On the general analytical solution of the kinematic Cosserat equations. (English) Zbl 1453.74051
Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 18th international workshop, CASC 2016, Bucharest, Romania, September 19–23, 2016. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 9890, 367-380 (2016).
Summary: Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.
For the entire collection see [Zbl 1346.68010].
For the entire collection see [Zbl 1346.68010].
MSC:
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74H05 | Explicit solutions of dynamical problems in solid mechanics |
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
Keywords:
Cosserat rods; differential Thomas decomposition; flagellated microswimmers; general analytical solution; kinematic equations; Lie symmetry analysis; Stokes flow; symbolic computationReferences:
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