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A general way of obtaining novel closed-form solutions for functionally graded columns

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Abstract

In this paper, we present a general methodology for solving buckling problems for inhomogeneous columns. Columns that are treated are functionally graded in axial direction. The buckling mode is postulated as the general order polynomial function that satisfies all boundary conditions. For specificity, we concentrate on the boundary conditions of simple support, and employ the second-order ordinary differential equation that governs the buckling behavior. A quadratic polynomial is adopted for the description of the column’s flexural rigidity. Satisfaction of the governing differential equation leads to a set of nonlinear algebraic equations that are solved exactly. In addition to the recovery of the solutions previously found by Duncan and Elishakoff, several new solutions are arrived at.

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Acknowledgements

Authors appreciate constructive comments of the anonymous reviewers.

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Authors and Affiliations

  1. Faculty of Civil and Environmental Engineering, Technical-Israel Institute of Technology, Haifa, 32000, Israel

    Moshe Eisenberger

  2. Department of Ocean and Mechanical Engineering, Florida Atlantic University, Boca Raton, FL, 33431, USA

    Isaac Elishakoff

Authors
  1. Moshe Eisenberger
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  2. Isaac Elishakoff
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Correspondence to Isaac Elishakoff.

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Eisenberger, M., Elishakoff, I. A general way of obtaining novel closed-form solutions for functionally graded columns. Arch Appl Mech 87, 1641–1646 (2017). https://doi.org/10.1007/s00419-017-1278-1

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  • DOI: https://doi.org/10.1007/s00419-017-1278-1

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