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Su içeresindeki çubuğun stabilite analizi için diferansiyel dönüşüm yöntemi ve dunkerley formülünün uygulanması

Year 2021, Volume: 7 Issue: 2, 169 - 174, 30.08.2021

Kanat Burak Bozdoğan Farshid Khosravı

Abstract

Bu çalışmada su içerisinde olan ve P tekil kuvvet ve yayılı kendi ağırlığı etkisinde burkulan çubukların kritik burkulma yükünün bulunması için iki yöntem önerilmiştir. Çalışmada üç farklı Euler durumu dikkate alınmıştır. Sunulan yöntemlerden ilkinde su içerindeki çubuğun stabilite diferansiyel denklemin çözümü Diferansiyel dönüşüm yöntemi (DTM) ile çözülürken, ikinci yöntemde Dunkerley Formula su içerisinde burkulan çubuğun kritik burkulma yük faktörünün belirlenmesi için uygulanmıştır. Çalışmanın sonunda bir örnek önerilen iki yöntem ile çözülerek elde edilen sonuçlar sonlu elamanlar yöntemi ile karşılaştırılmıştır. Sonlu elemanlar yöntemi ile analiz için SAP 2000 programı kullanılmıştır. Elde edilen sonuçlardan iki yönteminde sonlu elemanlar yöntemine yeter uygunlukta sonuç verdiği gözlenmiştir.

Keywords

Stabilite Burkulma DTM Dunkerley Suda kolon

References

  • [1] D. J. Wei, S. X. Yan, Z. P. Zhang, and X. F. Li, “Critical load for buckling of non-prismatic columns under self-weight and tip force,” Mech. Res. Commun., vol. 37, no. 6, pp. 554–558, 2010, doi: 10.1016/j.mechrescom.2010.07.024.
  • [2] S. M. Darbandi, R. D. Firouz-Abadi, and H. Haddadpour, “Buckling of Variable Section Columns under Axial Loading,” J. Eng. Mech., vol. 136, no. 4, pp. 472–476, 2010, doi: 10.1061/(asce)em.1943-7889.0000096.
  • [3] C. Y. Wang, “Stability of a braced heavy standing column with tip load,” Mech. Res. Commun., vol. 37, no. 2, pp. 210–213, 2010, doi: 10.1016/j.mechrescom.2009.12.001.
  • [4] Y. Huang and X.-F. Li, “Buckling Analysis of Nonuniform and Axially Graded Columns with Varying Flexural Rigidity,” J. Eng. Mech., vol. 137, no. 1, pp. 73–81, 2011, doi: 10.1061/(asce)em.1943-7889.0000206.
  • [5] Y. Krutii and V. Vandynskyi, “Exact solution of buckling problem of the column loaded by self-weight,” in IOP Conference Series: Materials Science and Engineering, Dec. 2019, vol. 708, no. 1, doi: 10.1088/1757-899X/708/1/012062.
  • [6] A. de M. Wahrhaftig, K. M. M. Magalhães, R. M. L. R. F. Brasil, and K. Murawski, “Evaluation of Mathematical Solutions for the Determination of Buckling of Columns Under Self-weight,” J. Vib. Eng. Technol., vol. 1, p. 3, 2020, doi: 10.1007/s42417-020-00258-7.
  • [7] Y. Pekbey, “Su İçerisinde Ağırlığı Dikkate Alınan Bir Kolonun Burkulma Analizi,” Pamukkale Üniversitesi Mühendislik Bilim. Derg., vol. 14, no. 2, pp. 195–203, 2005.
  • [8] J. K. Zhou, “Differential transformation and its applications for electrical circuits,” pp. 1279–1289, 1986.
  • [9] K. B. Bozdoğan and F. Khosravi Maleki, “Application of differential transformation method for free vibration analysis of wind turbine,” Wind Struct. An Int. J., vol. 32, no. 1, pp. 11–17, Jan. 2021, doi: 10.12989/was.2021.32.1.011.
  • [10] K. M. Abualnaja, “Numerical treatment of a physical problem in fluid film flow using the differential transformation method,” Int. J. Mod. Phys. C, vol. 31, no. 5, pp. 1–8, 2020, doi: 10.1142/S0129183120500679.
  • [11] O. A. Adeleye, M. Yusuf, and O. Balogun, “Dynamic Analysis of Viscoelastic Circular Diaphragm of a MEMS Capacitive Pressure Sensor using Modified Differential Transformation Method,” Karbala Int. J. Mod. Sci., vol. 6, 2020, doi: 10.33640/2405-609X.1706.
  • [12] B. J. Gireesha and G. Sowmya, “Heat transfer analysis of an inclined porous fin using Differential Transform Method,” Int. J. Ambient Energy, pp. 1–7, Sep. 2020, doi: 10.1080/01430750.2020.1818619.
  • [13] Y. M. Hamada, “Solution of a new model of fractional telegraph point reactor kinetics using differential transformation method,” Appl. Math. Model., vol. 78, pp. 297–321, Feb. 2020, doi: 10.1016/j.apm.2019.10.001.
  • [14] G. Sobamowo et al., “On the Efficiency of Differential Transformation Method to the Solutions of Large Amplitude Nonlinear Oscillation Systems Biomas Gasification View project Heat Transfer Enhancements and Dynamic Behaviour of Energy Systems View project On the Efficiency of,” vol. 139, no. November 2019, pp. 1–60, 2020, [Online]. Available: www.worldscientificnews.com.
  • [15] S. Aydin and K. B. Bozdogan, “Lateral stability analysis of multistory buildings using the differential transform method,” Struct. Eng. Mech., vol. 57, no. 5, pp. 861–876, Mar. 2016, doi: 10.12989/sem.2016.57.5.861.
  • [16] R. Holubowski and K. Jarczewska, “Lateral-Torsional Buckling of Nonuniformly Loaded Beam Using Differential Transformation Method,” Int. J. Struct. Stab. Dyn., vol. 16, no. 7, pp. 1–12, 2016, doi: 10.1142/S0219455415500340.
  • [17] S. Rajasekaran, “Buckling of fully and partially embedded non-prismatic columns using differential quadrature and differential transformation methods,” Struct. Eng. Mech., vol. 28, no. 2, pp. 221–238, Jan. 2008, doi: 10.12989/sem.2008.28.2.221.
  • [18] Y. H. Chai and C. M. Wang, “An application of differential transformation to stability analysis of heavy columns,” Int. J. Struct. Stab. Dyn., vol. 6, no. 3, pp. 317–332, 2006, doi: 10.1142/S0219455406001988.
  • [19] T. Tarnai, “The Southwell and the Dunkerley Theorems,” in Summation Theorems in Structural Stability, Springer Vienna, 1995, pp. 141–185.
  • [20] L. P. Kollar and G. Tarjan, Mechanics of Civil Engineering Structures, vol. 4, no. 3. Woodhead Publishing, 2020.

APPLICATION OF DIFFERENTIAL TRANSFORMATION METHOD AND DUNKERLEY FORMULA FOR STABILITY ANALYSIS OF BARS IN WATER

Year 2021, Volume: 7 Issue: 2, 169 - 174, 30.08.2021

Kanat Burak Bozdoğan Farshid Khosravı

Abstract

In this study, two methods have been proposed to find the critical buckling load of bars that are in water and buckled under the effect of P singular force and distributed self-weight. Three different Euler's cases were taken into account in the study. In the first method, the solution of the stability differential equation of the bar in water is solved by the Differential Transformation Method (DTM), while in the second method, the Dunkerley formula is applied to determine the critical buckling load factor of the buckled bar in water. Finally, the results obtained by solving an example with the two proposed methods were compared with the finite element method. SAP 2000 program was used for finite element analysis. From the results obtained, it was observed that the two methods gave results in good agreement to the finite element method.

Keywords

Stability Buckling DTM Dunkerley Bar in water

References

  • [1] D. J. Wei, S. X. Yan, Z. P. Zhang, and X. F. Li, “Critical load for buckling of non-prismatic columns under self-weight and tip force,” Mech. Res. Commun., vol. 37, no. 6, pp. 554–558, 2010, doi: 10.1016/j.mechrescom.2010.07.024.
  • [2] S. M. Darbandi, R. D. Firouz-Abadi, and H. Haddadpour, “Buckling of Variable Section Columns under Axial Loading,” J. Eng. Mech., vol. 136, no. 4, pp. 472–476, 2010, doi: 10.1061/(asce)em.1943-7889.0000096.
  • [3] C. Y. Wang, “Stability of a braced heavy standing column with tip load,” Mech. Res. Commun., vol. 37, no. 2, pp. 210–213, 2010, doi: 10.1016/j.mechrescom.2009.12.001.
  • [4] Y. Huang and X.-F. Li, “Buckling Analysis of Nonuniform and Axially Graded Columns with Varying Flexural Rigidity,” J. Eng. Mech., vol. 137, no. 1, pp. 73–81, 2011, doi: 10.1061/(asce)em.1943-7889.0000206.
  • [5] Y. Krutii and V. Vandynskyi, “Exact solution of buckling problem of the column loaded by self-weight,” in IOP Conference Series: Materials Science and Engineering, Dec. 2019, vol. 708, no. 1, doi: 10.1088/1757-899X/708/1/012062.
  • [6] A. de M. Wahrhaftig, K. M. M. Magalhães, R. M. L. R. F. Brasil, and K. Murawski, “Evaluation of Mathematical Solutions for the Determination of Buckling of Columns Under Self-weight,” J. Vib. Eng. Technol., vol. 1, p. 3, 2020, doi: 10.1007/s42417-020-00258-7.
  • [7] Y. Pekbey, “Su İçerisinde Ağırlığı Dikkate Alınan Bir Kolonun Burkulma Analizi,” Pamukkale Üniversitesi Mühendislik Bilim. Derg., vol. 14, no. 2, pp. 195–203, 2005.
  • [8] J. K. Zhou, “Differential transformation and its applications for electrical circuits,” pp. 1279–1289, 1986.
  • [9] K. B. Bozdoğan and F. Khosravi Maleki, “Application of differential transformation method for free vibration analysis of wind turbine,” Wind Struct. An Int. J., vol. 32, no. 1, pp. 11–17, Jan. 2021, doi: 10.12989/was.2021.32.1.011.
  • [10] K. M. Abualnaja, “Numerical treatment of a physical problem in fluid film flow using the differential transformation method,” Int. J. Mod. Phys. C, vol. 31, no. 5, pp. 1–8, 2020, doi: 10.1142/S0129183120500679.
  • [11] O. A. Adeleye, M. Yusuf, and O. Balogun, “Dynamic Analysis of Viscoelastic Circular Diaphragm of a MEMS Capacitive Pressure Sensor using Modified Differential Transformation Method,” Karbala Int. J. Mod. Sci., vol. 6, 2020, doi: 10.33640/2405-609X.1706.
  • [12] B. J. Gireesha and G. Sowmya, “Heat transfer analysis of an inclined porous fin using Differential Transform Method,” Int. J. Ambient Energy, pp. 1–7, Sep. 2020, doi: 10.1080/01430750.2020.1818619.
  • [13] Y. M. Hamada, “Solution of a new model of fractional telegraph point reactor kinetics using differential transformation method,” Appl. Math. Model., vol. 78, pp. 297–321, Feb. 2020, doi: 10.1016/j.apm.2019.10.001.
  • [14] G. Sobamowo et al., “On the Efficiency of Differential Transformation Method to the Solutions of Large Amplitude Nonlinear Oscillation Systems Biomas Gasification View project Heat Transfer Enhancements and Dynamic Behaviour of Energy Systems View project On the Efficiency of,” vol. 139, no. November 2019, pp. 1–60, 2020, [Online]. Available: www.worldscientificnews.com.
  • [15] S. Aydin and K. B. Bozdogan, “Lateral stability analysis of multistory buildings using the differential transform method,” Struct. Eng. Mech., vol. 57, no. 5, pp. 861–876, Mar. 2016, doi: 10.12989/sem.2016.57.5.861.
  • [16] R. Holubowski and K. Jarczewska, “Lateral-Torsional Buckling of Nonuniformly Loaded Beam Using Differential Transformation Method,” Int. J. Struct. Stab. Dyn., vol. 16, no. 7, pp. 1–12, 2016, doi: 10.1142/S0219455415500340.
  • [17] S. Rajasekaran, “Buckling of fully and partially embedded non-prismatic columns using differential quadrature and differential transformation methods,” Struct. Eng. Mech., vol. 28, no. 2, pp. 221–238, Jan. 2008, doi: 10.12989/sem.2008.28.2.221.
  • [18] Y. H. Chai and C. M. Wang, “An application of differential transformation to stability analysis of heavy columns,” Int. J. Struct. Stab. Dyn., vol. 6, no. 3, pp. 317–332, 2006, doi: 10.1142/S0219455406001988.
  • [19] T. Tarnai, “The Southwell and the Dunkerley Theorems,” in Summation Theorems in Structural Stability, Springer Vienna, 1995, pp. 141–185.
  • [20] L. P. Kollar and G. Tarjan, Mechanics of Civil Engineering Structures, vol. 4, no. 3. Woodhead Publishing, 2020.
There are 20 citations in total.

Details

Primary Language English
Subjects Civil Engineering, Mechanical Engineering
Journal Section Research Articles
Authors

Kanat Burak Bozdoğan 0000-0001-7528-2418

Farshid Khosravı 0000-0002-8866-114X

Publication Date August 30, 2021
Submission Date April 10, 2021
Acceptance Date August 10, 2021
Published in Issue Year 2021 Volume: 7 Issue: 2

Cite

IEEE K. B. Bozdoğan and F. Khosravı, “APPLICATION OF DIFFERENTIAL TRANSFORMATION METHOD AND DUNKERLEY FORMULA FOR STABILITY ANALYSIS OF BARS IN WATER”, GJES, vol. 7, no. 2, pp. 169–174, 2021.
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