Static Elastic Problems

OK, now we've got the formalism what problems can we solve? If we are dealing with anisotropic systems, not a lot. Even for isotropic elasticity, only quite simple problems can be solved easily.

One convenient way forward is to introduce two potentials

$$\bf$$u = div$$\phi$$ + curl$$\bf$$$$\psi$$

with the subsidiary condition that $\psi$ is divergenceless. What this means is that $\phi$ represents compression and $\psi$ represents shear. Under some conditions, though, one can get away with simpler approaches.