A thick anisotropic plate element in the framework of an absolute nodal coordinate formulation
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In this research, the incorporation of material anisotropy is proposed for the large-deformation analyses of highly flexible dynamical systems. The anisotropic effects are studied in terms of a generalized elastic forces (GEFs) derivation for a continuum-based, thick, and fully parameterized absolute nodal coordinate formulation plate element, of which the membrane and bending deformation effects are coupled. The GEFs are first derived for a fully anisotropic, linearly elastic material, characterized by 21 independent material parameters. Using the same approach, the GEFs are obtained for an orthotropic material, characterized by nine material parameters. Furthermore, the analysis is extended to the case of nonlinear elasticity; the GEFs are introduced for a nonlinear Cauchy-elastic material, characterized by four in-plane orthotropic material parameters. Numerical simulations are performed to validate the theory for statics and dynamics and to observe the anisotropic responses in terms of displacements, stresses, and strains. The presented formulations are suitable for studying the nonlinear dynamical behavior of advanced elastic materials of an arbitrary degree of anisotropy.
KeywordsAbsolute nodal coordinate formulation Thick plate Anisotropy Nonlinear elasticity Nonlinear dynamics Large deformation
The operation was partially financed by the European Union, European Social Fund.
- 1.Abbas, L.K., Rui, X., Hammoudi, Z.S.: Plate/shell element of variable thickness based on the absolute nodal coordinate formulation. Nonlinear Dyn. 224, 127–141 (2010) Google Scholar
- 4.Bronstein, I.N., Semendyayev, M.G.: Handbook of Mathematics, 4th edn. Springer, Berlin (2003) Google Scholar
- 5.Burden, R.L., Faires, D.J.: Numerical Analysis, 9th edn. Brooks Cole, California (2010) Google Scholar
- 6.Čepon, G., Boltežar, M.: Dynamics of a belt-drive system using a linear complementarity problem for the belt-pulley contact description. J. Sound Vib. 319(3–5), 1019–1035 (2009) Google Scholar
- 7.Čepon, G., Manin, L., Boltežar, M.: Introduction of damping into the flexible multibody belt-drive model: a numerical and experimental investigation. J. Sound Vib. 324(1–2), 283–296 (2009) Google Scholar
- 20.Newnham, R.E.: Properties of Materials: Anisotropy, Symmetry, Structure. Oxford University Press, London (2005) Google Scholar
- 24.Schwab, A.L., Gerstmayr, J., Meijaard, J.P.: Comparison of three-dimensional flexible thin plate elements for multibody dynamic analysis: finite element formulation and absolute nodal coordinate formulation. ASME Conf. Proc. 4806X, 1059–1070 (2007) Google Scholar