Research Papers

A Simple Shear and Torsion-Free Beam Model for Multibody Dynamics

[+] Author and Article Information
Juan Carlos García Orden

ETSI Caminos,
Technical University of Madrid,
c/Profesor Aranguren s/n,
Madrid 28040, Spain
e-mail: juancarlos.garcia@upm.es

Javier Cuenca Queipo

Special Projects Department,
Paseo de la Habana, 138,
Madrid 28036, Spain
e-mail: javier.queipo@ineco.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 14, 2015; final manuscript received February 4, 2017; published online April 17, 2017. Assoc. Editor: Firdaus Udwadia.

J. Comput. Nonlinear Dynam 12(5), 051006 (Apr 17, 2017) (8 pages) Paper No: CND-15-1291; doi: 10.1115/1.4036116 History: Received September 14, 2015; Revised February 04, 2017

This paper describes a very simple beam model, amenable to be used in multibody applications, for cases where the effects of torsion and shear are negligible. This is the case of slender rods connecting different parts of many space mechanisms, models useful in polymer physics, computer animation, etc. The proposed new model follows a lumped parameter method that leads to a rotation-free formulation. Axial stiffness is represented by a standard nonlinear truss model, while bending is modeled with a force potential. Several numerical experiments are carried out in order to assess accuracy, which is usually the main drawback of this type of approach. Results reveal a remarkable accuracy in nonlinear dynamical problems, suggesting that the proposed model is a valid alternative to more sophisticated approaches.

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Fig. 1

Single beam element

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Fig. 2

Beam composed by several elements

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Fig. 3

Simply supported beam with different discretizations: (a) n = 1, (b) n = 3, and (c)n = 5, 7, 9, …

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Fig. 4

Normalized deflections for different discretizations

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Fig. 5

Single beam element, internal forces

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Fig. 6

Linear tests. Convergence of deflection at the load location.

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Fig. 7

Nonlinear test, from Ref. [28]

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Fig. 8

Nonlinear test. Load–deflection curves.

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Fig. 9

Nonlinear test. Convergence of deflections for PL2/EI = 10.

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Fig. 10

Nonlinear test: Z-shaped cantilever

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Fig. 11

Nonlinear test: Z-shaped cantilever. Load versus tip vertical deflection.

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Fig. 12

Spinning beam. Endpoint deflection versus time, 40 elements.

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Fig. 13

Spinning beam. Convergence of maximum endpoint deflection, Δt = 0.01 s.

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Fig. 14

Flexible slider–crank. Deflection of the flexible rod midpoint.

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Fig. 15

Flexible slider–crank. Convergence of midpoint deflection during four turns, Δt = 0.0001 s.

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Fig. 16

Flexible spatial double pendulum, from Ref. [31]

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Fig. 17

Flexible double pendulum. X-displacement of point B versus time with ten elements, integrated with trapezoidal rule, Δt = 0.001 s.

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Fig. 18

Flexible double pendulum. X-displacement of point B versus time with ten elements, E = 0.06 GPa, Δt = 0.001 s.

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Fig. 19

Flexible double pendulum. Convergence of the X-displacement of point B, E = 0.06 GPa, Δt = 0.001 s.




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