Poisson modes and general nonlinear constitutive models in the large displacement analysis of beams

Multibody System Dynamics

Volumn 18, Issue 3, 2007, Pages 375-396

  Maqueda, Luis G ^a   Shabana, Ahmed A ^a  

^a 1120 Science and Engineering Offices   (United States)

Author keywords

Absolute nodal coordinate formulation; Finite beam elements; Large deformation; Nonlinear constitutive models; Nonlinear elasticity; Poisson modes

Indexed keywords

BEAMS AND GIRDERS; BENDING (DEFORMATION); CONSTITUTIVE MODELS; ELASTICITY; FINITE ELEMENT METHOD; PLATES (STRUCTURAL COMPONENTS);

ABSOLUTE NODAL COORDINATE FORMULATION; FINITE BEAM ELEMENTS; NONLINEAR CONSTITUTIVE MODELS; NONLINEAR ELASTICITY; POISSON MODES;

POISSON DISTRIBUTION;

EID: 34948869264     PISSN: 13845640     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11044-007-9077-z     Document Type: Article

References (23)

1. Bonet, J., Wood, R.D.: Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press, Cambridge (1997)
2. Dufva, K., Kerkkänen, K., Maqueda, L.G., Shabana, A.A.: Nonlinear dynamics of three-dimensional belt drives using the finite-element method. Nonlinear Dyn. 48, 449-466 (2007)
3. Gerstmayr, J., Shabana, A.A.: Analysis of thin beams and cables using the absolute nodal coordinate formulation. Technical Report MBS05-3-UIC (2005)
4. Hjelmstad, K.D.: Fundamentals of Structural Mechanics. 2nd edn. Springer, Berlin (2005)
5. Hussein, B.A., Sugiyama, H., Shabana, A.A.: Absolute nodal coordinate formulation coupled deformation modes: problem definition. Technical Report MBS06-1-UIC, Department of Mechanical Engineering, University of Illinois at Chicago (2006)
6. Kerkkanen, K.S., Garcia-Vallejo, D., Mikkola, A.M.: Modeling of belt-drives using a large deformation finite element formulation. Nonlinear Dyn. 43, 239-256 (2006)
7. Maqueda, L.G., Bauchau, O.A., Shabana, A.A.: Effect of the centrifugal forces on the finite element eigenvalue solution. Technical Report # MBS06-4-UIC, Department of Mechanical Engineering, The University of Illinois at Chicago, November 2006
8. Mikkola, A.M., Matikainen, M.K.: Development of elastic forces for the large deformation plate element based on the absolute nodal coordinate formulation. ASME J. Comput. Nonlinear Dyn. 1, 103-108 (2006)
9. Ogden, R.W.: Large deformation isotropic elasticity: on the correlation of theory and experiment for compressible rubber-like solids. Proc. Roy. Soc. Lond. Ser. A: Math. Phys. Sci. 328, 567-583 (1972)
10. Ogden, R.W.: Non-Linear Elastic Deformations. Horwood, Chichester (1984)
11. Omar, M.A., Shabana, A.A.: A two-dimensional shear deformable beam for large rotation and deformation problems. J. Sound Vib. 243, 565-576 (2001)
12. Reissner, E.: On a variational theorem for finite elastic deformation. J. Math. Phys. 32, 129-135 (1953)
13. Schwab, A.L., Meijaard, J.P.: Comparison of three-dimensional flexible beam elements for dynamic analysis: finite element method and absolute nodal coordinate formulation. In: Proceedings of ASME International Design Engineering Technical Conferences and Computer Information in Engineering Conference (DETC2005/ MSNDC-85104), Long Beach, CA, USA (2005)
14. Shabana, A.A.: Resonance conditions and deformable body co-ordinate systems. J. Sound Vib. 192, 389-398 (1996)
15. Shabana, A.A., Yakoub, R.Y.: Three-dimensional absolute nodal coordinate formulation for beam elements: theory. ASME J. Mech. Des. 123, 606-613 (2001)
16. Simo, J.C., Taylor, R.L.: Penalty function formulations for incompressible nonlinear elastostatic. Comput. Methods Appl. Mech. Eng. 35, 107-118 (1982)
17. Simo, J.C., Taylor, R.L., Pister, K.S.: Variational and projection methods for the volume constraint in finite deformation elastoplasticity. Comput. Methods Appl. Mech. Eng. 51, 177-208 (1985)
18. Simo, J.C., Taylor, R.L.: Quasi-incompressible finite elasticity in principle stretches. Continuum basis and numerical algorithms. Comput. Methods Appl. Mech. Eng. 85, 273-310 (1991)
19. Sopanen, J.T., Mikkola, A.K.: Description of elastic forces in absolute nodal coordinate formulation. Nonlinear Dyn. 34, 53-74 (2003)
20. Spencer, A.J.M.: Continuum Mechanics. Longman, Harlow (1980)
21. Treloar, L.R.G.: Physics of Rubber Elasticity. Oxford University Press, Oxford (1958)
22. Yakoub, R.Y., Shabana, A.A.: Three-dimensional absolute nodal coordinate formulation for beam elements: implementation and applications. ASME J. Mech. Des. 123, 614-621 (2001)
23. Yoo, W.S., Lee, J.H., Park, S.J., Sohn, J.H., Pogorelov, D., Dimitrochenko, O.: Large deflection analysis of a thin plate: computer simulation and experiment. Multibody Syst. Dyn. 11(2), 185-208 (2004)