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