Structural Engineering and Mechanics

  • 제68권6호
  • /
  • Pages.713-720
  • /
  • 2018
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Numerical method to determine the elastic curve of simply supported beams of variable cross-section

  • 투고 : 2017.08.22
  • 심사 : 2018.11.07
  • 발행 : 2018.12.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper a new numerical method to determine the elastic curve of the simply supported beams of variable cross-section is demonstrated. In general case it needs to solve linear or small nonlinear second order differential equations with prescribed boundary conditions. For numerical solution the initial values of the slope and the deflection of the end cross-section of the beam is necessary. For obtaining the initial values a lively procedure is developed: it is a special application of the shooting method because boundary value problems can be transformed into initial value problems. As a result of these transformations the initial values of the differential equations are obtained with high accuracy. Procedure is applied for calculating of elastic curve of a simply supported beam of variable cross-section. Results of these numerical procedures, analytical solution of the linearized version and finite element method are compared. It is proved that the suggested procedure yields technically accurate results.

키워드

참고문헌

  1. Biro, I. and Cveticanin, L. (2016), "Procedures for determination of elastic curve of simply and multiple supported beams", Struct. Eng. Mech., 60(1), 21-30. https://doi.org/10.12989/SEM.2016.60.1.021
  2. Fertis, D.G. (2006), Nonlinear Structural Engineering with Unique Theories and Methods to Solve Effectively Complex Nonlinear Problems, Springer.
  3. Kumar, R., Ramachandra, L.S. and Roy, D. (2004) "Techniques based on generic algorithms for large deflection analysis of beams", Sadhana, 29(6), 589-604. https://doi.org/10.1007/BF02901474
  4. Kumar, R., Ramachandra, L.S. and Roy, D. (2006), "A multi-step linearization techniques for a class of bending value problems in non-linear mechanics", Comput. Mech., 39, 73-81. https://doi.org/10.1007/s00466-005-0009-6
  5. Merli, R., Lazaro, S., Monleon, S. and Domingo, A. (2010), "Comparison of two linearization schemes for the nonlinear bending problem of a beam pinned at both ends", Int. J. Sol. Struct., 47(6), 865-874. https://doi.org/10.1016/j.ijsolstr.2009.12.001
  6. Ramachandra, L.S. and Roy, D. (2001), "A new method for nonlinear two-point boundary value problems in solid mechanics", J. Appl. Mech., 68(5), 776-785. https://doi.org/10.1115/1.1387444
  7. Ramachandra, L.S. and Roy, D. (2002), "The locally transversal linearization (LTL) method revisited: A simple error analysis" J. Sound Vibr., 256(3), 579-589. https://doi.org/10.1006/jsvi.2001.4222
  8. Rojas, A.L. (2014), "A mathematical model of elastic curve for simply supported beams subjected to uniformly distributed load taking into account the shear deformations", Int. J. Innovat. Comput. Informat. Contr., 5(3), 885-890.
  9. Rojas, A.L. and Espino, J.V.R. (2015), "Fixed-end moments for beams subjected to a concentrated forced localized anywhere taking into account the shear deformations", Int. J. Innovat. Comput. Informat. Contr., 11(2), 463-474.
  10. Rojas, A.L., Chavarria, S.L., Elizonda, M.M. and Kalashnikov, V.V. (2016), "A mathematical model of elastic curve for simply supported beams subjected to a concentrated load taking into account the shear deformations", Int. J. Innovat. Comput. Informat. Contr., 12(1), 41-54.
  11. Roy, D. and Kumar, R. (2005), "A multi-step transversal linearization (MLT) method in non-linear structural dynamics", J. Sound Vibr., 287(1-2), 203-226. https://doi.org/10.1016/j.jsv.2004.11.032
  12. Thankane, K.S. and Stys, T. (2009), "Finite difference method for beam equation with free ends using mathematica", South. Afr. J. Pure Appl. Math., 4, 61-78.
  13. Timoshenko, S. and Goodier, J.N. (1952), Theory of Elasticity, McGraw-Hill.
  14. Viswanath, A. and Roy, D. (2007) "Multi-step transversal and tangential linearization methods applied to a class of nonlinear beam equations", Int. J. Sol. Struct., 44(14-15), 4872-4891. https://doi.org/10.1016/j.ijsolstr.2006.12.008