A Primer on the Kinematics of Discrete Elastic Rods (Springerbriefs in Applied Sciences and Technology)

Jawed, M. Khalid/ Novelia, Alyssa/ O'Reilly, Oliver M.

Springer International Publishing AG（2018/05発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 118 p.
• 商品コード 9783319769646

Full 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.

Contents

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.