Error
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Error loading Modules:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering

DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

Main formulations of the finite element method for the problems of structural mechanics. Part 2

Vestnik MGSU 12/2014
  • 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 .

Pages 40-59

The author offers a classification of Finite Element formulations, which allows orienting in a great number of the published and continuing to be published works on the problem of raising the efficiency of this widespread numerical method. The second part of the article offers examination of straight formulations of FEM in the form of displacement approach, area method and classical mixed-mode method. The question of solution convergence according to FEM in the form of classical mixed-mode method is considered on the example of single-input single-output system of a beam in case of finite element grid refinement. The author draws a conclusion, that extinction of algebraic equations system of FEM in case of passage to the limit is not a peculiar feature of this method in general, but manifests itself only in some particular cases. At the same time the obtained results prove that FEM in mixed-mode form provides obtaining more stable results in case of finite element grid refinement in comparison with FEM in the form of displacement approach. It is quite obvious that the same qualities will appear also in two-dimensional systems.

DOI: 10.22227/1997-0935.2014.12.40-59

References
  1. Gorodetskiy A.S., Zavoritskiy V.I., Lantukh-Lyashñhenko A.I., Rasskazov A.O. Metod konechnykh elementov v proektirovanii transportnykh sooruzheniy [Finite Element Method in Transport Constructions Design]. Moscow, Transport Publ., 1981, 143 p. (In Russian)
  2. Postnov V.A., Kharkhurim I.Ya. Metod konechnykh elementov v raschetakh sudovykh konstruktsiy [Finite Element Method in Ship Structures Calculation]. Leningrad, Sudostroenie Publ., 1974, 344 p. (In Russian)
  3. Sekulovich M. Metod konechnykh elementov [Finite Element Method]. Translated from Serbian Yu.N. Zueva, editor V.Sh. Barbakadze. Moscow, Stroyizdat Publ., 1993, 664 p. (In Russian)
  4. Ignat’ev A.V. Osnovnye formulirovki metoda konechnykh elementov v zadachakh stroitel’noy mekhaniki. Chast’ 1 [Essential FEM Statements Applied to Structural Mechanics Problems. Part 1]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2014, no. 11, pp. 37—57. (In Russian)
  5. Bogner F., Fox R., Schmit L. A Cylindrical Shell Discrete Element. AIAA. 1967, vol. 5, no. 4, pp. 745—750. DOI: http://dx.doi.org/10.2514/3.4056.
  6. Allman D.J. Treugol’nye konechnye elementy dlya rascheta izgibaemykh plastin pri postoyannykh i lineyno raspredelennykh izgibayushchikh momentakh [Trigonal Finite Elements for Bending Plates Calculation in Case of Permanent and Linearly Distributed Bending Moments]. Raschet uprugikh konstruktsiy s ispol’zovaniem EVM [Calculation of Elastic Structures Using Computer]. Translated from English, editor A.P. Filin. Leningrad, Sudostroenie Publ., 1974, pp. 80—101. (In Russian)
  7. Klochkov Yu.V. Razvitie teorii lineynogo i nelineynogo deformirovaniya obolochek na osnove MKE s uchetom smeshcheniya kak zhestkogo tselogo i izmeneniya tolshchiny [Development of the Theory of Linear and Non-linear Deformation of Shells Basing on FEM with Account for the Displacement as Stiff Entire and Change of the Width]. Dissertation of the Doctor of Technical Sciences. Volgograd, Volgogradskaya GSKhA Publ., 2001, 326 p. (In Russian)
  8. Bathe K.-J., Wilson E.L. Numerical Methods in Finite Element Analysis, New Jersey, Prentice-Hall, 1976, 528 p.
  9. Bathe K. Metody konechnykh elementov [Finite Elements Methods]. Transl. from English by V.P. Shidlovskiy. Moscow, FIZMATLIT Publ., 2010, 1024 p. (In Russian)
  10. Tsybenko A.S. Primenenie treugol’nykh trekhuzlovykh nesoglasovannykh elementov dlya resheniya osesimmetrichnykh zadach teorii uprugosti [Application of Trigonal Nonconforming Elements for Solving Axisymmetric Tasks of Elasticity Theory]. Problemy plastichnosti [Elasticity Problems]. 1986, no. 3, pp. 79—83.
  11. Semenov V.A., Semenov P.Yu. Hybrid Finite Elements for Analysis of Shell Structures. Proc. International Congress ICSS—98, 22—26 June 1998, Moscow, Russia. Moscow, 1998, vol. 1, pp. 244—251.
  12. Bathe K.J. Finite Element Procedures. Prent. Hall, Englewood Cliffs, 1996, 1036 p.
  13. Fraeijs de Veubeke B., Sander G. An Equilibrium Model for Plate Bending. International J. Solids and Structures. 1968, vol. 4, no. 4, pp. 447—468. DOI: http://dx.doi.org/10.1016/0020-7683(68)90049-8.
  14. Tyukalov Yu.A. Reshenie zadach stroitel’noy mekhaniki metodom konechnykh elementov v napryazheniyakh na osnove funktsionala dopolnitel’noy energii i printsipa vozmozhnykh peremeshcheniy [Solving the Tasks of Structural Mechanics by Finite Element Method in Strains Basing on Additional Energy Functional and Principle of Possible Sisplacements]. Dissertation of the Doctor of Technical Sciences. Kirov, VyatGY Publ., 2006, 314 p. (In Russian)
  15. 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). (In Russian)
  16. Ignat’ev A.V., Gabova V.V. Algoritm staticheskogo rascheta ploskikh sterzhnevykh sistem po metodu konechnykh elementov v smeshannoy forme [Algorithm of Static Analysis of Flat Truss Structures Using Finite Element Method in Mixed Mode Form]. Vestnik Volgogradskogo gosudarstvennogo arkhitekturno-stroitel’nogo universiteta. Seriya: Estestvennye nauki [Proceedings of Volgograd State University of Architecture and Civil Engineering. Series: Natural Sciences]. 2007, no. 6 (23), pp. 72—77. (In Russian)
  17. Rekunov S.S., Voronkova G.V. Osobennosti rascheta plastinok po metodu konechnykh elementov v smeshannoy forme [Features of Calculating Plates Using Finite Elements Method in Mixed-Mode Form]. Vestnik Volgogradskogo gosudarstvennogo arkhitekturno-stroitel’nogo universiteta. Seriya: Stroitel’stvo i arkhitektura [Proceedings of Volgograd State University of Architecture and Civil Engineering. Series: Construction and Architecture]. 2007, no. 7 (26), pp. 74—77. (In Russian)
  18. Maslennikov A.M. Raschet stroitel’nykh konstruktsiy chislennymi metodami [Calculation of Building Structures Using Numerical Methods]. Leningrad, LGU Publ., 1987, 224 p. (In Russian)
  19. Pokrovskiy A.A. Smeshannaya forma MKE v raschetakh sterzhnevykh sistem i sploshnoy sredy [Mixed-Mode Form of FEM in Calculation of Truss Systems and Continuous Medium]. Dissertation of the Doctor of Technical Sciences. Penza, PGASA Publ., 2000, 308 p. (In Russian)

Download

Results 1 - 1 of 1