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Research Papers

An Exact Three-Dimensional Beam Element With Nonuniform Cross Section

[+] Author and Article Information
M. Jafari

School of Mechanical Engineering, College of Engineering, University of Tehran, Campus No. 2, Tehran, Iranm.jafari@hotmail.com

M. J. Mahjoob

School of Mechanical Engineering, College of Engineering, University of Tehran, Campus No. 2, Tehran, Iranmmahjoob@ut.ac.ir

The calculations is done on MATLAB R12 Symbolic math toolbox, Pentium III processor 1 GHz, 640 MB of RAM.

General curved beam element with constant strains and constant curvatures.

General curved beam element with linear strains and linear curvatures.

J. Appl. Mech 77(6), 061009 (Aug 20, 2010) (7 pages) doi:10.1115/1.4002000 History: Received September 25, 2008; Revised June 12, 2010; Posted June 17, 2010; Published August 20, 2010; Online August 20, 2010

In this paper, the exact stiffness matrix of curved beams with nonuniform cross section is derived using direct method. The considered element has two nodes and 12 degrees of freedom, with three forces and three moments applied at each node. The noncoincidence effect of shear center and center of area is also considered in this element. The deformations of the beam are due to bending, torsion, tensile, and shear loads. The line passing through center of area is a general three-dimensional curve and the cross section properties may change arbitrarily along it. The method is extended to deal with distributed loads on the curved beams. The stiffness matrix of some selected types of beams is determined by this method. The results are compared (where possible) with previously published results, simple beam finite element analysis and analytic solution. It is shown that the determined stiffness matrix is exact and that any type of beam can be analyzed by this method.

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Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 8

Straight beam with varying C-shape cross section

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Figure 7

Schematic of the helical spring and loading on its free end

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Figure 6

Distributed load on a tapered beam

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Figure 5

Pinched circular ring and its quarter model

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Figure 4

Distributed load on a curved beam

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Figure 3

Constrained beam loaded at the free end

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Figure 2

Cross section of beam and local coordinates

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Figure 1

Three-dimensional general curved beam

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