A Primer on the Kinematics of Discrete Elastic Rods

Description

This primer discusses a numerical formulation of the theory of an elastic rod, known as a discrete elastic rod, that was recently developed in a series of papers by Miklós Bergou et al. Their novel formulation of discrete elastic rods represents an exciting new method to simulate and analyze the behavior of slender bodies that can be modeled using an elastic rod. The formulation has been extensively employed in computer graphics and is highly cited. In the primer, we provide relevant background from both discrete and classical differential geometry so a reader familiar with classic rod theories can appreciate, comprehend, and use Bergou et al.’s computational efficient formulation of a nonlinear rod theory. The level of coverage is suitable for graduate students in mechanics and engineering sciences. Front Matter ....Pages i-xiii Introduction (M. Khalid Jawed, Alyssa Novelia, Oliver M. O’Reilly)....Pages 1-9 Kirchhoff’s Theory of an Elastic Rod (M. Khalid Jawed, Alyssa Novelia, Oliver M. O’Reilly)....Pages 11-23 The Discretized Curve: Vertices, Edges, and Curvature (M. Khalid Jawed, Alyssa Novelia, Oliver M. O’Reilly)....Pages 25-32 Bishop Frames and Reference Frames Along the Discretized Curve (M. Khalid Jawed, Alyssa Novelia, Oliver M. O’Reilly)....Pages 33-46 Material Frames and Measures of Twists (M. Khalid Jawed, Alyssa Novelia, Oliver M. O’Reilly)....Pages 47-57 Variations, Gradients, and Hessians (M. Khalid Jawed, Alyssa Novelia, Oliver M. O’Reilly)....Pages 59-73 Spherical Excess and Reference Twist (M. Khalid Jawed, Alyssa Novelia, Oliver M. O’Reilly)....Pages 75-92 Equations of Motion and Energetic Considerations (M. Khalid Jawed, Alyssa Novelia, Oliver M. O’Reilly)....Pages 93-112 Back Matter ....Pages 113-118