Research Papers

Design of Axially Graded Columns Under a Central Force

[+] Author and Article Information
Roberta Santoro

Dipartimento di Ingegneria Civile,
Informatica, Edile, Ambientale
e Matematica Applicata,
University of Messina,
C.da Di Dio,
98166 Messina, Italy
e-mail: roberta.santoro@unime.it

Isaac Elishakoff

Department of Ocean and Mechanical
Florida Atlantic University,
Boca Raton, FL 33431-0991
e-mail: elishako@fau.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 24, 2010; final manuscript received April 18, 2013; accepted manuscript posted May 6, 2013; published online September 16, 2013. Assoc. Editor: Glaucio H. Paulino.

J. Appl. Mech 81(2), 021001 (Sep 16, 2013) (6 pages) Paper No: JAM-10-1295; doi: 10.1115/1.4024400 History: Received August 24, 2010; Revised April 18, 2013; Accepted May 06, 2013

Structures made of functionally graded materials have attracted much interest recently. The idea is to create a material that fulfills a specified function in accordance to the identified purpose of structure's utilization. In this study, a semi-inverse problem is posed of determining the needed variation of the axial grading of an inhomogeneous column subjected to a central force, generalizing the ungraded column case. Remarkably, it turns out that for a specific combination of parameters, there could exist three different axially graded columns, that possess the same buckling load. Whereas this fact is not immediately apparent, the proposed formulation leads to the design of the axially graded column in such a manner that the buckling load is not less than a prespecified load. Purpose-oriented design demands columns have at least a prespecified buckling load. To solve the problem, a combined analytical-numerical procedure is developed in this study.

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Grahic Jump Location
Fig. 5

Variation of D(ξ)/|b2| for a simply-supported column at both ends (solution 1)

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Fig. 2

Variation of D(ξ)/|b2| for a clamped-pinned column

Grahic Jump Location
Fig. 3

Variation of D(ξ)/|b2| for a column loaded by a central force for different values of αL (-0.9 < αL < -0.3)

Grahic Jump Location
Fig. 4

Variation of D(ξ)/|b2| for a column loaded by a central force for values αL=-0.2 and αL=-0.1

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Fig. 1

Elastic cantilever subjected to a central force

Grahic Jump Location
Fig. 6

Variation D(ξ)/|b2| for a simply-supported column at both ends (a) solution 2, solid line; (b) solution 3, dashed line

Grahic Jump Location
Fig. 7

Variation of D(ξ)/|b2| for a column loaded by a central force for different values of αL (-0.1 < αL < 1) (first possible axial grading)

Grahic Jump Location
Fig. 8

Variation of D(ξ)/|b2| for a column loaded by a central force for different values of αL (-0.1 < αL < 1) (second possible axial grading)

Grahic Jump Location
Fig. 9

Variation of D(ξ)/|b2| for a column loaded by a central force for different values of αL (-0.1 < αL < 1) (third possible axial grading)




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