Application of Differential Transform Method to Buckling Problems at Pined-Pined Boundary Conditions

Abstract:

Differential Transform Method (DTM) is a new semi-analytical, semi-numerical algorithm, which transforms differential equations to the form of Taylor series. The method derives an approximate numerical solution based on Taylor series expansion, which is a analytical solution built on polynomial form. Traditional Taylor series method is used for symbolic computation, while the Differential Transform Method obtained the solution of the polynomials through itineration calculations. Applying DTM to buckling problems, the critical length of a bar at Pined-Pined boundary is studied. The computational results are compared with analytical solutions and shown excellent agreement between those two algorithms. The method adds a new tool for computational engineering mechanics.

• Periodical: Applied Mechanics and Materials (Volumes 313-314)
• Pages: 1155-1158
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.313-314.1155
• Online since: March 2013
• Authors: Ling Feng Han, Shi Yuan Wu
• Keywords: Buckling, Differential Transform Method, Taylor Series

References

[1] J.K. Zhou. Differential transformation and its applications for electrical circuits. Huazhong Tech University Press. Wuhan, China, 1986. (in Chinese).

[2] C. K. Chen, S. H. Ho. Solving partial differential equations by two-dimensional differential transform method [J]. Applied Mathematics and Computation. 1999, (106):171-179.

DOI: 10.1016/s0096-3003(98)10115-7

[3] Muhammet Kurulay, Bayram Ali Ibrahimo_lu and Mustafa Bayram. Solving a system of nonlinear fractional partial differential equations using three dimensional differential transform method [J]. International Journal of the Physical Sciences. 2010, 5(6): 906-912.

[4] A Kurnaz, G Oturanc, M Kiris. n-Dimensional differential transformation method for solving linear and nonlinear PDE's [J]. International Journal of Computer Mathematics. 2005, (82): 369–80.

DOI: 10.1080/0020716042000301725

[5] MJ Jang, CL Chen, YC Liy. On solving the initial-value problems using the differential transformation method [J]. Applied Mathematics and Computation. 2000, (115): 145-160.

DOI: 10.1016/s0096-3003(99)00137-x

[6] H. Zeng, C.W. Bert. Vibration analysis of a tapered bar by differential transformation [J]. Journal of Sound and Vibration. 2001, (242): 737–739.

DOI: 10.1006/jsvi.2000.3372

[7] C.W. Bert, and H. Zeng, Analysis of axial vibration of compound bars by differential transformation method [J]. Journal of Sound and Vibration. 2004, (275): 641-647.

DOI: 10.1016/j.jsv.2003.06.019

[8] S Momani, VS Ertürk. Solutions of non-linear oscillators by the modified differential transform method [J]. Computers & Mathematics with Applications. 2008, (55): 833-842.

DOI: 10.1016/j.camwa.2007.05.009

[9] Z Odibat, et al. A Multi-step differential transform method and application to non-chaotic and chaotic systems [J]. Computer and mathematics with applications. Accepted. 2010.

DOI: 10.1016/j.camwa.2009.11.005