0
Research Papers

Comparisons of Probabilistic and Two Nonprobabilistic Methods for Uncertain Imperfection Sensitivity of a Column on a Nonlinear Mixed Quadratic-Cubic Foundation

[+] Author and Article Information
Xiaojun Wang

Institute of Solid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100083, P.R.C.xjwang@buaa.edu.cn

Isaac Elishakoff

Department of Mechanical Engineering, Florida Atlantic University, Boca Raton, FL 33431-0991elishako@fau.edu

Zhiping Qiu

Institute of Solid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100083, P.R.C.zpqiu@buaa.edu.cn

Lihong Ma

Institute of Solid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100083, P.R.C.lhma@ase.buaa.edu.cn

J. Appl. Mech 76(1), 011007 (Oct 31, 2008) (8 pages) doi:10.1115/1.2998763 History: Received January 10, 2008; Revised June 20, 2008; Published October 31, 2008

Two nonprobabilistic set-theoretical treatments of the initial imperfection sensitive structure—a finite column on a nonlinear mixed quadratic-cubic elastic foundation—are presented. The minimum buckling load is determined as a function of the parameters, which describe the range of possible initial imperfection profiles of the column. The two set-theoretical models are “interval analysis” and “convex modeling.” The first model represents the range of variation of the most significant N Fourier coefficients by a hypercuboid set. In the second model, the uncertainty in the initial imperfection profile is expressed by an ellipsoidal set in N-dimensional Euclidean space. The minimum buckling load is then evaluated in both the hypercuboid and the ellipsoid. A comparison between these methods and the probabilistic method are performed, where the probabilistic results at different reliability levels are taken as the benchmarks of accuracy for judgment. It is demonstrated that a nonprobabilistic model of uncertainty may be an alternative method for buckling analysis of a column on a nonlinear mixed quadratic-cubic elastic foundation under limited information on initial imperfection.

FIGURES IN THIS ARTICLE
<>
Copyright © 2009 by American Society of Mechanical Engineers
Topics: Stress , Buckling , Modeling
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

A column on a nonlinear mixed quadratic-cubic elastic foundation

Grahic Jump Location
Figure 2

External axial load α versus the additional deflection ξm∗

Grahic Jump Location
Figure 3

Buckling load α∗ versus the initial imperfection amplitude

Grahic Jump Location
Figure 4

Buckling load α∗ from interval analysis

Grahic Jump Location
Figure 5

The ellipse enclosed by a rectangle

Grahic Jump Location
Figure 6

Buckling load α computed from convex modeling

Grahic Jump Location
Figure 7

Probability density function for a truncated normally distributed random variable

Grahic Jump Location
Figure 11

Comparison of the buckling loads computed from probabilistic and nonprobabilistic methods for case of b=1.0: (a) ξ¯c=0.0, and (b) ξ¯c=0.02

Grahic Jump Location
Figure 10

Comparison of the buckling loads computed from probabilistic and nonprobabilistic methods for case of b=0.1: (a) ξ¯c=0.0, and (b) ξ¯c=0.02

Grahic Jump Location
Figure 9

Comparison of the buckling loads computed from probabilistic and nonprobabilistic methods for case of b=1.0: (a) ξ¯c=0.0, and (b) ξ¯c=0.01

Grahic Jump Location
Figure 8

Comparison of the buckling load computed from probabilistic and nonprobabilistic methods for cases of b=0.1: (a) ξ¯c=0.0, and (b) ξ¯c=0.01

Tables

Errata

Discussions

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