## 3. A simple element analysis (cont'd)

If we define
\(\lambda^2 = \sigma \omega^2 / T\) and \(g = p/T\),
then it can be shown (Forsythe & Wasow, 1960,
Chap. 3) that the energy functional corresponding to this system is

$$F(w)=\frac{1}{2}\iint {\left|\nabla w\right|}^{2}\text{d}S+\frac{1}{2}\iint {\lambda}^{2}{w}^{2}\text{d}S-\iint wg\text{d}S$$
| (Eqn. 4) |

where the integrals are over the entire region of interest, in this
case the triangular element.
The three integral terms on the
right-hand side represent energy due to membrane tension, inertia, and
the applied pressure, respectively.

R. Funnell
Last modified: 2018-11-07 12:52:06
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