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A thick anisotropic plate element in the framework of an absolute nodal coordinate formulation

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Abstract

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.

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Acknowledgement

The operation was partially financed by the European Union, European Social Fund.

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Authors and Affiliations

  1. Knauf Insulation d.o.o., Central Engineering Europe, Trata 32, 4220, Škofja Loka, Slovenia

    M. Langerholc

  2. Faculty of mechanical engineering, Aškerčeva 6, 1000, Ljubljana, Slovenia

    M. Langerholc, J. Slavič & M. Boltežar

Authors
  1. M. Langerholc
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  2. J. Slavič
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  3. M. Boltežar
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Corresponding author

Correspondence to M. Boltežar.

Appendix

Appendix

The element shape-function matrix S is defined as

$$ \mathbf{S}= [S_1\mathbf{I},S_2\mathbf{I},\ldots,S_{16}\mathbf{I} ], $$
(69)

where I is a 3×3 identity matrix, and

where a, b, and h are the length, width, and height of the element, respectively. The presented shape function S ensures positions and position-vector gradients’ continuity at the nodal points; however, it does not ensure the gradients’ continuity at the element’s interface.

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Langerholc, M., Slavič, J. & Boltežar, M. A thick anisotropic plate element in the framework of an absolute nodal coordinate formulation. Nonlinear Dyn 73, 183–198 (2013). https://doi.org/10.1007/s11071-013-0778-y

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  • DOI: https://doi.org/10.1007/s11071-013-0778-y

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