Research Papers

Sliding and Nonsliding Joint Constraints of B-Spline Plate Elements for Integration With Flexible Multibody Dynamics Simulation

[+] Author and Article Information
Yuta Mizuno

Department of Mechanical Engineering
Tokyo University of Science,
Tokyo 125-8585, Japan

Hiroyuki Sugiyama

Department of Mechanical and
Industrial Engineering,
The University of Iowa,
2416 C Seamans Center,
Iowa City, IA 52242
e-mail: hiroyuki-sugiyama@uiowa.edu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received August 22, 2012; final manuscript received April 17, 2013; published online September 25, 2013. Assoc. Editor: Aki Mikkola.

J. Comput. Nonlinear Dynam 9(1), 011001 (Sep 25, 2013) (10 pages) Paper No: CND-12-1129; doi: 10.1115/1.4025277 History: Received August 22, 2012; Revised April 17, 2013

In this investigation, a numerical procedure for modeling sliding and nonsliding joint constraints for the B-spline thin plate element is developed for the large deformation analysis of multibody systems. A concept of intermediate reference coordinates proposed for the absolute nodal coordinate formulation is generalized for B-spline elements such that a wide variety of joint constraints can be modeled using existing joint constraint libraries already implemented in multibody dynamics codes. This procedure allows for modeling sliding joints for B-spline elements that requires a solution to moving boundary problems by introducing time-variant surface parameters in the B-spline parametric domain. Since surface parameters treated as knot variables in the basis function are defined in the entire parametric domain rather than the element domain, the location of the constraint definition point can be determined without knowing in which elements the sliding point is located. Furthermore, using the B-spline recurrence formula, control points used for describing the constraint equations can be systematically extracted. It is shown that many types of nonsliding joints fixed on the flexible body can also be modeled as a special case of the sliding joint formulation developed in this investigation, leading to a unified joint constraint formulation for B-spline elements. Several numerical examples are presented in order to demonstrate the use of the numerical procedure developed in this investigation.

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Fig. 2

Joint constraint for B-spline element using intermediate reference coordinates

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Fig. 5

Flexible linkage model

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Fig. 6

X, Y, and Z coordinates at points A (quartic C2 element)

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Fig. 13

X coordinates at Points A, B, and C

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Fig. 14

Z coordinates at Points A, B, and C

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Fig. 3

Recurrence formula for B-spline basis functions

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Fig. 4

Basis function of B-spline surface

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Fig. 7

X, Y, and Z coordinates at points A (cubic C1 element)

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Fig. 8

Comparison of quartic C2 element and cubic C1 element

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Fig. 9

X, Y, and Z coordinates at points B (quartic C2 element; DOF = 1351)

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Fig. 10

Motion of flexible linkage

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Fig. 11

Double pendulum sliding on inclined flexible plate

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Fig. 12

Motion of double pendulum coupled with flexible plate




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