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Research Article

Analytical and numerical calculation of the critical buckling load in compound columns

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Pages 838-854 | Received 11 Jan 2020, Accepted 09 Apr 2020, Published online: 12 May 2020

References

  • Al-ansari, L. S.; “Calculating Static Deflection And Natural Frequency Of Stepped Cantilever Beam Using Modified Rayleigh Method”; International Journal of Mechanical and Production Engineering Research and Development (IJMPERD); Vol. 3, 4, October 2013, 113–124
  • Al-Ansari, L. S., M. Ali, H. Al-Hajjar, and J. A. Husam. 2018. “Calculating the Natural Frequency of Cantilever Tapered Beam Using Classical Rayleigh, Modified Rayleigh and Finite Element Methods.” International Journal of Engineering & Technology, 7 (4), 4866–4872.
  • Alansari, L. S., H. Z. Zainy, A. A. Yaseen, and M. Aljanabi. 2019. “Calculating the Natural Frequency of Hollow Stepped Cantilever Beam.” International Journal of Mechanical Engineering and Technology (IJMET); Volume 10, 1, January, pp. 898–914, Article ID: IJMET_10_01_093
  • Barnes, D. C. (1988). “The Shape of the Strongest Column Is Arbitrary Close the Shape of the Weakest Column.” Quar Appl Math, 4, 605–609.
  • Clausen, T. (1851). “Uber die Form architektonischer Saulen.” Bulletin physico mathematiques et Astronumiques, 1: 279–294.
  • Cox, S. J., and M. L. Overton (1992). “On the Optimal Design of Columns against Buckling.” SIAM J Math Analy, 23: 287–325. https://doi.org/10.1137/0523015
  • Euler, L. (1744). “De Curvis Elasticis, in Methodus Inveniendi Leneas Curva Maximi Minimive Proprietate Gaudentes, Sive Solutio Problematis Isoperimetrici Lattisimo Sensu Accepti, Lausannae, 65A.” O. O. Ser. I., 24: 231–297, 174
  • Keller, J. B. (1960). “The Shape of the Strongest Column.” Arch Ration Mechanical Analysis, 5: 275–285. https://doi.org/10.1007/BF00252909
  • Khurmi, R. S. 2008. “Strength of Materials – Mechanics of Solids, Multicolor Edition, S.” Chand & Company LTD, RAM NAGAR, NEW DELHI, India, P: 800.
  • Lagrange, J. L. (1773). “Sur la figure des colonnes.” Miscellanea Taurinensia, P: 123.
  • Luay, S., and Al-Ansari (2012), “ Calculating of Natural Frequency of Stepping Cantilever Beam”, International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS, Vol.:12 (5), pp. 59–68.
  • Luay, S. A., A. Muhannad, and M. H. Y. Ali 2012. “Vibration Analysis of Hyper Composite Material Beam Utilizing Shear Deformation and Rotary Inertia Effects.” International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS, 12 (4), P: 76-87.
  • Masur, E. (1984). “Optimal Structural Design Under Multiple Eigenvalue Constraints.” Inter J Sol Struct,20: 211–231. https://doi.org/10.1016/0020-7683(84)90034-9
  • Myers, M. K., and W. R. Spillers (1986). “A Note on the Strongest Fixed–Fixed Column.” Quar Appl Math, 3: 583–588. https://doi.org/10.1090/qam/860907
  • Nash, W., and M. C. Potter, Strength of Materials, Fifth Edition, Schaum’s Outline Series, Mc Graw Hill, 2011, USA.
  • Olhoff, N., and S. H. Rasmussen (1977). “On the Single and Bimodal Optimum Buckling Loads of Clamped Columns.” Inter J Sol and Struct, 13: 605–614. https://doi.org/10.1016/0020-7683(77)90043-9
  • Olhoff, N., and A. P. Seyranian (2002). “Initial Post-buckling Behaviour of Bimodal Optimal Columns.” In CD-Proc. 1st Int. Congress on Mechatronics, A. Guran and H. Bremer (eds), 3–6 July 2002,Linz,Austria, Johannes Kepler University, Linz, Austria, p. 4.
  • PEKBEY, Y., A. Ozdamar, and O. Sayman 2007. “Buckling Optimization of Composite Columns with Variable Thickness”; Journal Of Reinforced Plastics And Composites, Vol. 26, 13, 1337–1356. https://doi.org/10.1177/0731684407079772
  • Robert, L. M., and A. Joseph Untener, Applied Strength of Materials, Sixth Edition, Taylor & Francis Group, LLC, 2017, USA.
  • Seyranian, A. P., and O. G. Privalova (2003). “The Lagrange Problem on an Optimal Column.” Old and New Results, Struct Multidisc Optim, 25: 393–410. https://doi.org/10.1007/s00158-003-0333-4
  • Tadjbakhsh, I., and J. B. Keller (1962). “Strongest Columns and Isoperimetric Inequalities for Eigenvalues.” Journal of Applied Mechanics, 29: 159–164. https://doi.org/10.1115/1.3636448
  • Zainy, H. Z., L. S. Al-Ansari, A. M. H. Al-Hajjar, M. Mahdi, and S. Shareef. 2018. “Analytical and Numerical Approaches for Calculating the Static Deflection of Functionally Graded Beam under Mechanical Load.” International Journal of Engineering & Technology, 7 (4), 3889–3896.

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