Unimodal Optimization of Axially Compressed Shear Deformable Columns

Year 2019, Volume: 5 Issue: 2, 100 - 104, 31.07.2019

İzzet Ufuk Çagdaş

https://doi.org/10.22399/ijcesen.591907

Abstract

In this study, the
unimodal optimality conditions for axially compressed shear deformable columns
are formulated and the optimal design problems defined are numerically solved
using an iterative procedure based on the finite element method. The results
presented show that the optimization results are more reliable than the ones
obtained using classical beam theory as cross-sectional  area does not vanish at points where the
bending moment is equal to zero.

Keywords

Optimal column, shear deformation, optimality condition, iterative solution

Thanks

The author is grateful to Prof. Sarp Adali for his generous support during this research study.

References

• [1]. C.M. Wang, C.Y. Wang, J.N. Reddy, ‘Exact Solutions for buckling of structural members’, CRC Press, Florida, USA, 2005.
• [2]. M.J. Maurizi, P.M. Belles, Comments on ‘The effect of shear deformations on the critical buckling of columns’. Journal of Sound and Vibration, 185:5, 908-909, 1995.
• [3]. J.B. Kosmatka, An improved two-node finite element for stability and natural frequencies of axial-loaded timoshenko beams. Computers & Structures, 57:1, 141-149, 1995.
• [4]. J.R. Banarjee, F.W. Williams, The effect of shear deformation on the critical buckling of columns. Journal of Sound and Vibration, 174:5, 607-616, 1994.
• [5]. C.M. Wang, R.P.S. Han, A further note on the effect of shear deformation on the critical buckling of columns. Journal of Sound and Vibration, 185:5, 895-896, 1995.
• [6]. Cagdas, I. U., & Adali, S. Optimization of clamped columns under distributed axial load and subject to stress constraints. Engineering Optimization, 39(4), 453-469, 2007.
• [7]. Adali, S., & Cagdas, I. U. Optimal design of simply supported columns subject to distributed axial load and stress constraint. Optimal Control Applications and Methods, 30(5), 505-520, 2009.
• [8]. Cagdas, I. U., & Adali, S. Optimal shapes of clamped–simply supported columns under distributed axial load and stress constraint. Engineering Optimization, 45(2), 123-139, 2013.
• [9]. H. Ziegler, Arguments for and against Engesser’s buckling formulas. Ingenieur-Archiv, 52, 105-113, 1982.
• [10]. Haichang Hu, Variational Principles of Theory of Elasticity with Applications. Gordon and Breach, Science Publishers Inc., NY, 1984.
• [11]. Hinton E, Owen D.P., Finite element programming. AW Billitt, Droitwich, 1977.