. Development of a hierarchy of finite elements with variable number of nodes on the edge to investigate stress–strain state of engineering equipment. Systems. Methods. Technologies, 2014, no.3 (23), pp.90–94.
Rabotnov Yu.N. Soprotivlenie materialov [Resistance of materials]. Moscow, Fizmatgiz Publ., 1963, 456 p.
Kuznetsova T.V., Krasnokutsky A.N. Experience of transfer line analysis and designs. Oil and Gas Technologies, 2012, no.3 (80), pp.54–55.


Трутаев С.Ю. О построении адекватных и экономичных математических моделей в задачах постоянного мониторинга особо опасных и технически сложных объектов. Математическое моделирование и численные методы, 2021, № 1, с. 31–48.



Download article

Количество скачиваний: 23