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Research Papers

Ideal Compliant Joints and Integration of Computer Aided Design and Analysis

[+] Author and Article Information
Ashraf M. Hamed, Antonio M. Recuero, Ahmed A. Shabana

Department of Mechanical
and Industrial Engineering,
University of Illinois at Chicago,
842 West Taylor Street,
Chicago, IL 60607

Paramsothy Jayakumar, Michael D. Letherwood, David J. Gorsich

U.S. Army RDECOM-TARDEC,
6501 E. 11 Mile Road,
Warren, MI 48397-5000

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 5, 2013; final manuscript received June 26, 2014; published online January 12, 2015. Assoc. Editor: Dan Negrut.

This material is declared a work of the US Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.

J. Comput. Nonlinear Dynam 10(2), 021015 (Mar 01, 2015) (14 pages) Paper No: CND-13-1316; doi: 10.1115/1.4027999 History: Received December 05, 2013; Revised June 26, 2014; Online January 12, 2015

This paper discusses fundamental issues related to the integration of computer aided design and analysis (I-CAD-A) by introducing a new class of ideal compliant joints that account for the distributed inertia and elasticity. The absolute nodal coordinate formulation (ANCF) degrees of freedom are used in order to capture modes of deformation that cannot be captured using existing formulations. The ideal compliant joints developed can be formulated, for the most part, using linear algebraic equations, allowing for the elimination of the dependent variables at a preprocessing stage, thereby significantly reducing the problem dimension and array storage needed. Furthermore, the constraint equations are automatically satisfied at the position, velocity, and acceleration levels. When using the proposed approach to model large scale chain systems, differences in computational efficiency between the augmented formulation and the recursive methods are eliminated, and the central processing unit (CPU) times resulting from the use of the two formulations become similar regardless of the complexity of the system. The elimination of the joint constraint equations and the associated dependent variables also contribute to the solution of a fundamental singularity problem encountered in the analysis of closed loop chains and mechanisms by eliminating the need to repeatedly change the chain or mechanism independent coordinates. It is shown that the concept of the knot multiplicity used in computational geometry methods, such as B-spline and NURBS (nonuniform rational B-spline), to control the degree of continuity at the breakpoints is not suited for the formulation of many ideal compliant joints. As explained in this paper, this issue is closely related to the inability of B-spline and NURBS to model structural discontinuities. Another contribution of this paper is demonstrating that large deformation ANCF finite elements can be effective, in some multibody systems (MBS) applications, in solving small deformation problems. This is demonstrated using a heavily constrained tracked vehicle with flexible-link chains. Without using the proposed approach, modeling such a complex system with flexible links can be very challenging. The analysis presented in this paper also demonstrates that adding significant model details does not necessarily imply increasing the complexity of the MBS algorithm.

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References

Hamed, A. M., 2014, “New Finite Element Mesh for Efficient Modelling of Spatial Flexible Link Articulated Systems,” Ph.D. dissertation, University of Illinois at Chicago, Chicago, IL.
Shabana, A. A., 2014, Dynamics of Multibody Systems, 4th ed., Cambridge University, Cambridge, UK.
Korkealaakso, P., Mikkola, A., Rantalainen, T., and Rouvinen, A., 2009, “Description of Joint Constraints in the Floating Frame of Reference Formulation,” Proc. Inst. Mech. Eng., Part K, 223(2), pp. 133–144. [CrossRef]
Shabana, A. A., Hamed, A. M., Mohamed, A. A., Jayakumar, P., and Letherwood, M. D., 2012, “Use of B-spline in the Finite Element Analysis: Comparison With ANCF Geometry,” ASME J. Comput. Nonlinear Dyn., 7(4), pp. 81–88. [CrossRef]
Hamed, A. M., Shabana, A. A., Jayakumar, P., and Letherwood, M. D., 2011, “Non-Structural Geometric Discontinuities in Finite Element/Multibody System Analysis,” Nonlinear Dyn., 66(4), pp. 809–824. [CrossRef]
Shabana, A. A., 2010, “General Method for Modeling Slope Discontinuities and T-Sections Using ANCF Gradient Deficient Finite Elements,” ASME J. Comput. Nonlinear Dyn., 6(2), p. 024502. [CrossRef]
Shabana, A. A., 2012, Computational Continuum Mechanics, Cambridge University, Cambridge, UK.
Dmitrochenko, O. N., and Pogorelov, D. Y., 2003, “Generalization of Plate Finite Elements for Absolute Nodal Coordinate Formulation,” Multibody Syst. Dyn., 10(1), pp. 17–43. [CrossRef]
Abbas, L. K., Rui, X., and Hammoudi, Z. S., 2010, “Plate/Shell Element of Variable Thickness Based on the Absolute Nodal Coordinate Formulation,” Proc. Inst. Mech. Eng., Part K, 224(2), pp. 127–141. [CrossRef]
Dufva, K. E., Sopanen, J. T., and Mikkola, A. M., 2005, “A Two-Dimensional Shear Deformable Beam Element Based on the Absolute Nodal Coordinate Formulation,” J. Sound Vib., 280(3–5), pp.719–738. [CrossRef]
Dufva, K., Kerkkänen, K., Maqueda, L. G., and Shabana, A. A., 2007, “Nonlinear Dynamics of Three-Dimensional Belt Drives Using the Finite-Element Method,” Nonlinear Dyn., 48(4), pp. 449–466. [CrossRef]
Schwab, A. L., and Meijaard, J. P., 2010, “Comparison of Three-Dimensional Flexible Beam Elements for Dynamic Analysis: Classical Finite Element Formulation and Absolute Nodal Coordinate Formulation,” ASME J. Comput. Nonlinear Dyn., 5(1), p. 011010. [CrossRef]
Shabana, A. A., and Mikkola, A. M., 2003, “Use of the Finite Element Absolute Nodal Coordinate Formulation in Modeling Slope Discontinuity,” ASME J. Mech. Des., 125(2), pp. 342–350. [CrossRef]
Tian, Q., Chen, L. P., Zhang, Y. Q., and Yang, J. Z., 2009, “An Efficient Hybrid Method for Multibody Dynamics Simulation Based on Absolute Nodal Coordinate Formulation,” ASME J. Comput. Nonlinear Dyn., 4(2), p. 021009. [CrossRef]
Yakoub, R. Y., and Shabana, A. A., 2001, “Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Implementation and Application,” ASME J. Mech. Des., 123(4), pp. 614–621. [CrossRef]
Omar, M. A., and Shabana, A. A., 2001, “A Two-Dimensional Shear Deformation Beam for Large Rotation and Deformation,” J. Sound Vib., 243(3), pp. 565–576. [CrossRef]
Gerstmayr, J., and Shabana, A. A., 2006, “Analysis of Thin Beams and Cables Using the Absolute Nodal Co-ordinate Formulation,” Nonlinear Dyn., 45(1–2), pp. 109–130. [CrossRef]
Galaitsis, A. G., 1984, “A Model for Predicting Dynamic Track Loads in Military Vehicles,” ASME J. Vib. Acoust., 106(2), pp. 286–291. [CrossRef]
Bando, K., Yoshida, K., and Hori, K., 1991, “The Development of the Rubber Track for Small Size Bulldozers,” International Off-Highway & Powerplants Congress & Exposition, Milwaukee, WI. [CrossRef]
Nakanishi, T., and Shabana, A. A., 1994, “On the Numerical Solution of Tracked Vehicle Dynamic Equations,” Nonlinear Dyn., 6, pp. 391–417. [CrossRef]
Choi, J. H., Lee, H. C., and Shabana, A. A., 1998, “Spatial Dynamics of Multibody Tracked Vehicles, Part I: Contact Forces and Simulation Results,” Veh. Syst. Dyn., 29(1), pp. 27–49. [CrossRef]
Choi, J. H., Lee, H. C., and Shabana, A. A., 1998, “Spatial Dynamics of Multibody Tracked Vehicles, Part II: Contact Forces and Simulation Results,” Veh. Syst. Dyn., 29(2), pp. 113–137. [CrossRef]
Maqueda, L. G., Mohamed, A. A., and Shabana, A. A., 2010, “Use of General Nonlinear Material Models in Beam Problems: Application to Belts and Rubber Chains,” ASME J. Comput. Nonlinear Dyn., 5(2), pp. 849–859. [CrossRef]
Sugiyama, H., Escalona, J. L., and Shabana, A. A, 2003, “Formulation of Three-Dimensional Joint Constraints Using the Absolute Nodal Coordinates,” Nonlinear Dyn., 31(2), pp. 167–195. [CrossRef]
Vallejo, D. G., Escalona, J. L., Mayo, J., and Dominguez, J., 2003, “Describing Rigid-Flexible Multibody Systems Using Absolute Coordinates,” Nonlinear Dyn., 34(1–2), pp. 75–94. [CrossRef]
Hughes, T. J. R., Cottrell, J. A., and Bazilevs, Y., 2005, “Isogeometric Analysis: CAD, Finite Elements, NURBS, Exact Geometry and Mesh Refinement,” Comput. Methods Appl. Mech. Eng., 197(49–50), pp. 4104–4412. [CrossRef]
Piegl, L., and Tiller, W., 1997, The NURBS Book, 2nd ed., Springer, New York.
Lan, P., and Shabana, A. A., 2010, “Integration of B-spline Geometry and ANCF Finite Element Analysis,” Nonlinear Dyn., 61(1–2), pp. 193–206. [CrossRef]
Mikkola, A., Shabana, A. A., Rebollo, C. S., and Octavio, J. R. J., 2013, “Comparison Between ANCF and B-spline Surfaces,” Multibody Syst. Dyn., 30(2), pp. 119–138. [CrossRef]
Berzeri, M., Campanelli, M., and Shabana, A. A., 2001, “Definition of the Elastic Forces in the Finite-Element Absolute Nodal Coordinate Formulation and the Floating Frame of Reference Formulation,” Multibody Syst. Dyn., 5(1), pp. 21–54. [CrossRef]
Gerstmayr, J., and Irschik, H., 2008, “On the Correct Representation of Bending and Axial Deformation in the Absolute Nodal Coordinate Formulation with an Elastic Line Approach,” J. Sound Vib., 318(3), pp. 461–487. [CrossRef]
Mohamed, A. A., and Shabana, A. A., 2011, “Nonlinear Visco-Elastic Constitutive Model for Large Rotation Finite Element Formulation,” Multibody Syst. Dyn., 26(1), pp. 57–79. [CrossRef]
Vallejo, D. G., Valverde, J., and Domínguez, J., 2005, “An Internal Damping Model for the Absolute Nodal Coordinate Formulation,” Nonlinear Dyn., 42(4), pp. 347–369. [CrossRef]
Mohamed, A. A., 2011, Visco-Elastic Nonlinear Constitutive Model for the Large Displacement Analysis of Multibody Systems, University of Illinois at Chicago, Chicago, IL.
Hussein, B., Negrut, D., and Shabana, A. A, 2008, “Implicit and Explicit Integration in the Solution of the Absolute Nodal Coordinate Differential/Algebraic Equations,” Nonlinear Dyn., 54(4), pp. 283–296. [CrossRef]
Hilber, H. M., Hughes, T. J. R., and Taylor, R. L, 1977, “Improved Numerical Dissipation for Time Integration Algorithms in Structural Dynamics,” Earthquake Eng. Struct. Dyn., 5(3), pp. 283–292. [CrossRef]
Aboubak, A. K., and Shabana, A. A., 2014, “Efficient Implementation of the TLISMNI Method,” Technical Report No. MBS 2014-10-UIC, Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, IL.
Maqueda, L. G., and Shabana, A. A., 2007, “Poisson Modes and General Nonlinear Constitutive Models in the Large Displacement Analysis of Beams,” J. Multibody Syst. Dyn., 18(3), pp. 375–396. [CrossRef]

Figures

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Fig. 1

Euler–Bernoulli beam element

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Fig. 2

Structure without slope discontinuity

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Fig. 3

Structure with slope discontinuity

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Fig. 4

Intermediate coordinate system

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Fig. 6

Algorithm flow chart: (a) nonlinear constraints and (b) new linear constraints

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Fig. 8

Deformation modes: (a) stretch mode, (b) bending mode, and (c) cross section deformation

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Fig. 9

Tracked vehicle model

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Fig. 10

Sprocket rotational velocity

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Fig. 11

Chassis forward velocity (-·-·-·-·- rigid model, ----- closed loop flexible model, - - - - - - open loop flexible model)

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Fig. 12

Forward displacement of the chassis (-·-·-·-·- rigid model, ----- closed loop flexible model, - - - - - - open loop flexible model)

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Fig. 13

Vertical displacement of the chassis (-·-·-·-·- rigid model, ----- closed loop flexible model, - - - - - - open loop flexible model)

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Fig. 14

Node-32 forward position (----- rigid model, - - - - - - flexible models)

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Fig. 15

Motion trajectory of a flexible track link point

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Fig. 16

First joint longitudinal forces (----- rigid model, - - - - - - flexible models)

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Fig. 17

First joint vertical forces (----- rigid model, - - - - - - flexible models)

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Fig. 18

Axial deformation of first link of the right chain at t = 5s magnified by a factor of 105 (- - - - - - initial configuration, ----- deformed configuration)

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Fig. 19

Transverse deformation of first link of the right chain at t = 5s magnified by a factor of 105 (- - - - - - initial configuration, ----- deformed configuration)

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Fig. 20

Right chain axial stress at t = 5s

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Fig. 21

Right chain axial force distribution at t = 5s

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