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Volumetric locking suppression method for nearly incompressible nonlinear elastic multi-layer beams using ANCF elements

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Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The analysis and solution of many modern flexible multibody dynamic problems require formulations that are able to effectively model bodies with nonlinear materials undergoing large displacements and deformations. The absolute nodal coordinate formulation (ANCF) in connection with a continuum-based approach is one way to deal with these systems. The main objective of this work is to extend an existent approach for the modelling of slender structures within the ANCF framework with nonlinear, nearly incompressible materials using the volumetric energy penalty technique. The main part of the study is devoted to the evaluation of multi-layer beam models and simplifications in the locking suppression method based on F-bar projection. The results present significantly better agreement with the reference solution for multi-layer structures built with the standard ANCF beam element as compared with the earlier implementation.
Rocznik
Strony
977--990
Opis fizyczny
Bibliogr. 33 poz., rys., tab.
Twórcy
  • Warsaw University of Technology, Institute of Aeronautics and Applied Mechanics, Warsaw, Poland
autor
  • Warsaw University of Technology, Institute of Aeronautics and Applied Mechanics, Warsaw, Poland
Bibliografia
  • 1. Adler J.H., Dorfmann L., Han D., MacLachlan S., Paetsch C., 2014, Mathematical and computational models of incompressible materials subject to shear, IMA Journal of Applied Mathematics, 79, 5, 889-914
  • 2. ANSYS®Academic Research, 2010, ANSYS Mechanical APDL Documentation, ANSYS Inc., release 13.0
  • 3. Bathe K.J., 1996, Finite Element Procedures, Prentice Hall, New Jersey
  • 4. Bonet J., Wood R.D., 1997, Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press, Cambridge; New York, NY, USA
  • 5. Brenan K.E., Campbell S.L., Petzold L.R., 1996, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, SIAM, Philadelphia
  • 6. Elguedj T., Bazilevs Y., Calo V.M., Hughes T.J., 2008, B-bar and F-bar projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order NURBS elements, Computer Methods in Applied Mechanics and Engineering, 197, 33-40, 2732-2762
  • 7. Garc´ıa de Jalón J., Bayo E., 1994, Kinematic and Dynamic Simulation of Multibody Systems. The Real-Time Challenge, Springer, New York
  • 8. Garcia-Vallejo D., Escalona J.L., Mayo J., Dom´inguez J., 2003, Describing rigid-flexible multibody systems using absolute coordinates, Nonlinear Dynamics, 34, 1-2, 75-94
  • 9. Gear C.W., Leimkuhler B., Gupta G.K., 1985, Automatic integration of Euler-Lagrange equations with constraints, Journal of Computational and Applied Mathematics, 12-13, 77-90
  • 10. Gerstmayr J., Matikainen M.K., Mikkola A.M., 2008, A geometrically exact beam element based on the absolute nodal coordinate formulation, Multibody System Dynamics, 20, 4, 359-384
  • 11. Gerstmayr J., Shabana A.A., 2006, Analysis of thin beams and cables using the absolute nodal co-ordinate formulation, Nonlinear Dynamics, 45, 1, 109-130
  • 12. Hairer E., Wanner G., 1996, Solving Oridinary Differential Equations II. Stiff and Differential-Algebraic Problems, Springer, Berlin, 2nd edition
  • 13. Hughes T.J.R., 1987, The Finite Element Method. Linear Static and Dynamic Finite Element Analysis, Prentice Hall, New Jersey
  • 14. Jung S., Park T., Chung W., 2011, Dynamic analysis of rubber-like material using absolute nodal coordinate formulation based on the non-linear constitutive law, Nonlinear Dynamics, 63, 1, 149-157
  • 15. Liu C., Tian Q., Hu H., 2011, Dynamics of a large scale rigid-flexible multibody system composed of composite laminated plates, Multibody System Dynamics, 26, 3, 283-305
  • 16. Maqueda L.G., Mohamed A.N.A., Shabana A.A., 2010, Use of general nonlinear material models in beam problems: Application to belts and rubber chains, Journal of Computational and Nonlinear Dynamics, 5, 2, 021003, 10 pages
  • 17. Maqueda L.G., Shabana A.A., 2007, Poisson modes and general nonlinear constitutive models in the large displacement analysis of beams, Multibody System Dynamics, 18, 3, 375-396
  • 18. Orzechowski G., 2012, Analysis of beam elements of circular cross section using the absolute nodal coordinate formulation, Archive of Mechanical Engineering, LIX, 3, 283-296
  • 19. Orzechowski G., Frączek J., 2015, Nearly incompressible nonlinear material models in the large deformation analysis of beams using ANCF, Nonlinear Dynamics, 82, 1, 451-464
  • 20. Orzechowski G., Shabana A.A., 2016, Analysis of warping deformation modes using higher order ANCF beam element, Journal of Sound and Vibration, 363, 428-445
  • 21. Patel M., Orzechowski G., Tian Q., Shabana A.A., 2016, A new multibody system approach for tire modeling using ANCF finite elements, Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 230, 1, 69-84
  • 22. Shabana A.A., 1997a, Definition of the slopes and the finite element absolute nodal coordinate formulation, Multibody System Dynamics, 1, 3, 339-348
  • 23. Shabana A.A., 1997b, Flexible multibody dynamics: review of past and recent developments, Multibody System Dynamics, 1, 2, 189-222
  • 24. Shabana A.A., 2008, Computational Continuum Mechanics, Cambridge University Press, Cambridge, first edition
  • 25. Shabana A.A., 2013, Dynamics of Multibody Systems, Cambridge University Press, 4th edition
  • 26. Shabana A.A., Yakoub R.Y., 2001, Three dimensional absolute nodal coordinate formulation for beam elements: theory, Journal of Mechanical Design, 123, 4, 606-613
  • 27. Sopanen J.T., Mikkola A.M., 2003, Description of elastic forces in absolute nodal coordinate formulation, Nonlinear Dynamics, 34, 1, 53-74
  • 28. Sugiyama H., Escalona J.L., Shabana A.A., 2003, Formulation of three-dimensional joint constraints using the absolute nodal coordinates, Nonlinear Dynamics, 31, 2, 167-195
  • 29. Sugiyama H., Gerstmayr J., Shabana A.A., 2006, Deformation modes in the finite element absolute nodal coordinate formulation, Journal of Sound and Vibration, 298, 4-5, 1129-1149
  • 30. Wasfy T.M., Noor A.K., 2003, Computational strategies for flexible multibody systems, Applied Mechanics Reviews, 56, 6, 553-613
  • 31. Wehage R.A., Haug E.J., 1982, Generalized coordinate partitioning for dimension reduction in analysis of constrained dynamic systems, Journal of Mechanical Design, 104, 1, 247-255
  • 32. Yakoub R.Y., Shabana A.A., 2001, Three dimensional absolute nodal coordinate formulation for beam elements: implementation and applications, Journal of Mechanical Design, 123, 4, 614-621
  • 33. Zienkiewicz O.C., Taylor R.L., 2005, The Finite Element Method for Solid and Structural Mechanics, Butterworth-Heinemann, Oxford, 6th edition
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-442dcd91-b00a-468a-8a6a-8dc197ce5ebe
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