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TECHNICAL PAPERS

Application of Plasticity Theory and Absolute Nodal Coordinate Formulation to Flexible Multibody System Dynamics

[+] Author and Article Information
Hiroyuki Sugiyama, Ahmed A. Shabana

Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, Illinois 60607

J. Mech. Des 126(3), 478-487 (Nov 01, 2003) (10 pages) doi:10.1115/1.1737491 History: Received January 01, 2003; Revised November 01, 2003
Copyright © 2004 by ASME
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References

Shabana, A. A., 1998, Dynamics of Multibody Systems, 2nd, Cambridge University Press.
Ambrósio,  J. A. C., and Nikravesh,  P. E., 1992, “Elasto-Plastic Deformations in Multibody Dynamics,” Nonlinear Dyn., 3, pp. 85–104.
Gerstmayr, J., and Irschik, H., 2002, “Computational Methods for Elasto-Plastic Multibody Dynamic Systems,” Proceedings of Fifth World Congress on Computational Mechanics, Vienna, Austria.
Gerstmayr,  J., Holl,  H. J., and Irschik,  H., 2001, “Development of Plasticity and Damage in Vibrating Structural Elements Performing Guided Rigid-Body Motions,” Arch. Appl. Mech., 71, pp. 135–145.
Hill, R., 1950, The Mathematical Theory of Plasticity, Clarendon Press.
Naghdi,  P. M., 1990, “A Critical Review of the State of Finite Plasticity,” Journal of Applied Mathematics and Physics (ZAMP), 41, pp. 315–394.
Lee,  E. H., and Liu,  D. T., 1967, “Finite Strain Elastic-Plastic Theory Particularly for Plane Wave Analysis,” J. Appl. Phys., 38, pp. 19–27.
Lee,  E. H., 1969, “Elastic-Plastic Deformation at Finite Strains,” ASME J. Appl. Mech., 36, pp. 1–6.
Johnson,  G. C., and Bammann,  D. J., 1984, “Discussion of Stress Rates in Finite Deformation Problems,” Int. J. Solids Struct., 20, pp. 725–737.
Khan, A. S., and Huang, S., 1995, Continuum Theory of Plasticity, Wiley.
Nagtegaal, J. C., and De Jong, J. E., 1982, “Some Aspects of Non-Isotropic Work Hardening in Finite Strain Plasticity,” Plasticity of Metal at Finite Strain, Stanford University Press, pp. 65–102.
Green,  A. E., and Naghdi,  P. M., 1965, “A General Theory of Elasto-Plastic Continuum,” Arch. Ration. Mech. Anal., 18, pp. 221–281.
Green,  A. E., and Naghdi,  P. M., 1971, “Some Remarks on Elastic-Plastic Deformation at Finite Strain,” Int. J. Eng. Sci., 9, pp. 1219–1229.
Lee,  E. H., 1981, “Some Comments on Elastic-Plastic Analysis,” Int. J. Solids Struct., 17, pp. 859–872.
Nemat-Nasser,  S., 1982, “On Finite Deformation Elasto-Plasticity,” Int. J. Solids Struct., 18, pp. 857–872.
Nagtegaal,  J. C., 1982, “On the Implementation of Inelastic Constitutive Equations with Special Reference to Large Deformation Problems,” Comput. Methods Appl. Mech. Eng., 33, pp. 469–484.
Simo,  J. C., 1988, “A Framework for Finite Strain Elastoplasticity Based on Maximum Plastic Dissipation and the Multiplicative Decomposition: Part I Continuum Formulation,” Comput. Methods Appl. Mech. Eng., 66, pp. 199–219.
Simo, J. C., and Hughes, T. J. R., 1998, Computational Inelasticity, Springer.
Simo,  J. C., 1992, “Algorithms for Static and Dynamic Multiplicative Plasticity That Preserve the Classical Return Mapping Schemes of the Infinitesimal Theory,” Comput. Methods Appl. Mech. Eng., 99, pp. 61–112.
Crisfield, M. A., 1996, Non-Linear Finite Element Analysis of Solids and Structures, Volume 2, Wiley.
Eterovic,  A. L., and Bathe,  K. J., 1990, “A Hyperelastic-Based Large Strain Elastoplastic Constitutive Formulation with Combined Isotropic-Kinematic Hardening Using the Logarithmic Stress and Strain Measures,” Int. J. Numer. Methods Eng., 30, pp. 1099–1114.
Weber,  G., and Anand,  L., 1990, “Finite Deformation Constitutive-Equations and a Time Integration Procedure for Isotropic, Hyperelastic Viscoplastic Solids,” Comput. Methods Appl. Mech. Eng., 79, pp. 173–202.
Papadopoulos,  P., and Lu,  J., 1998, “A General Framework for the Numerical Solution of Problems in Finite Elasto-Plasticity,” Comput. Methods Appl. Mech. Eng., 159, pp. 1–18.
Meng,  X. N., and Laursen,  T. A., 2002, “Energy Consistent Algorithms for Dynamic Finite Deformation Plasticity,” Comput. Methods Appl. Mech. Eng., 191, pp. 1639–1675.
Shabana,  A. A., and Yakoub,  R. Y., 2001, “Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements,” ASME J. Mech. Des., 123, pp. 606–621.
Mikkola,  A. M., and Shabana,  A. A., 2003, “A Non-Incremental Finite Element Procedure for the Analysis of Large Deformation of Plates and Shells in Mechanical System Applications,” Multibody System Dynamics, 9, pp. 283–309.
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, pp. 342–350.
Sugiyama,  H., Escalona,  J. L., and Shabana,  A. A., 2003, “Formulation of Three-Dimensional Joint Constraints Using the Absolute Nodal Coordinates,” Nonlinear Dyn., 31, pp. 167–195.
Bonet, J., and Wood, R. D., 1997, Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press.
Wilkins, M. L., 1964, “Calculation of Elasto-Plastic Flow,” Methods of Computational Physics 3, Academic Press.
Krieg, R. D., and Key, S. W., 1976, “Implementation of a Time Dependent Plasticity Theory into Structural Computer Programs,” Constitutive Equations in Viscoplasticity: Computational and Engineering Aspects, AMD-20, ASME.
Simo,  J. C., Taylor,  R. L., and Pister,  K. S., 1985, “Variational and Projection Methods for the Volume Constraint in Finite Deformation Elasto-Plasticity,” Comput. Methods Appl. Mech. Eng., 51, pp. 177–208.
Yakoub,  R. Y., and Shabana,  A. A., 1999, “Use of Cholesky Coordinates and the Absolute Nodal Coordinate Formulation in the Computer Simulation of Flexible Multibody Systems,” Nonlinear Dyn., 20, pp. 267–282.
Simo,  J. C., and Taylor,  R. L., 1985, “Consistent Tangent Operators for Rate-Independent Elastoplasticity,” Comput. Methods Appl. Mech. Eng., 48, pp. 101–118.
ANSYS Theory Reference 6.1, 2002, SAS IP, Inc.
Simo,  J. C., and Vu-Quoc,  L., 1986, “Three-Dimensional Finite-Strain Rod Model. Part II: Computational Aspects,” Comput. Methods Appl. Mech. Eng., 58, pp. 79–116.
Campanelli,  M., Berzeri,  M., and Shabana,  A. A., 2000, “Performance of the Incremental and Non-Incremental Finite Element Formulations in Flexible Multibody Problems,” ASME J. Mech. Des., 122, pp. 498–507.

Figures

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Absolute nodal coordinates of the beam element
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Absolute nodal coordinates of the plate element
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Schematic representation of radial return mapping
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Beam subject to plastic deformations
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Longitudinal displacement at the free end (uniaxial loading/unloading)
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Stretches of the cross section at mid-point (uniaxial loading/unloading).
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Global Z-displacement at the free end (elastic pendulum)
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Global Z-displacement at the free end (elasto-plastic pendulum)
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Deformed shapes of the pendulum
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Cylindrical shell (can) subject to lateral crushing forces
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Deformed shapes of cylindrical shell (can)
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Force–displacement curve at point A

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