A discrete formulation of Kirchhoff rods in large-motion dynamics. (May 2020)

• Record Type: Journal Article
• Authors: Giorgio, Ivan
• Is Part Of: Mathematics and mechanics of solids. Volume 25:Number 5(2020)
• Page Start: 1081
• Page End: 1100
• Publication Date: 2020-05
• Subjects: Kirchhoff viscoelastic beam -- nonlinear rod -- large displacements and rotations -- discrete formulation -- Lagrange multipliers; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/1081286519900902
• Languages: English
• ISSNs: 1081-2865

Abstract

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.