Buckling Analysis of Nonuniform and Axially Graded Columns with Varying Flexural Rigidity
Publication: Journal of Engineering Mechanics
Volume 137, Issue 1
Abstract
In this paper, we present a novel analytic approach to solve the buckling instability of Euler-Bernoulli columns with arbitrarily axial nonhomogeneity and/or varying cross section. For various columns including pinned-pinned columns, clamped columns, and cantilevered columns, the governing differential equation for buckling of columns with varying flexural rigidity is reduced to a Fredholm integral equation. Critical buckling load can be exactly determined by requiring that the resulting integral equation has a nontrivial solution. The effectiveness of the method is confirmed by comparing our results with existing closed-form solutions and numerical results. Flexural rigidity may take a majority of functions including polynomials, trigonometric and exponential functions, etc. Examples are given to illustrate the enhancement of the load-carrying capacity of tapered columns for admissible shape profiles with constant volume or weight, and the proposed method is of benefit to optimum design of columns against buckling in engineering applications. This method can be further extended to treat free vibration of nonuniform beams with axially variable material properties.
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Acknowledgments
The writers would like to thank three anonymous reviewers for their helpful suggestions for improving the original manuscript. This work was supported by the NSFC (Grant No. NSFC10672189) and by SRF for ROCS, SEM, China.
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Information
Published In
Journal of Engineering Mechanics
Volume 137 • Issue 1 • January 2011
Pages: 73 - 81
Copyright
© 2011 ASCE.
History
Received: Jan 5, 2010
Accepted: Jul 26, 2010
Published online: Jul 28, 2010
Published in print: Jan 2011
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