DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

Calculation of the three-layer shallow shell taking into account the creep of the middle layer

Vestnik MGSU 7/2015
  • Andreev Vladimir Igorevich - Moscow State University of Civil Engineering (National Research University) (MGSU) Doctor of Technical Sciences, Professor, corresponding member of Russian Academy of Architecture and Construction Sciences, chair, Department of Strength of Materials, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Yazyev Batyr Meretovich - Rostov State University of Civil Engineering (RSUCE) Doctor of Technical Sciences, Professor, Chair, Depart- ment of Strength of Materials; +7 (863) 201-91-09, Rostov State University of Civil Engineering (RSUCE), 162 Sotsialisticheskaya St., Rostov-on-Don, 344022, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Chepurnenko Anton Sergeevich - Don State Technical University (DGTU) Candidate of Engineering Science, teaching assistant of the strength of materials department, Don State Technical University (DGTU), 162 Sotsialisticheskaya str., Rostov-on-Don, 344022; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Litvinov Stepan Viktorovch - Rostov State University of Civil Engineering (RSUCE) , Rostov State University of Civil Engineering (RSUCE), 162 Sotsialisticheskaya str., Rostov-on-Don, 344022, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 17-24

The equations of the finite element method for calculation of sandwich shells taking into account creep were obtained. The shell is represented as a set of flat triangular elements. The thickness of the carrier layers is supposed to be small compared to the total thickness of the shell. It is assumed that the outer layers perceive normal stresses, and the average layer perceives the shear forces. In the derivation of governing equations we used variational Lagrange principle. According to this principle, the true moves of all the possible ones satisfying the boundary conditions, are the ones that give a minimum of the total energy. Total energy is the sum of the strain energy and the work of external forces. The problem is reduced to a system of linear algebraic equations. On the right side of this system there is the vector of the sum of the external nodal forces and the contribution of creep strains to the load vector. The calculations were performed in mathematical package Matlab. As the law for description of the relationship between stress and creep strain, we used linear creep theory of heredity. If the core of creep is exponential, the creep law can be written in differential form. This allows the calculation by step method using a linear approximation of the time derivative. The model problem has been solved for a spherical shell hinged along the contour. The relationship between the curvature of shell and the growth of deflections was analyzed. It was found out that for the shells of large curvature the creep has no appreciable effect on the deflections.

DOI: 10.22227/1997-0935.2015.7.17-24

References
  1. Kovalenko V.A., Kondrat’ev A.V. Primenenie polimernykh kompozitsionnykh materialov v izdeliyakh raketno-kosmicheskoy tekhniki kak rezerv povysheniya ee massovoy i funktsional’noy effektivnosti [The Use of Polymeric Composite Materials in Rocket and Space Technology as a Reserve to Increase Its Mass and Functional Efficiency]. Aviatsionno-kosmicheskaya tekhnika i tekhnologiya [Aerospace Technics and Technology]. 2011, no. 5, pp. 14—20. (In Russian)
  2. Leonenko D.V. Radial’nye sobstvennye kolebaniya uprugikh trekhsloynykh tsilindricheskikh obolochek [Radial Natural Vibrations of Elastic Three-Layer Cylindrical Shells]. Mekhanika mashin, mekhanizmov i materialov [Mechanics of Machines, Tools and Materials]. 2010, no. 3 (12), pp. 53—56. (In Russian)
  3. Bakulin V.N. Neklassicheskie utochnennye modeli v mekhanike trekhsloynykh obolochek [Non-classical Refined Models in the Mechanics of Sandwich Shells]. Vestnik Nizhegorodskogo universiteta im. N.I. Lobachevskogo [Vestnik of Lobachevsky State University of Nizhni Novgorod]. 2011, no. 4-5, pp. 1989—1991. (In Russian)
  4. Zemskov A.V., Pukhliy V.A., Pomeranskaya A.K., Tarlakovskiy D.V. K raschetu napryazhenno-deformirovannogo sostoyaniya trekhsloynykh obolochek peremennoy zhestkosti [Calculation of the stress-Strain State of Sandwich Shells with Variable Rigidity]. Vestnik Moskovskogo aviatsionnogo institute [Bulletin of Moscow Aviation Institute]. 2011, vol. 18, no. 1, p. 26. (In Russian)
  5. Kirichenko V.F. O sushchestvovanii resheniy v svyazannoy zadache termouprugosti dlya trekhsloynykh obolochek [Existence of the Solutions to a Connected Problem of Thermoelasticity of Sandwich Shells]. Izvestiya vysshikh uchebnykh zavedeniy. Matematika [Russian Mathematics]. 2012, no. 9, pp. 66—71. (In Russian)
  6. Sukhinin S.N. Matematicheskoe i fizicheskoe modelirovanie v zadachakh ustoychivosti trekhsloynykh kompozitnykh obolochek [Mathematical and physical Modeling in Problems оf Stability оf Three-Layer Composite Shells]. Vestnik Nizhegorodskogo universiteta im. N.I. Lobachevskogo [Vestnik of Lobachevsky State University of Nizhni Novgorod]. 2011, no. 4-5, pp. 2521—2522. (In Russian)
  7. Grigorenko Ya.M., Vasilenko A.T. O nekotorykh podkhodakh k postroeniyu utochnennykh modeley teorii anizotropnykh obolochek peremennoy tolshchiny [On Some Approaches to the Construction of the Specified Models of the Theory of Anisotropic Shells of Variable Thickness]. Matematichnі metodi ta fіziko-mekhanіchnі polya [Mathematical Methods and Physical-Mechanical Fields]. 2014, vol. 7, pp. 21—25. (In Russian)
  8. Bakulin V.N. Effektivnye modeli dlya utochnennogo analiza deformirovannogo sostoyaniya trekhsloynykh neosesimmetrichnykh tsilindricheskikh obolochek [Effective Models for Proximate Analysis of the Deformed State of Three-Layered Non-Axisymmetric Cylindrical Shells]. Doklady Akademii nauk [Reports of the Russian Academy of Sciences]. 2007, vol. 414, no. 5, pp. 613—617. (In Russian)
  9. Smerdov A.A., Fan Tkhe Shon. Raschetnyy analiz i optimizatsiya mnogostenochnykh kompozitnykh nesushchikh obolochek [Design Analysis and Optimization of Composite Bearing Shells]. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie [Proceedings of Higher Educational Institutions. Маchine Building]. 2014, no. 11 (656), pp. 90—98. (In Russian)
  10. Bakulin V.N. Postroenie approksimatsiy i modeley dlya issledovaniya napryazhenno-deformirovannogo sostoyaniya sloistykh neosesimmetrichnykh obolochek [Construction of Approximations and Models for Investigation of Stressed-Stained State of Layered Not- Axisymmetric Shells]. Matematicheskoe modelirovanie [Mathematical Modeling]. 2007, vol. 19, no. 12, pp. 118—128. (In Russian)
  11. Garrido M., Correia J., Branco F. Creep Behavior of Sandwich Panels with Rigid Polyurethane Foam Core and Glass-Fibre Reinforced Polymer Faces: Experimental Tests and Analytical Modeling. Journal of Composite Materials. 2013, pp. 21—28. DOI: http://dx.doi.org/10.1177/0021998313496593.
  12. Yazyev B.M., Chepurnenko A.S., Litvinov S.V., Yazyev S.B. Raschet trekhsloynoy plastinki metodom konechnykh elementov s uchetom polzuchesti srednego sloya [Calculation of Three-Layer Plates Using Finite Element Method Taking into Account the Creep of the Middle Layer]. Vestnik Dagestanskogo gosudarstvennogo tekhnicheskogo universiteta. Tekhnicheskie nauki [Herald of Dagestan State Technical University. Technical Sciences]. 2014, no. 33, pp. 47—55. (In Russian)
  13. Rabotnov Yu.N. Polzuchest’ elementov konstruktsiy [Creep of Structural Elements]. Moscow, Nauka Publ., 1966, 752 p. (In Russian)
  14. Kachanov L.M. Teoriya polzuchesti [Creep Theory]. Moscow, Fizmatgiz Publ., 1960, 680 p. (In Russian)
  15. Vol’mir A.S. Gibkie plastinki i obolochki [Flexible Plates and Shells]. Moscow, Izdatel’stvo Tekhniko-teoreticheskoy literatury Publ., 1956, 419 p. (In Russian)
  16. Andreev V.I., Yazyev B.M., Chepurnenko A.S. On the Bending of a Thin Plate at Nonlinear Creep. Advanced Materials Research. Trans Tech Publications, Switzerland. 2014, vol. 900, pp. 707—710. DOI: http://dx.doi.org/10.4028/www.scientific.net/AMR.900.707.
  17. Andreev V.I. Ob ustoychivosti polimernykh sterzhney pri polzuchesti [The Stability of Polymer Rods at Creep]. Mekhanika kompozitnykh materialov [Mechanics of Composite Materials]. 1968, no. 1, pp. 22—28. (In Russian)
  18. Chepurenko A.S., Andreev V.I., Yazyev B.M. Energeticheskiy metod pri raschete na ustoychivost’ szhatykh sterzhney s uchetom polzuchesti [Energy Method of Analysis of Stability of Compressed Rods with Regard for Creeping]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2013, no. 1, pp. 101—108. (In Russian)
  19. Andreev V.I., Yazyev B.M., Chepurnenko A.S. Osesimmetrichnyy izgib krugloy gibkoy plastinki pri polzuchesti [Axisymmetric Bending of a Round Elastic Plate in Case of Creep]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2014, no. 5, pp. 16—24. (In Russian)
  20. Kozel’skaya M.Yu., Chepurnenko A.S., Litvinov S.V. Raschet na ustoychivost’ szhatykh polimernykh sterzhney s uchetom temperaturnykh vozdeystviy i vysokoelasticheskikh deformatsiy [Stability Calculation of Compressed Polymer Rods with Account for Temperature Effects and Vysokoelaplastic Deformations]. Nauchno-tekhnicheskiy vestnik Povolzh’ya [Scientific and Technical Volga region Bulletin]. 2013, no. 4, pp. 190—194. (In Russian)

Download

Results 1 - 1 of 1