Introduction to Nonlinear Buckling Analysis – Part 1
Mar 31, 2015 News Archive
There are two major categories for mechanical failure for a structural steel component: material failure and stability (or buckling). Thus a proper buckling analysis is an essential part of the assessment checks for any offshore structure. The buckling strength of common structures is very well documented and typically easily analyzed using empirical formulas published by multiple classification societies. However; novel structures are quite common within the offshore industry and determining the applicable formulas can be difficult.
Typically an engineer will resort to extremely conservative assumptions to assure that a novel structure is not at risk for buckling failure. This still does not provide complete assurance that all buckling modes were considered and can result in excessive structure.
A proper buckling analysis using finite element methods provides an alternative to the empirical formulations. For novel structures, both the formulations provided by class and a finite element method may be necessary to assure the adequacy of the structure. As ABS [Ref 3] notes,
“If appropriate documentation is presented, proven numerical methods [FEM] to establish the buckling strength of structural components subjected to various loads and their combinations are accepted as an alternative to the formulations presented in the previous Sections of this Guide. In some cases, especially those involving novel structural designs and loading situations, reliance on such analytical methods are to be pursued to provide added assurance of a proposed design’s adequacy.”
There are two common methods for performing a finite element buckling analysis:
1. Eigenvalue buckling analysis
2. Nonlinear buckling analysis
An eigenvalue analysis predicts the theoretical buckling strength of an ideal elastic structure [Ref 5]. While this analysis can provide an indication of the potential areas of concern for buckling, the quantitative results are typically non-conservative. This is because certain characteristics inherent to a real world structure typically result in a lower buckling strength than the ideal structure. Thus an eigenvalue analysis should only be seen as a qualitative check of areas of concern.
To obtain results of the buckling strength of a structure, a nonlinear buckling analysis must be considered. The proper application of a nonlinear buckling analysis involves the inclusion of numerous variables that must be considered carefully. Hughes and Paik [Ref 4] note that,
“The accuracy of nonlinear finite element method solutions is governed by the ability of the structural modeling techniques to idealize various factors of influence, including geometric and material properties, load application, boundary conditions, and initial imperfections.”
A short literature review of the rules and guidelines from three major classification societies provides for the different characteristics to be considered within a nonlinear buckling analysis. A summary of the review is provided within the following Table.
From the literature it is evident that the following factors must be considered within a nonlinear buckling analysis:
• Material Nonlinearity
• Construction Tolerances and Material Imperfections
• Residual Stresses
Future articles will focus on the application of these factors to a nonlinear buckling analysis along with the proper modeling techniques and boundary conditions.
- Bureau Veritas. NR 445.B1. Rules for the Classification of Offshore Units, Part B – Structural Safety. April 2013.
- DNV. DNV-RP-C202. Buckling Strength of Shells. January 2013.
- American Bureau of Shipping. Guide for Buckling and Ultimate Strength Assessment for Offshore Structures. February 2014.
- Hughes, Owen F. and Paik, Jeom Kee. Ship Structural Analysis and Design. 2010.
- ANSYS. ANSYS Help Viewer. Version 15.0.0. 2013.