Analisis Tekuk Nonlinier (Nonlinear Buckling) pada Struktur Fleksibel Tinggi (Highly Flexible Structures)

Anwar Dolu; Amrinsyah  Nasution; Agus Rivani

doi:10.22487/renstra.v7i2.881

Authors

Anwar Dolu Jurusan Teknik Sipil, Fakultas Teknik Universitas Tadulako, Palu, Indonesia
Amrinsyah Nasution Jurusan Teknik Sipil, Fakultas Teknik Sipil dan Perencanaan, Institut Teknologi Bandung (ITB), Bandung, Indonesia
Agus Rivani Jurusan Teknik Sipil, Fakultas Teknik Universitas Tadulako, Palu, Indonesia 94112

DOI:

https://doi.org/10.22487/renstra.v7i2.881

Keywords:

highly flexible structure (HFS), Euler buckling, nonlinear buckling, elliptic integral, post-buckling

Abstract

In contemporary construction engineering, many structural systems adopt slender and flexible models known as Highly Flexible Structures (HFS), as a result of efforts to minimize structural dimensions and weight while improving efficiency and aerodynamic design. This study examines the nonlinear buckling phenomenon in cantilever structures. The analytical solution for the nonlinear buckling case is obtained by solving the first and second kinds of elliptic integrals. The values of the elliptic integrals are computed using the open-source software R (RStudio). The analysis results under nonlinear buckling conditions show that the critical load obtained is greater than the Euler critical load at the onset of initial buckling, also referred to as the post-buckling load. The critical load is P=4,315EI/L^2, with a maximum lateral deflection of xmax=0,8063.L , and axial deflection of dy=0,1947.L . Based on the load–lateral displacement (x-direction) curve during the post-buckling stage, the load increases beyond the Euler buckling load while the lateral displacement decreases after reaching the maximum lateral deflection. In contrast, the load–axial displacement curve shows that displacement tends to increase proportionally with increasing load.

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References

P.F. Pai, Highly Flexible Structures: Modeling, Computation, and Experimentation, Reston, VA, USA: American Institute of Aeronautics and Astronautics, 2007.

A. Ohtsuki, “Analysis of the Characteristics of Fishing Rods Based on the Large-Deformation Theory,” Materials and Science in Sports, pp. 161–170, 2001.

A.B. Sotiropoulou and D.E. Panayotounakos, “Exact Parametric Analytic Solutions of the Elastica ODEs for Bars Including Effects of the Transverse Deformation,” International Journal of Non-Linear Mechanics, vol. 39, pp. 1555-1570, 2004 https://doi.org/10.1016/j.ijnonlinmec.2003.09.004.

A. Abolfathi, M.J. Brennan, and T.P. Waters, “Large Deflection of a Simply Supported Beam,” ISVR Technical Memorandum, no. 988, Institute of Sound and Vibration Research, University of Southampton, Southampton, UK, 2010.

A. Khavvaji, M.H. Pashaei, M. Dardel, and R.A. Alashti, “Large Deflection Analysis of Compliant Beams of Variable Thickness and Non-Homogenous Material under Combined Load and Multiple Boundary Conditions,” IJE Transactions C: Aspects, vol. 25, no. 4, pp. 353–362, 2012.

S.P. Timoshenko and J.M. Gere, Theory of Elastic Stability, 2nd ed., New York, USA: McGraw-Hill Book Company, 1961.

P. Villaggio, Mathematical Models for Elastic Structures, Cambridge, UK: Cambridge University Press, 1997 https://doi.org/10.1017/CBO9780511529665.

I.S. Sokolnikoff and R.M. Redheffer, Mathematics of Physics and Modern Engineering, 2nd ed., New York, USA: McGraw-Hill Book Company, 1966.

M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 10th printing, Washington, DC, USA: U.S. Government Printing Office, National Bureau of Standards, Applied Mathematics Series 55, 1972.

N.G.R. Iyengar, Structural Stability of Columns and Plates, Chichester, UK: Ellis Horwood Limited, 1988.

M. Sathyamoorthy, Nonlinear Analysis of Structures, Boca Raton, FL, USA: CRC Press, 1998.

D.G. Fertis, Nonlinear Mechanics, Boca Raton, FL, USA: CRC Press, 1999.

G.M. Scarpello and D. Ritelli, “Elliptic Integral Solutions of Spatial Elastica of a Thin Straight Rod Bent Under Concentrated Terminal Forces,” Meccanica, vol. 41, no. 5, pp. 519–527, 2006 https://doi.org/10.1007/s11012-006-9000-3.

A. Zhang and G. Chen, “A Comprehensive Elliptic Integral Solution to the Large Deflection Problems of Thin Beams in Compliant Mechanisms,” Journal of Mechanisms and Robotics, vol. 5, no. 2, 021006, 2013 https://doi.org/10.1115/1.4023558.

A. Heck, Introduction to Maple, 3rd ed., New York, USA: Springer Science+Business Media, 2003, 828 pp. https://doi.org/10.1007/978-1-4613-0023-6.

R Core Team, The R v4.6.1 Manuals, 2026. https://rstudio.github.io/r-manuals/, accessed June 19, 2026.

T. Beléndez, C. Neipp, and A. Beléndez, “Large and Small Deflections of a Cantilever Beam,” European Journal of Physics, vol. 23, no. 3, pp. 371–379, 2002 https://doi.org/10.1088/0143-0807/23/3/317.

W.C. Young and R.G. Budynas, Roark's Formulas for Stress and Strain, 7th ed., New York, USA: McGraw-Hill Companies, Inc., 2002.

T.X. Yu and W. Johnson, “The Plastica: The Large Elastic-Plastic Deflection of a Strut,” International Journal of Non-Linear Mechanics, vol. 17, no. 3, pp. 195–209, 1982 https://doi.org/10.1016/0020-7462(82)90019-1.

W.J. Stronge and T.X. Yu, Dynamic Models for Structural Plasticity, London, UK: Springer-Verlag, 1995. https://doi.org/10.1007/978-1-4471-0397-4.