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Year 2016, Volume: 3 Issue: 1, 9 - 14, 30.06.2016
https://doi.org/10.17350/HJSE19030000026

Abstract

References

  • S. Coskun, M. Atay, Determination of critical buckling load for elastic columns of constant and variable cross- sections using variational iteration method, Computers and Mathematics with Applications 58 (2009) 2260-2266.
  • S. Coskun, Determimation of critical buckling loads for euler columns of variable exural stiness with a continuous elastic restraint using homotopy perturbation method, International Journal of Nonlinear Sciences and Numerical Simulation 10 (2009) 191-197.
  • S. Coskun, Analysis of tilt-buckling of Euler columns with varying exural stiness using homotopy perturbation method, Mathematical Modelling and Analysis 15 (2010) 275-286.
  • F. Okay, M. Atay, S. Coskun, Determination of buckling loads and mode shapes of a heavy vertical column under its own weight using the variational iteration method, International Journal of Nonlinear Sciences and Numerical Simulation 11 (2010) 851-857.
  • S. Pnarba14s, Lateral torsional buckling of rectangular beams using variational iteration methodlateral torsional buckling of rectangular beams using variational iteration method, Scientic Research and Essays 6 (2011) 1445-1457.
  • S. Pinarbasi, Stability analysis of nonuniform rectangular beams using homotopy perturbation method, Mathematical Problems in Engineering (2012) 2012 1-18.
  • S. Pinarbasi, Buckling analysis of nonuniform columns with elastic end restraints, Journal of Mechanics of Materials and Structures 7 (5) (2012) 485-507.
  • S. Pinarbasi et al., Analytical, numerical and experimental studies on stability of three segment compression members with pinned ends, in: S. Co14skun (Ed.), Advances in Computational Stability Analysis, InTech, 2012, pp. 673-9.
  • S. Pinarbasi et al., Stability analysis of two-segment stepped columns with dierent end conditions and internal axial loads, Mathematical Problems in Engineering 2013 (2013) 1-9.
  • Y. Huang, Q. Luo, A simple method to determine the critical buckling loads for axially inhomogenous beams with elastic restraint, Computers and Mathematics with Applications 61 (2011) 2510-2517.
  • Z.X. Yuan, X.W. Wang, Buckling and post-buckling analysis of extensible beam-coloumns by using the differential quadrature method, Computers and Mathematics with Applications 62 (2011) 4499-4513.
  • A. Eryilmaz et al., Buckling of Euler columns with a continuous elastic restraint via homotopy analysis method, Journal of Applied Mathematics 2013 (2013) 1-8.
  • M. Basbuk, M. Atay, A. Eryilmaz, Numerical solutions for buckling loads of elastic columns with constant cross- section, Transaction on IoT and Cloud Computing 2 (2014) 1-13.
  • J. Reddy, Energy Principles and Variational Methods in Applied Mechanics, John-Wiley, New York, 2002.
  • Z. Bazant, L. Cedolin, Stability of Structures: Elastic, Inelastic Fracture and Damage Theories, World Scientic Publishing, Singapore, 2010.
  • C.M.Wang, C.Y.Wang, J.N. Reddy, Exact Solutions for Buckling of Structural Members, CRC Press, Florida, 2005, pp. 22-24.

On Critical Buckling Loads Of Euler Columns With Elastic End Restraints

Year 2016, Volume: 3 Issue: 1, 9 - 14, 30.06.2016
https://doi.org/10.17350/HJSE19030000026

Abstract

I n recent years, a great number of analytical approximate solution techniques have been introduced to find a solution to the nonlinear problems that arised in applied sciences. One of these methods is the homotopy analysis method HAM . HAM has been successfully applied to various kinds of nonlinear differential equations. In this paper, HAM is applied to find buckling loads of Euler columns with elastic end restraints. The critical buckling loads obtained by using HAM are compared with the exact analytic solutions in the literature. Perfect match of the results veries that HAM can be used as an efficient, powerfull and accurate tool for buckling analysis of Euler columns with elastic end restraints

References

  • S. Coskun, M. Atay, Determination of critical buckling load for elastic columns of constant and variable cross- sections using variational iteration method, Computers and Mathematics with Applications 58 (2009) 2260-2266.
  • S. Coskun, Determimation of critical buckling loads for euler columns of variable exural stiness with a continuous elastic restraint using homotopy perturbation method, International Journal of Nonlinear Sciences and Numerical Simulation 10 (2009) 191-197.
  • S. Coskun, Analysis of tilt-buckling of Euler columns with varying exural stiness using homotopy perturbation method, Mathematical Modelling and Analysis 15 (2010) 275-286.
  • F. Okay, M. Atay, S. Coskun, Determination of buckling loads and mode shapes of a heavy vertical column under its own weight using the variational iteration method, International Journal of Nonlinear Sciences and Numerical Simulation 11 (2010) 851-857.
  • S. Pnarba14s, Lateral torsional buckling of rectangular beams using variational iteration methodlateral torsional buckling of rectangular beams using variational iteration method, Scientic Research and Essays 6 (2011) 1445-1457.
  • S. Pinarbasi, Stability analysis of nonuniform rectangular beams using homotopy perturbation method, Mathematical Problems in Engineering (2012) 2012 1-18.
  • S. Pinarbasi, Buckling analysis of nonuniform columns with elastic end restraints, Journal of Mechanics of Materials and Structures 7 (5) (2012) 485-507.
  • S. Pinarbasi et al., Analytical, numerical and experimental studies on stability of three segment compression members with pinned ends, in: S. Co14skun (Ed.), Advances in Computational Stability Analysis, InTech, 2012, pp. 673-9.
  • S. Pinarbasi et al., Stability analysis of two-segment stepped columns with dierent end conditions and internal axial loads, Mathematical Problems in Engineering 2013 (2013) 1-9.
  • Y. Huang, Q. Luo, A simple method to determine the critical buckling loads for axially inhomogenous beams with elastic restraint, Computers and Mathematics with Applications 61 (2011) 2510-2517.
  • Z.X. Yuan, X.W. Wang, Buckling and post-buckling analysis of extensible beam-coloumns by using the differential quadrature method, Computers and Mathematics with Applications 62 (2011) 4499-4513.
  • A. Eryilmaz et al., Buckling of Euler columns with a continuous elastic restraint via homotopy analysis method, Journal of Applied Mathematics 2013 (2013) 1-8.
  • M. Basbuk, M. Atay, A. Eryilmaz, Numerical solutions for buckling loads of elastic columns with constant cross- section, Transaction on IoT and Cloud Computing 2 (2014) 1-13.
  • J. Reddy, Energy Principles and Variational Methods in Applied Mechanics, John-Wiley, New York, 2002.
  • Z. Bazant, L. Cedolin, Stability of Structures: Elastic, Inelastic Fracture and Damage Theories, World Scientic Publishing, Singapore, 2010.
  • C.M.Wang, C.Y.Wang, J.N. Reddy, Exact Solutions for Buckling of Structural Members, CRC Press, Florida, 2005, pp. 22-24.
There are 16 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Musa Basbuk This is me

Aytekin Eryilmaz This is me

Safa B. Coskun This is me

Mehmet Tarik Atay This is me

Publication Date June 30, 2016
Published in Issue Year 2016 Volume: 3 Issue: 1

Cite

Vancouver Basbuk M, Eryilmaz A, Coskun SB, Atay MT. On Critical Buckling Loads Of Euler Columns With Elastic End Restraints. Hittite J Sci Eng. 2016;3(1):9-14.

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