Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T06:21:32.000Z Has data issue: false hasContentIssue false
  • English
  • Français

Power Law of Critical Buckling in Structural Members Supported by a Winkler Foundation

Published online by Cambridge University Press:  12 December 2016

M. Sato ,
S. Harasawa ,
Y. Konishi ,
T. Maruyama  and
S. J. Park
M. Sato*
Affiliation:
Division of Engineering and Policy for Sustainable EnvironmentFaculty of EngineeringHokkaido UniversitySapporo, Japan
S. Harasawa
Affiliation:
Division of Engineering and Policy for Sustainable EnvironmentGraduate School of EngineeringHokkaido UniversitySapporo, Japan
Y. Konishi
Affiliation:
Division of Engineering and Policy for Sustainable EnvironmentGraduate School of EngineeringHokkaido UniversitySapporo, Japan
T. Maruyama
Affiliation:
Division of Engineering and Policy for Sustainable EnvironmentGraduate School of EngineeringHokkaido UniversitySapporo, Japan
S. J. Park
Affiliation:
Department of Urban and Environment EngineeringIncheon National UniversityIncheon, Korea
*
*Corresponding author ([email protected])
Get access

Abstract

In the fields of engineering, nanoscience, and biomechanics, thin structural members, such as beams, plates, and shells, that are supported by an elastic medium are used in several applications. There is a possibility that these thin structures might buckle under severe loading conditions; higher-order, complicated elastic buckling modes can be found owing to the balance of rigidities between the thin members and elastic supports. In this study, we have shown a new and simple ‘power law’ relation between the critical buckling strain (or loads) and rigidity parameters in structural members supported by an elastic medium, which can be modelled as a Winkler foundation. The following structural members have been considered in this paper: i) a slender beam held by an outer elastic support under axial loading, ii) cylindrical shells supported by an inner elastic core under hydrostatic pressure (plane strain condition), and iii) complete spherical shells that are filled with an inner elastic medium.

Keywords

Structural memberBucklingWinkler foundationPower law
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 3 , June 2017 , pp. 369 - 374
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Brush, D. O. and Almroth, B. O., Buckling of Bars, Plates, and Shells, McGraw-Hill, Inc., Columbus Ohio, USA, (1975).Google Scholar
2. Yang, H. K. and Wang, X., “Torsional buckling of multi-wall carbon nanotubes embedded in an elastic medium,” Composite Structures, 77, pp. 182–192 (2007).Google Scholar
3. Wang, X., Lu, G. and Lu, Y.J., “Buckling of embedded multi-walled carbon nanotubes under combined torsion and axial loading,” International Journal of Solids and Structures, 44, pp. 336–351 (2007).Google Scholar
4. Sato, M., Taira, H., Ikeda, T. and Shima, H., “Embedding effect on the mechanical stability of pressurised carbon nanotubes,” Journal of Nanomaterials, pp. 767249_1-767249_9 (2013).Google Scholar
5. Esbati, A. H. and Irani, S., “Mechanical properties and fracture analysis of functionalized carbon nanotube embedded by polymer matrix,” Aerospace Science and Technology, 55, pp. 120–130 (2016).Google Scholar
6. Dawson, M. A. and Gibson, L. J., “Optimization of cylindrical shells with compliant cores,” International Journal of Solids and Structures, 44, pp. 1145–1160 (2007).Google Scholar
7. Gibson, L. J. “Biomechanics of cellular solids,” Journal of Biomechanics, 38, pp. 377–399 (2005).Google Scholar
8. Karam, G. N. and Gibson, L. J., “Biomimicking of animal quills and plant stems: natural cylindrical shells with foam cores,” Materials Science and Engineering: C, 2, pp. 113–132 (1994).Google Scholar
9. Hetenyi, M., Beams on Elastic Foundation, The University of Michigan Press, Ann Arbor (1974).Google Scholar
10. Harasawa, S. and Sato, M., “Helical buckling of slender beam structures surrounded by an elastic medium,” Journal of mechanics, 31, pp. 241–247 (2015).Google Scholar
11. Sato, M. and Patel, M. H., “Exact and Simplified Estimations for Elastic Buckling Pressures of Structural Pipe-in-Pipe Cross-sections under External Hydrostatic Pressure,” Journal of Marine Science and Technology, 12, pp. 251–262 (2007).Google Scholar
12. Sato, M., Patel, M. H. and Trarieux, F., “Static Displacement and Elastic Buckling Characteristics of Structural Pipe-in-Pipe Cross-sections,” Structural Engineering and Mechanics, An International Journal, 30, pp. 263–278 (2008).Google Scholar
13. Sato, M., Wadee, M. A., Iiboshi, K., Sekizawa, T. and Shima, H., “Buckling Patterns of Complete Spherical Shells Filled with an Elastic Medium under External Pressure,” International Journal of Mechanical Sciences, 59, pp. 22–30 (2012).Google Scholar
14. Sato, M., Konishi, Y. and Park, S. J., “Interlayer coupling effect on buckling modes of spherical bilayers,” Journal of mechanics, 31, pp. 29–36 (2015).Google Scholar
15. Sato, M. and Ishiwata, Y., “Brazier effect of single and double walled elastic tubes under pure bending,” Structural Engineering and Mechanics, An International Journal, 53, pp. 17–26 (2015).CrossRefGoogle Scholar