This paper is concerned with the 2D elasticity solution for the buckling of a thick orthotropic ring under external hydrostatic pressure loading. The bifurcation buckling problem is first formulated using two methods, distinguished by the manner in which the external work done by the pressure loading during the buckling transition is treated. In doing so, the correct buckling equations and associated traction boundary conditions are derived. The resulting sets of equations and associated boundary conditions are then cast in a weak form, amenable to a numerical solution using the finite element method. The necessity of using the correct pairs of energetically conjugate stress and strain measures for the buckling problem is pointed out. Errors in using the incorrect traction boundary condition and terms that influence the buckling load and that have been omitted in popular commercial codes are pointed out and their significance in influencing the buckling load is identified. Results from the present two-dimensional analysis to predict the critical pressure are compared with previous theoretical results. The formulation and results presented here can be used as the correct benchmark solution to establish the accuracy in computing the buckling load of thick orthotropic composite structures, of contemporary interest, due to the increased use of thick-walled composite shell type structures in diverse engineering applications.
Skip Nav Destination
Article navigation
January 2014
Research-Article
The Two-Dimensional Elasticity Solution for the Buckling of a Thick Orthotropic Ring Under External Pressure Loading
Anthony M. Waas
Anthony M. Waas
1
Felix Pawlowski Collegiate Professor
e-mail: dcw@umich.edu
Department of Aerospace Engineering,
Composite Structures Laboratory,
e-mail: dcw@umich.edu
Department of Aerospace Engineering,
Composite Structures Laboratory,
University of Michigan
,Ann Arbor, MI 48109
1Corresponding author.
Search for other works by this author on:
Wooseok Ji
Research Fellow
Anthony M. Waas
Felix Pawlowski Collegiate Professor
e-mail: dcw@umich.edu
Department of Aerospace Engineering,
Composite Structures Laboratory,
e-mail: dcw@umich.edu
Department of Aerospace Engineering,
Composite Structures Laboratory,
University of Michigan
,Ann Arbor, MI 48109
1Corresponding author.
Manuscript received November 12, 2012; final manuscript received January 25, 2013; accepted manuscript posted February 14, 2013; published online August 22, 2013. Editor: Yonggang Huang.
J. Appl. Mech. Jan 2014, 81(1): 011005 (12 pages)
Published Online: August 22, 2013
Article history
Received:
November 12, 2012
Revision Received:
January 25, 2013
Accepted:
February 14, 2013
Citation
Ji, W., and Waas, A. M. (August 22, 2013). "The Two-Dimensional Elasticity Solution for the Buckling of a Thick Orthotropic Ring Under External Pressure Loading." ASME. J. Appl. Mech. January 2014; 81(1): 011005. https://doi.org/10.1115/1.4023682
Download citation file:
Get Email Alerts
Cited By
Hamiltonian System-Based Symplectic Framework for Analytical Vibration Analysis of Microplates
J. Appl. Mech (December 2024)
Related Articles
Postbuckling of Shear Deformable Geodesically Stiffened Anisotropic Laminated Cylindrical Shell Under External Pressure
J. Pressure Vessel Technol (April,2011)
Nonlinear Buckling and Postbuckling Behavior of 3D Braided Composite Cylindrical Shells Under External Pressure Loads in Thermal Environments
J. Pressure Vessel Technol (December,2009)
Buckling of Barreled Shells Subjected to External Hydrostatic Pressure
J. Pressure Vessel Technol (May,2001)
Buckling of Unstiffened Steel Cones Subjected to Axial Compression and External Pressure
J. Offshore Mech. Arct. Eng (August,2012)
Related Chapters
Subsection NB—Class 1 Components
Companion Guide to the ASME Boiler and Pressure Vessel Code, Volume 1, Third Edition
Openings
Guidebook for the Design of ASME Section VIII Pressure Vessels
Part 2, Section II—Materials and Specifications
Companion Guide to the ASME Boiler and Pressure Vessel Code, Volume 1, Third Edition