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.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Shabana, A. A., 2005, Dynamics of Multibody Systems, Cambridge University Press, New York.
Sanborn, G. G., and Shabana, A. A., 2009, “On the Integration of Computer Aided Design and Analysis Using the Finite Element Absolute Nodal Coordinate Formulation,” Multibody Syst. Dyn., 22, pp. 81–197. [CrossRef]
Lan, P., and Shabana, A. A., 2010, “Integration of B-Spline Geometry and ANCF Finite Element Analysis,” Nonlin. Dyn., 61, pp. 193–206. [CrossRef]
Yamashita, H., and Sugiyama, H., 2012, “Numerical Convergence of Finite Element Solutions of Non-Rational B-Spline Element and Absolute Nodal Coordinate Formulation,” Nonlin. Dyn., 67, pp. 177–189. [CrossRef]
Mikkola, A., and Shabana, A., 2012, “Comparison Between ANCF and B-Spline Surfaces,” Proceedings of the Second Joint International Conference on Multibody System Dynamics, Stuttgart, Germany.
Hughes, T. J. R., CottrellJ. A., and Bazilevs, Y., 2005, “Isogeometric Analysis: CAD, Finite Elements, NURBS, Exact Geometry and Mesh Refinement,” Comput. Meth. Appl. Mech. Eng., 194, pp. 4135–4195. [CrossRef]
Cottrell, J. A., HughesT. J. R., and Bazilevs, Y., 2009, Isogeometric Analysis: Toward Integration of CAD and FEA, Wiley, United Kingdom.
Piegl, L. A., and Tiller, W., 1996, The NURBS Book, Springer, Berlin.
Shabana, A. A., Hamed, A. M., Mohamed, A. N. A., Jayakumar, P., and Letherwood, M. D., 2012, “Use of B-Spline in the Finite Element Analysis: Comparison With ANCF Geometry,” ASME J. Computat. Nonlin. Dyn., 7(1), p. 011008. [CrossRef]
Dmitrochenko, O., and Pogorelov, D. Y., 2003, “Generalization of Plate Finite Elements for Absolute Nodal Coordinate Formulation,” Multibody Syst. Dyn., 10, pp. 17–43. [CrossRef]
Shabana, A. A., 2008, Computational Continuum Mechanics, Cambridge University Press, New York.
Hughes, T. J. R., Reali, A., and Sangalli, G., 2010, “Efficient Quadrature for NURBS-Based Isogeometric Analysis,” Comput. Meth. Appl. Mech. Eng., 199, pp. 301–313. [CrossRef]
Sugiyama, H., Escalona, J. L., and Shabana, A. A., 2003, “Formulation of Three-Dimensional Joint Constraints Using the Absolute Nodal Coordinates,” Nonlin. Dyn., 31, pp. 167–195. [CrossRef]
Bauchau, O. A., and Bottasso, C. L., 2001, “Contact Conditions for Cylindrical, Prismatic, and Screw Joints in Flexible Multibody Systems,” Multibody Syst. Dyn., 5, pp. 251–278. [CrossRef]
Sugiyama, H., and Yamashita, H., 2011, “Spatial Joint Constraints for the Absolute Nodal Coordinate Formulation Using the Non-Generalized Intermediate Coordinates,” Multibody Syst. Dyn., 26, pp. 15–36. [CrossRef]
Bae, B. S., Han, J. M., and Choi, J. H., 2000, “An Implementation Method for Constrained Flexible Multibody Dynamics Using a Virtual Body and Joint,” Multibody Syst. Dyn., 4, pp. 297–315. [CrossRef]


Grahic Jump Location
Fig. 2

Joint constraint for B-spline element using intermediate reference coordinates

Grahic Jump Location
Fig. 5

Flexible linkage model

Grahic Jump Location
Fig. 6

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

Grahic Jump Location
Fig. 11

Double pendulum sliding on inclined flexible plate

Grahic Jump Location
Fig. 3

Recurrence formula for B-spline basis functions

Grahic Jump Location
Fig. 4

Basis function of B-spline surface

Grahic Jump Location
Fig. 10

Motion of flexible linkage

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
Fig. 8

Comparison of quartic C2 element and cubic C1 element

Grahic Jump Location
Fig. 9

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

Grahic Jump Location
Fig. 12

Motion of double pendulum coupled with flexible plate

Grahic Jump Location
Fig. 13

X coordinates at Points A, B, and C

Grahic Jump Location
Fig. 14

Z coordinates at Points A, B, and C




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In