Research Papers: Structures and Safety Reliability

Theoretical and Applied Insights on Pistons Buckling According to DNV Regulation

[+] Author and Article Information
Nicholas Fantuzzi

Department of Civil, Chemical, Environmental
and Materials Engineering,
University of Bologna,
Viale del Risorgimento 2,
Bologna 40136, Italy
e-mail: nicholas.fantuzzi@unibo.it

Fabio Borgia

Department of Civil, Chemical, Environmental
and Materials Engineering,
University of Bologna,
Viale del Risorgimento 2,
Bologna 40136, Italy
e-mail: fabioborgia42@gmail.com

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received August 25, 2018; final manuscript received November 4, 2018; published online January 17, 2019. Assoc. Editor: Jonas W. Ringsberg.

J. Offshore Mech. Arct. Eng 141(4), 041604 (Jan 17, 2019) (10 pages) Paper No: OMAE-18-1133; doi: 10.1115/1.4041999 History: Received August 25, 2018; Revised November 04, 2018

Pistons are fundamental structural elements in any engineering practices such as mechanical, civil, aerospace, and offshore engineering. Their strength strongly depends on buckling load, and such information is a major requirement in the design process. Euler's linear buckling equation is the most common and most used model in design. It is well suited for linear elastic members without geometrical imperfections and nonlinear behavior. Several analytical and experimental investigations of typical hydraulic cylinders have been carried out through the years but most of the available standards still use a linear approach with many simplifications. Pistons are slender beams with not-uniform cross section, which need a stronger effort than the classical Euler's approach. The present paper aims to discuss limitations of current DNV standards for piston design in offshore technologies when compared to classical numerical approaches and reference results provided by the existing literature.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.


DNVGL, 2017, “Class Guideline: Hydraulic Cylinders,” DNVGL, Oslo, Norway, Standard No. DNVGL-CG-0194.
Timoshenko, S. , 2010, Theory of Elasticity, 3rd ed., McGraw-Hill, New York.
Farghaly, S. H. , 1994, “Vibration and Stability Analysis of Timoshenko Beams With Discontinuities in Cross-Section,” J. Sound Vib., 174(5), pp. 591–605. [CrossRef]
Gamez-Montero, P. J. , Salazar, E. , Castilla, R. , Freire, J. , Khamashta, M. , and Codina, E. , 2009, “Misalignment Effects on the Load Capacity of a Hydraulic Cylinder,” Int. J. Mech. Sci., 51(2), pp. 105–113. [CrossRef]
Borgia, F. , 2017, Kinematic Optimization of an Overboarding Chute Mechanism, University of Bologna, Bologna, Italy.
Fantuzzi, N. , Borgia, F. , Formenti, M. , and Righini, R. , 2018, “Mechanical Optimization of an Innovative Overboarding Chute for Floating Umbilical Systems,” Ocean Eng., (Under review).
Timoshenko, S. , and Gere, J. M. , 1985, Theory of Elastic Stability, 2nd ed., McGraw-Hill, New York.
Eslami, M. R. , 2018, Buckling and Postbuckling of Beams, Plates, and Shells (Structural Integrity), Vol. 1, Springer, Cham, Switzerland.
Lee, H. P. , and Ng, T. Y. , 1994, “Vibration and Buckling of a Stepped Beam,” Appl. Acous., 42(3), pp. 257–266. [CrossRef]
Chen, C.-N. , 2003, “Buckling Equilibrium Equations of Arbitrarily Loaded Nonprismatic Composite Beams and the DQEM Buckling Analysis Using EDQ,” Appl. Math. Model., 27(1), pp. 27–46. [CrossRef]
Ioakimidis, N. I. , 2018, “The Energy Method in Problems of Buckling of Bars With Quantifier Elimination,” Structures, 13, pp. 47–65. [CrossRef]
Gamez-Montero, P. J. , Salazar, E. , Castilla, R. , Freire, J. , Khamashta, M. , and Codina, E. , 2009, “Friction Effects on the Load Capacity of a Column and a Hydraulic Cylinder,” Int. J. Mech. Sci., 51(2), pp. 145–151. [CrossRef]
Nicoletto, G. , and Marin, T. , 2011, “Failure of a Heavy-Duty Hydraulic Cylinder and Its Fatigue Re-Design,” Eng. Failure Anal., 18(3), pp. 1030–1036. [CrossRef]
Tomski, L. , and Uzny, S. , 2011, “A Hydraulic Cylinder Subjected to Euler's Load in Aspect of the Stability and Free Vibrations Taking Into Account Discrete Elastic Elements,” Arch. Civ. Mech. Eng., 11(3), pp. 769–785. [CrossRef]
Narvydas, E. , 2016, “Buckling Strength of Hydraulic Cylinders—An Engineering Approach and Finite Element Analysis,” Mechanika, 22, pp. 474–477.
Tavares, S. M. O. , Viriato, N. , Vaz, M. , and de Castro, P. M. S. T. , 2016, “ Failure Analysis of the Rod of a Hydraulic Cylinder, XV Portuguese Conference on Fracture (PCF 2016), Paço de Arcos, Portugal, Feb. 10–12, pp. 173–180.
Balavignesh, V. N. , Balasubramaniam, B. , and Kotkunde, N. , 2017, “Numerical Investigations of Fracture Parameters for a Cracked Hydraulic Cylinder Barrel and Its Redesign,” Fifth International Conference on Materials Processing and Characterization (ICMPC 2016), Goa Campus, pp. 927–936.
Kuliński, K. , and Przybylski, J. , 2017, “Piezoelectric Effect on Transversal Vibrations and Buckling of a Beam With Varying Cross Section,” Mech. Res. Commun., 82(1), pp. 43–48.
Wang, X. , and Duan, G. , 2014, “Discrete Singular Convolution Element Method for Static, Buckling and Free Vibration Analysis of Beam Structures,” App. Math. Comput., 234, pp. 36–51. [CrossRef]
Konstantakopoulos, T. G. , Raftoyiannis, I. G. , and Michaltsos, G. T. , 2012, “Stability of Steel Columns With Non-Uniform Cross-Sections,” Open Constr. Build. Technol. J., 6, pp. 1–7. [CrossRef]
Naguleswaran, S. , 2005, “Vibration and Stability of Uniform Euler–Bernoulli Beams With Step Change in Axial Force,” Int. J. Mech. Eng. Educ., 33(1), pp. 64–76. [CrossRef]
Naguleswaran, S. , 2003, “Vibration and Stability of an Euler–Bernoulli Beam With up to Three-Step Changes in Cross-Section and in Axial Force,” Int. J. Mech. Sci., 45(9), pp. 1563–1579. [CrossRef]
Ermopoulos, J. C. , 1999, “Buckling Length of Non-Uniform Members Under Stepped Axial Loads,” Comput. Struct., 73(6), pp. 573–582. [CrossRef]
Ferreira, A. J. M. , 2009, MATLAB Codes for Finite Element Analysis, Springer, Berlin, Germany.
Gottlieb, D. , and Orszag, S. A. , 1977, Numerical Analysis of Spectral Methods. Theory and Applications Old Dominion University, Norfolk, VA.
Tornabene, F. , Fantuzzi, N. , Ubertini, F. , and Viola, E. , 2015, “Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey,” ASME Appl. Mech. Rev., 67(1), pp. 1–55. [CrossRef]
Shu, C. , 2000, Differential Quadrature and Its Application in Engineering, Springer-Verlag, London.
Viola, E. , and Tornabene, F. , 2005, “Vibration Analysis of Damaged Circular Arches With Varying Cross Section,” SID-SDHM, 1(2), pp. 155–169. http://www.techscience.com/doi/10.3970/sdhm.2005.001.155.pdf
E., Viola , M., Dilena , F. , and Tornabene, F. , 2007, “Analytical and Numerical Results for Vibration Analysis of Multi-Stepped and Multi-Damaged Circular Arches,” J. Sound Vib., 299(1–2), pp. 143–163. [CrossRef]
Marzani, A. , Tornabene, F. , and Viola, E. , 2008, “Nonconservative Stability Problems Via Generalized Differential Quadrature Method,” J. Sound Vib., 315(1–2), pp. 176–196. [CrossRef]
Viola, E. , Marzani, A. , and Fantuzzi, N. , 2016, “Interaction Effect of Cracks on Flutter and Divergence Instabilities of Cracked Beams Under Subtangential Forces,” Eng. Fract. Mech., 151, pp. 109–129. [CrossRef]
Viola, E. , Miniaci, M. , Fantuzzi, N. , and Marzani, A. , 2015, “Vibration Analysis of Multi-Stepped and Multi-Damaged Parabolic Arches Using GDQ,” Curved Layer Struct., 2(1), pp. 28–49. https://www.researchgate.net/publication/272022310_Vibration_analysis_of_multi-stepped_and_multi-damaged_parabolic_arches_using_GDQ


Grahic Jump Location
Fig. 1

Piston design and current model: (a) main piston components and (b) piston sketch from DNV [1]

Grahic Jump Location
Fig. 2

I2 computed by following DNV certification

Grahic Jump Location
Fig. 3

Fixed free ends configuration

Grahic Jump Location
Fig. 4

Three studied geometries, dimensions in (mm)

Grahic Jump Location
Fig. 5

Deformed configuration for the first mode and buckling loads: (a) geometry 1, (b) geometry 2, and (c) geometry 3

Grahic Jump Location
Fig. 6

Double hinged configuration

Grahic Jump Location
Fig. 7

(a) Piston buckled configuration modeled with 3D FEM and (b) deformation comparison in the first modal shape between 1D and 3D FEM models

Grahic Jump Location
Fig. 8

Dimensionless Z representation by DNV and numerical procedures

Grahic Jump Location
Fig. 9

Piston's elements length



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In