Stability analysis of nonuniform rectangular beams using homotopy perturbation method. (English) Zbl 1264.74286
Summary: The design of slender beams, that is, beams with large laterally unsupported lengths, is commonly controlled by stability limit states. Beam buckling, also called “lateral torsional buckling,” is different from column buckling in that a beam not only displaces laterally but also twists about its axis during buckling. The coupling between twist and lateral displacement makes stability analysis of beams more complex than that of columns. For this reason, most of the analytical studies in the literature on beam stability are concentrated on simple cases: uniform beams with ideal boundary conditions and simple loadings. This paper shows that complex beam stability problems, such as lateral torsional buckling of rectangular beams with variable cross-sections, can successfully be solved using homotopy perturbation method (HPM).
MSC:
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74G60 | Bifurcation and buckling |
References:
| [1] | S. P. Timoshenko and J. M. Gere, Theory of Elastic Stability, McGraw-Hill Book Co., New York, NY, USA, 2nd edition, 1961. |
| [2] | A. Chajes, Principles of Structural Stability Theory, Prentice Hall, Englewood Cliffs, NJ, USA, 1974. |
| [3] | C. M. Wang, C. Y. Wang, and J. N. Reddy, Exact Solutions for Buckling of Structural Members, CRC Press, Boca Raton, Fla, USA, 2005. |
| [4] | G. J. Simitses and D. H. Hodges, Fundamentals of Structural Stability, Elsevier, New York, NY, USA, 2006. · Zbl 1112.74001 |
| [5] | J.-H. He, “A review on some new recently developed nonlinear analytical techniques,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 1, no. 1, pp. 51-70, 2000. · Zbl 0966.65056 · doi:10.1515/IJNSNS.2000.1.1.51 |
| [6] | J.-H. He, “Homotopy perturbation technique,” Computer Methods in Applied Mechanics and Engineering, vol. 178, no. 3-4, pp. 257-262, 1999. · Zbl 0956.70017 · doi:10.1016/S0045-7825(99)00018-3 |
| [7] | J.-H. He, “Recent development of the homotopy perturbation method,” Topological Methods in Nonlinear Analysis, vol. 31, no. 2, pp. 205-209, 2008. · Zbl 1159.34333 |
| [8] | S. B. Co\cskun, “Determination of critical buckling loads for euler columns of variable flexural stiffness with a continuous elastic restraint using homotopy perturbation method,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 10, no. 2, pp. 191-197, 2009. |
| [9] | S. B. Co\cskun, “Analysis of tilt-buckling of Euler columns with varying flexural stiffness using homotopy perturbation method,” Mathematical Modelling and Analysis, vol. 15, no. 3, pp. 275-286, 2010. · Zbl 1428.74084 · doi:10.3846/1392-6292.2010.15.275-286 |
| [10] | M. T. Atay, “Determination of critical buckling loads for variable stiffness euler columns using homotopy perturbation method,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 10, no. 2, pp. 199-206, 2009. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
