Understanding Rod, Plate, and Shell Theory

The theories of plates, shells, and rods are important both for engineering practice and for understanding complex physical phenomena, but developing a good understanding of these fundamental theories is not easy.

The general theory of rod (1968 Green&Laws)

We consider a curve in three-dimensional space, defined as:

$\theta$ is used to define points on the curve, and $t$ denotes time. A rod can be viewed as a set of points on a curve plus two local director vectors. At any instant, the two director vectors are defined as

where $\alpha$ is 1 or 2. $\mathbf{a}_3$