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.

Autorentext

Dr. M. Khalid Jawed is an Assistant Professor in the Department of Mechanical and Aerospace Engineering at the University of California, Los Angeles.

Alyssa Novelia is a graduate student in the Department of Mechanical Engineering at the University of California, Berkeley.

Dr. Oliver M. O'Reilly is a Professor in the Department of Mechanical Engineering at the University of California, Berkeley.

Inhalt

Discrete Elastic Rods.- Kirchhoff's Theory of an Elastic Rod.- Variations, Gradients, and Hessians.- Rotation of the Cross Section of the Rod, Spherical Excess, and Holonomy.- Kinetic Energy, Potential Energy, and Internal Forces.