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Construction of discrete shell models by geometric finite differences
(2012)
- In the presented work, we make use of the strong reciprocity between kinematics and geometry to build a geometrically nonlinear, shearable low order discrete shell model of Cosserat type defined on triangular meshes, from which we deduce a rotation–free Kirchhoff type model with the triangle vertex positions as degrees of freedom. Both models behave physically plausible already on very coarse meshes, and show good convergence properties on regular meshes. Moreover, from the theoretical side, this deduction provides a common geometric framework for several existing models.
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Geometrically exact Cosserat rods with Kelvin-Voigt type viscous damping
(2012)
- We present the derivation of a simple viscous damping model of Kelvin–Voigt type for geometrically exact Cosserat rods from three–dimensional continuum theory. Assuming a homogeneous and isotropic material, we obtain explicit formulas for the damping parameters of the model in terms of the well known stiffness parameters of the rod and the retardation time constants defined as the ratios of bulk and shear viscosities to the respective elastic moduli. We briefly discuss the range of validity of our damping model and illustrate its behaviour with a numerical example.
