Analytical study of geometrically nonlinear bending of the composite bars of the action of a concentrated load
- 1 Ph. D. (Phys.-Math.), Associate Professor, Adviser of General Director, JSC Academician M.F. Reshetnev «Information Satellite Systems» (Zheleznogorsk)
Abstract
The problem of finding the equilibrium configurations of various forms of two- and three-link cantilever composite flexible rod under longitudinal compression. Statement of the problem takes into account the geometric nonlinearity. Analytical solutions of the corres-ponding nonlinear boundary value problems recorded in parametric form using Jacobi elliptic functions. These solutions describe various forms of bending the rod at any number of points of inflection. Our study allows to determine the equilibrium shape of a curved rod and load thresholds. The solution can be used to model stem cells and transformed umbrella spacecraft antennas in the case when you need accurate records of geometric nonlinearity.
How to cite
Охоткин К.Г. Аналитическое исследование геометрически-нелинейного изгиба составного стержня переменной жесткости при действии сосредоточенной нагрузки // Наукоемкие технологии. 2016. № 5. С. 35–42.
References
- Milan Batista. AnalyticaltreatmentofequilibriumconfigurationsofcantileverunderterminalloadsusingJacobiellipticalfunctions // InternationalJournalofSolidsandStructures. 2014. V. 51. Issue 13. P. 2308−2326.
- S.S. Antman. NonlinearProblemsofElasticity. Springer. NewYork. NY. USA. 1995.
- Y. Goto, etall. Ellipticintegralsolutionsofplaneelasticawithaxialandsheardeformations // InternationalJournalofSolidsandStructures. 1990. V. 26. № 4. P. 375−390.
- D.E. Panayotounakos, P.S. Theocaris. Exactsolutionofthenon-lineardifferentialequationconcerningtheelasticlineofastraightrodduetoterminalloading // InternationalJournalofNon-LinearMechanics. 1982. V. 17. № 5−6. P. 395−402.
- D.E. Panayotounakos, A.B. Sotiropoulos. ExactparametricanalyticsolutionsoftheelasticODEsforbarsincludingeffectsofthetransversedeformation // InternationalJournalofNon-LinearMechanics. 2004. V. 39. № 10. P. 1555−1570.
- Giovanni M. Scarpello, Daniele Ritelli.ExactSolutionsofNonlinearEquationofRodDeflectionsInvolvingtheLauricellaHypergeometricFunctions // InternationalJournalofMathematicsandMathematicalSciencesV. 2011. 22 p. doi:10.1155/2011/838924.
- Gabriel Cederbaum.Post-bucklingbehaviorofporoelasticcolumns // InternationalJournalofMechanicalSciences. April 2000. V. 42. № 4. P. 771−783.
- Levyakov S.V., Kuznetsov V.V., 2010. Stabilityanalysisofplanarequilibriumconfigurationsofelasticrodssubjectedtoendloads // ActaMech. 211 (1−2). P. 73−87.
- Timoshenko S., Gere J.M., 1961. Theoryofelasticstability // EngineeringSocietiesMonographs. 2nded. McGraw-HillBookCompany. NewYork. London. P. 541.
- Popov E.P.TheoryandCalculationofFlexibleElasticBars. Nauka. Moscow. 1986.
- Harry BatemanandArthur Erdélyi.Highertranscendentalfunctions. NewYork. Toronto. London. MCGraw-HillBookCompany. Inc. 1953.
- Y.V. ZakharovandK.G. Okhotkin. Nonlinearbendingofthinelasticrods // JournalofAppliedMechanicsandTechnicalPhysics. 2002. V. 43. P. 739−744.