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Research Papers

Modeling Beams With Various Boundary Conditions Using Fully Intrinsic Equations

[+] Author and Article Information
Zahra Sotoudeh, Dewey H. Hodges

Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150

Since the numerical values do not represent any specific structure, one can select any consistent system of units, including SI, and thereby obtain the same numerical results as reported here.

J. Appl. Mech 78(3), 031010 (Feb 15, 2011) (9 pages) doi:10.1115/1.4003239 History: Received October 12, 2010; Revised December 08, 2010; Posted December 13, 2010; Published February 15, 2011; Online February 15, 2011

The fully intrinsic equations for beams comprise a relatively new set of equations for nonlinear modeling of structures comprised of beams. These equations are geometrically exact and constitute a closed set of equations even though they include neither displacement nor rotation variables. They do not suffer from the singularities and infinite-degree nonlinearities normally associated with finite rotation variables. In fact, they have a maximum degree of nonlinearity equal to 2. In spite of these and other advantages of these equations, using them for problems with certain boundary conditions may not be straightforward. This paper will examine the challenges of modeling various boundary conditions using fully intrinsic equations, thus helping future researchers to decide whether or not the fully intrinsic equations are suitable for solving a specific problem and elucidating pathways for their application to more general problems.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Sketch of beam kinematics

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Figure 2

Typical element of a beam

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Figure 3

Dimensionless axial force and velocity distribution along a clamped-clamped rotating beam

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Figure 4

Convergence of axial force

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Figure 5

Convergence of shear force

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Figure 6

Convergence of out-of-plane bending moment

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Figure 7

Computational time for incremental method

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Figure 8

Axial displacement along the beam

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Figure 9

Out-of-plane displacement along the beam

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Figure 10

Axial force along the beam

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Figure 11

Shear force along the beam

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Figure 12

Out-of-plane bending moment along the beam

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Figure 13

Schematic of a beam restrained by rotational spring

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Figure 14

Schematic of a beam restrained by longitudinal spring attached to its root

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Figure 15

Real and imaginary parts of the eigenvalues versus angular speed for a rotating beam restrained at its root by a longitudinal spring

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Figure 16

Steady-state axial force distribution, for example, 4

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