BUCKLING OF SIMPLY SUPPORTED – CLAMPED FUNCTIONALLY GRADED MATERIAL COLUMNS: NEW CLOSED-FORM SOLUTIONS

Author Type

Faculty

Co-Author Type 1

Faculty

Co-Author Type 2

Outside Researcher

Co-Author Type 3

Outside Researcher

College

Engineering and Computer Science

Department

Ocean and Mechanical Engineering

Document Type

Article

Publication/Event/Conference Title

Journal of Mechanics of Materials and Structures

Publication Status

Version of Record

Abstract

This study deals with the buckling of inhomogeneous columns whose flexural rigidity is graded along the axial direction, being simply supported at one end and clamped at the other. The buckling load, mode shape, and grading profile are jointly analyzed under the requirement that the mode shape be of polynomial form. Satisfaction of the governing differential equation leads to a set of polynomial equations in the coefficients of the shape polynomial. This system of polynomial equations is amenable to solution in terms of an appropriately chosen algebraic number. Thus we find new solutions in analytic form associated to polynomials ranging from order four to seven. The method, introduced by Eisenberger and Elishakoff (2017) for a column simply supported at both ends, can in principle provide polynomial solutions or any order; in addition, solutions associated to lower-degree polynomials reappear in higher degrees. It is remarkable that multiple solutions can appear for the postulated polynomial of a certain degree.

First Page

19

Last Page

33

DOI

10.2140/jomms.2022.17.19

Publication Date

1-1-2022

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