American Society of Civil Engineers


Buckling Analysis of Nonuniform and Axially Graded Columns with Varying Flexural Rigidity


by Y. Huang, (Lecturer, Ph.D. Candidate, Dept. of Mathematics, Foshan Univ., Foshan, Guangdong 528000; School of Civil Engineering and Architecture, Central South Univ., Changsha 410075, People’s Republic of China.) and X.-F. Li, (corresponding author), (Professor, School of Civil Engineering and Architecture, Central South Univ., Changsha 410075, People’s Republic of China E-mail: xfli@mail.csu.edu.cn)

Journal of Engineering Mechanics, Vol. 137, No. 1, January 2011, pp. 73-81, (doi:  http://dx.doi.org/10.1061/(ASCE)EM.1943-7889.0000206)

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Document type: Journal Paper
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.


ASCE Subject Headings:
Buckling
Critical loads
Bending
Stiffness
Columns

Author Keywords:
Buckling instability
Critical load
Varying bending stiffness
Columns made of FGM
Nonuniform columns