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A discrete formulation of Kirchhoff rods in large-motion dynamics. (English) Zbl 1482.74105

Summary: A nonlinear model for the dynamics of a Kirchhoff rod in the three-dimensional space is developed in the framework of a discrete elastic theory. The formulation avoids the use of Euler angles for the orientation of the rod cross-sections to provide a computationally singularity-free parameterization of rotations along the motion trajectories. The material directions related to the principal axes of the cross-sections are specified using auxiliary points that must satisfy constraints enforced by the Lagrange multipliers method. A generalization of this approach is presented to take into account Poisson’s effect in an orthotropic rod. Numerical simulations are performed to test the presented formulation.

MSC:

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74S99 Numerical and other methods in solid mechanics
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