DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

Possibility of using finite element method in the form of classical mixed method for geometrical nonlinear analysis of hinged-rod systems

Vestnik MGSU 12/2015
  • Ignat’ev Aleksandr Vladimirovich - Volgograd State University of Architecture and Civil Engineering (VSUACE) Candidate of Technical Sciences, Associate Professor, Department of Structural Mechanics, Volgograd State University of Architecture and Civil Engineering (VSUACE), 1 Akademicheskaya str., Volgograd, 400074, Russian Federation.
  • Ignat’ev Vladimir Aleksandrovich - Volgograd State University of Architecture and Civil Engineering (VSUACE) Doctor of Technical Sciences, head, Department of Structural Mechanics, Volgograd State University of Architecture and Civil Engineering (VSUACE), 1 Akademicheskaya str., Volgograd, 400074, Russian Federation.
  • Onishchenko Ekaterina Valer’evna - Volgograd State University of Architecture and Civil Engineering (VSUACE) external student, Department of Structural Mechanics, Volgograd State University of Architecture and Civil Engineering (VSUACE), 1 Akademicheskaya str., Volgograd, 400074, Russian Federation.

Pages 47-58

At the present time a great number of works have been published, in which the problems of numerical solution of geometrical nonlinear tasks of calculating different types of structures are considered. Nevertheless the problem of the certainty of the numerical solution of geometrical nonlinear tasks of rod structures deformation (large displacements) still provokes great interest. The quality of the solution for a certain task is proved only by the coincidence of the results obtained before using two different methods or with the experiment. The authors consider the numerical solution algorithm of geometrical nonlinear tasks of the deformation of hinged-rod systems (large displacements and turns) both in case of high and gentle loading basing on the finite element method in the form of classical mixed method being developed by the authors. Solving the problem of static deformation of a flat mechanical hinged-rod system consisting of two linear-elastic rods the authors show the simplicity and efficiency of the algorithm when finding all the range equilibrium system states. The quality of the solution is proved by the coincidence of the results in case of gentle and heavy loading of the system and with the results of other investigations.

DOI: 10.22227/1997-0935.2015.12.47-58

References
  1. Belytschko T., Liu W., Moran B. Nonlinear Finite Elements for Continua and Structures. J.Wiley & Sons, 2000, 300 p.
  2. Bonet J., Wood R. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press, 1997, 248 p.
  3. Crisfield M.A. Non-Linear Finite Element Analysis of Solids and Structures. J. Wiley & Sons, 1996, vol. 1, 362 p.
  4. Kyther P., Wie D. An Introduction to Linear and Nonlinear Finite Element Analysis. Birkhauer Verlag, 2004, 445 p. DOI: http://dx.doi.org/10.1007/978-0-8176-8160-9.
  5. Reddy J.N. An Introduction to Nonlinear Finite Element Analysis. Oxford University Press, 2004, 488 p.
  6. Danilin A.N., Zuev N.N., Snegovskiy D.V., Shalashilin V.I. Ob ispol’zovanii metoda konechnykh elementov pri reshenii geometricheski nelineynykh zadach [On the Use of Finite Element Method when Solving Geometry Nonlinear Tasks]. SAPR i grafika [CAD and Graphics]. 2000, no. 4, pp. 26—31. (In Russian)
  7. Perel’muter A.V., Slivker V.I. Ustoychivost’ ravnovesiya konstruktsiy i rodstvennye problemy [Equilibrium Stability of Structures and Related Problems]. Moscow, SKAD SOFT Publ., 2007, 653 p. (In Russian)
  8. Kheydari A., Galishnikova V.V. Pryamoy uprugoplasticheskiy raschet stal’nykh ferm s bol’shimi peremeshcheniyami na predel’noe ravnovesie i prisposoblyaemost’ [Straight Elastic-Plastic Calculation of the Limit Equilibrium and Adaptability of Steel Trusses with Large Displacements]. Stroitel’naya mekhanika inzhenernykh konstruktsiy i sooruzheniy [Structural Mechanics of Engineering Constructions and Buildings]. 2014, no. 3, pp. 51—64. (In Russian)
  9. Gorodetskiy A.S., Evzerov I.D. Komp’yuternye modeli konstruktsiy [Computer Models and Structures]. Kiev, «Fakt» Publ., 2007, 394 p. (In Russian)
  10. Pokrovskiy A.A., Khechumov R.A. Smeshannaya forma MKE v raschetakh sterzhnevykh sistem s uchetom fizicheskoy i geometricheskoy nelineynostey [Mixed Form of FEM in Calculation of Truss Systems with Account for Physical and Geometric Nonlinearity]. Stroitel’naya mekhanika i raschet sooruzheniy [Structural Mechanica and Calculation of Structures]. 1991, no. 2, pp. 5—11. (In Russian)
  11. Pokrovskiy A.A., Khechumov R.A. Predel’noe i zapredel’noe sostoyanie sterzhnevykh sistem [Limit and Beyond Limit State of Truss Systems]. Stroitel’naya mekhanika i raschet sooruzheniy [Structural Mechanics and Calculation of Structures]. 1991, no. 4, pp. 18—21. (In Russian)
  12. Nazarov D.I. Geometricheski nelineynyy analiz v metode konechnykh elementov, real’nosti i mify [Geometric Nonlinear Analysis in Finite Element Method, Reality and Myths]. Problemy dinamiki, prochnosti i iznosostoykosti mashin [Problems of Dynamics, Stability and Durability of Machines]. 2000, no. 6. (In Russian)
  13. Nazarov D.I. Obzor sovremennykh programm konechno-elementnogo analiza [Review of the Modern Programs of Finite Element Analysis]. SAPR i grafika [CAD and Graphics]. 2000, no. 2, pp. 52—55. (In Russian)
  14. Kurguzov V.D. O chislennom reshenii geometricheski nelineynykh zadach stroitel’noy mekhaniki [On Numerical Solution of Geometric Nonlinear Tasks of Structural Mechanics]. Izvestiya vuzov. Stroitel’stvo [News of Higher Educational Institutions. Construction]. 2009, no. 3—4, pp. 14—22. (In Russian)
  15. Evzerov I.D., Geraymovich Yu.D., Laznyuk M.V., Marchenko D.V. Chislennoe reshenie zadach sil’nogo izgiba [Numerical Solution of Strong Bend Tasks]. Sayt podderzhki pol’zovateley SAPR [Site of CAD User Support]. Available at: http://www.cad.dp.ua/obzors/lira.php/. Date of access: 30.10.2015. (In Russian)
  16. Levyakov S.V. O chislennom reshenii geometricheski nelineynykh zadach statiki uprugikh konstruktsiy [On Numerical Solution of Geometric Nonlinear Tasks of Elastic Structures’ Statics]. Sayt podderzhki pol’zovateley SAPR [Site of CAD User Support]. Available at: http://www.cad.dp.ua/obzors/fem3.php/. Date of access: 30.10.2015. (In Russian)
  17. Ignat’ev V.A., Ignat’ev A.V., Zhidelev A.V. Smeshannaya forma metoda konechnykh elementov v zadachakh stroitel’noy mekhaniki [Mixed Form of Finite Element Method in Problems of Structural Mechanics]. Volgograd, VolgGASU Publ., 2006, 172 p. (In Russian)
  18. Ignat’ev V.A., Ignat’ev A.V., Galishnikova V.V., Onishchenko E.V. Nelineynaya stroitel’naya mekhanika sterzhnevykh sistem. Osnovy teorii. Primery rascheta [Nonlinear Structural Mechanics of Truss Systems. Foundation of the Theory. Calculation Examples]. Volgograd, VolgGASU Publ., 2014, 84 p. (In Russian)
  19. Petrov V.V. Nelineynaya inkremental’naya stroitel’naya mekhanika [Nonlinear Incremental Structural Mechanics]. Moscow, Infra — Inzheneriya Publ., 2014, 480 p. (In Russian)
  20. Petrov V.V. Metod posledovatel’nykh nagruzheniy v nelineynoy teorii plastinok i obolochek [Method of Continuous Loadings in Nonlinear Theory of Plates and Shells]. Saratov, Izdatel’stvo Saratovskogo gosudarstvennogo universiteta Publ., 1975, 120 p. (In Russian)

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Solving geometrically nonlinear tasks of the statics of hinged-rod systems basing on finite element method in the form of classical mixed method

Vestnik MGSU 2/2016
  • Ignat’ev Aleksandr Vladimirovich - Volgograd State University of Architecture and Civil Engineering (VSUACE) Candidate of Technical Sciences, Associate Professor, Department of Structural Mechanics, Volgograd State University of Architecture and Civil Engineering (VSUACE), 1 Akademicheskaya str., Volgograd, 400074, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Ignat’ev Vladimir Aleksandrovich - Volgograd State University of Architecture and Civil Engineering (VSUACE) Doctor of Technical Sciences, head, Department of Structural Mechanics, Volgograd State University of Architecture and Civil Engineering (VSUACE), 1 Akademicheskaya str., Volgograd, 400074, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Onishchenko Ekaterina Valer’evna - Volgograd State University of Architecture and Civil Engineering (VSUACE) external student, Department of Structural Mechanics, Volgograd State University of Architecture and Civil Engineering (VSUACE), 1 Akademicheskaya str., Volgograd, 400074, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 20-33

The most widely used numerical method used in linear calculation of building structures is finite element method in traditional form of displacements. Different software is developed on its basis. Though it is only possible to check the certainty of these numerical solutions, especially of non-linear tasks of engineering structures’ deformation by the coincidence of the results obtained by two different methods. The authors solved geometrically nonlinear task of the static deformation of a flat hinged-rod system consisting of five linear elastic rods undergoing great tension-compression strains. The solution was obtained basing on the finite element method in the form of classical mixed method developed by the authors. The set of all equilibrium states of the system, both stable and unstable, and all the limit points were found. The certainty of the solution was approved by the coincidence of the results obtained by other authors basing on traditional finite element method in displacements.

DOI: 10.22227/1997-0935.2016.2.20-33

References
  1. Belytschko T., Liu W., Moran B. Nonlinear Finite Elements for Continua and Structures. J Wiley & Sons, 2000, 300 p.
  2. Bonet J., Wood R. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press, 1997, 248 p.
  3. Crisfield M.A. Non-Linear Finite Element Analysis of Solids and Structures. J. Wiley & Sons, 1996, vol. 1, 362 p.
  4. Kyther P., Wie D. An Introduction to Linear and Nonlinear Finite Element Analysis. Birkhauer Verlag, 2004, 445 p. DOI: http://dx.doi.org/10.1007/978-0-8176-8160-9.
  5. Reddy J.N. An Introduction to Nonlinear Finite Element Analysis. Oxford University Press, 2004, 488 p.
  6. Danilin A.N., Zuev N.N., Snegovskiy D.V., Shalashilin V.I. Ob ispol'zovanii metoda konechnykh elementov pri reshenii geometricheski nelineynykh zadach [On the Use of Finite Element Method when Solving Geometry Nonlinear Tasks]. SAPR i grafika [CAD and Graphics]. 2000, no. 4, pp. 26—31. (In Russian)
  7. Perel’muter A.V., Slivker V.I. Ustoychivost’ ravnovesiya konstruktsiy i rodstvennye problemy [Equilibrium Stability of Structures and Related Problems]. Moscow, SKAD SOFT Publ., 2007, vol. 1, 653 p. (In Russian).
  8. Galishnikova V.V. Stability Analysis of Space Trusses. International Journal for Computational Civil and Structural Engineering. 2009, vol. 5, no. 1—2, pp. 35—44.
  9. Galishnikova V.V. Chislennyy analiz ustoychivosti ravnovesiya prostranstvennykh ferm v geometricheski nelineynoy postanovke [Numerical Analysis of the Stability of Space Trusses in Geometrical Nonlinear Statement]. Stroitel’naya mekhanika inzhenernykh konstruktsiy i sooruzheniy [Structural Mechanics of Engineering Structures and Constructions]. 2010, no. 1, pp. 42a—50. (In Russian)
  10. Gorodetskiy A.S., Evzerov I.D. Komp’yuternye modeli konstruktsiy [Computer Models and Structures]. Kiev, «Fakt» Publ., 2007, 394 p. (In Russian)
  11. Kurguzov V.D. O chislennom reshenii geometricheski nelineynykh zadach stroitel'noy mekhaniki [On Numerical Solution of Geometric Nonlinear Tasks of Structural Mechanics]. Izvestiya vuzov. Stroitel’stvo [News of Higher Educational Institutions. Construction]. 2009, no. 3—4, pp. 14—22. (In Russian)
  12. Evzerov I.D., Geraymovich Yu.D., Laznyuk M.V., Marchenko D.V. Chislennoe reshenie zadach sil’nogo izgiba [Numerical Solution of Strong Bend Tasks]. Sayt podderzhki pol’zovateley SAPR [Site of CAD User Support]. Available at: http://www.cad.dp.ua/obzors/lira.php/. Date of access: 30.10.2015. (In Russian)
  13. Poceski A. Mixed Finite Element Method. Springer-Verlag Berlin Heidelberg, 1992, 356 p. DOI: http://dx.doi.org/10.1007/978-3-642-84676-2.
  14. Pokrovskiy A.A., Khechumov R.A. Smeshannaya forma MKE v raschetakh sterzhnevykh sistem s uchetom fizicheskoy i geometricheskoy nelineynostey [Mixed Form of FEM in Calculation of Truss Systems with Account for Physical and Geometric Nonlinearity]. Stroitel’naya mekhanika i raschet sooruzheniy [Structural Mechanic and Calculation of Structures]. 1991, no. 2, pp. 5—11. (In Russian)
  15. Pokrovskiy A.A., Khechumov R.A. Predel’noe i zapredel’noe sostoyanie sterzhnevykh sistem [Limit and Beyond Limit State of Truss Systems]. Stroitel’naya mekhanika i raschet sooruzheniy [Structural Mechanics and Calculation of Structures]. 1991, no. 4, pp. 18—21. (In Russian)
  16. Ignat’ev V.A., Ignat’ev A.V., Zhidelev A.V. Smeshannaya forma metoda konechnykh elementov v zadachakh stroitel’noy mekhaniki [Mixed Form of Finite Element Method in Problems of Structural Mechanics]. Volgograd, VolgGASU Publ., 2006, 172 p. (In Russian)
  17. Ignat’ev V.A., Ignat’ev A.V., Galishnikova V.V., Onishchenko E.V. Nelineynaya stroitel’naya mekhanika sterzhnevykh sistem. Osnovy teorii. Primery rascheta [Nonlinear Structural Mechanics of Truss Systems. Foundation of the Theory. Calculation Examples]. Volgograd, VolgGASU Publ., 2014, 84 p. (In Russian)
  18. Nazarov D.I. Geometricheski nelineynyy analiz v metode konechnykh elementov, real’nosti i mify [Geometric Nonlinear Analysis in Finite Element Method, Reality and Myths]. Problemy dinamiki, prochnosti i iznosostoykosti mashin [Problems of Dynamics, Stability and Durability of Machines]. 2000, no. 6. (In Russian)
  19. Nazarov D.I. Obzor sovremennykh programm konechno-elementnogo analiza [Review of the Modern Programs of Finite Element Analysis]. SAPR i grafika [CAD and Graphics]. 2000, no. 2, pp. 52—55. (In Russian)
  20. Levyakov S.V. O chislennom reshenii geometricheski nelineynykh zadach statiki uprugikh konstruktsiy [On Numerical Solution of Geometric Nonlinear Tasks of Elastic Structures]. Statics Sayt podderzhki pol’zovateley SAPR [Site of CAD User Support]. Available at: http://www.cad.dp.ua/obzors/fem3.php/. Date of access: 30.10.2015. (In Russian)
  21. Toroptsev A.V. Reshenie chetyrekh testovykh zadach dlya Nazarova D.I. [Solution of Four Test Tasks for Nazarov D.I.]. Sayt podderzhki pol’zovateley SAPR [Site of CAD User Support]. Available at: http:// www.cad.dp.ua/obzors/paper1.php/. Date of access: 30.10.2015. (In Russian)
  22. Ignat’ev A.V., Ignat’ev V.A., Onishchenko E.V. Vozmozhnost’ ispol’zovaniya metoda konechnykh elementov v forme klassicheskogo smeshannogo metoda dlya geometricheski nelineynogo analiza sharnirno-sterzhnevykh sistem [Possibility of Using Finite Element Method in the Form of Classical Mixed Method for Geometrical Nonlinear Analysis of Hinged-Rod Systems]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2015, no. 12, pp. 47—58. (In Russian)
  23. Petrov V.V. Nelineynaya inkremental’naya stroitel’naya mekhanika [Nonlinear Incremental Structural Mechanics]. Moscow, Infra — Inzheneriya Publ., 2014, 480 p. (In Russian)
  24. Petrov V.V. Metod posledovatel’nykh nagruzheniy v nelineynoy teorii plastinok i obolochek [Method of Continuous Loadings in Nonlinear Theory of Plates and Shells]. Saratov, SGU im. N.G. Chernyshevskogo Publ., 1975, 119 p. (In Russian)

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