  The geologic activity at Enceladus's south pole remains unexplained, though
tidal deformations are probably the ultimate cause. Recent gravity and
libration data indicate that Enceladus's icy crust floats on a global ocean, is
rather thin, and has a strongly non-uniform thickness. Tidal effects are
enhanced by crustal thinning at the south pole, so that realistic models of
tidal tectonics and dissipation should take into account the lateral variations
of shell structure. I construct here the theory of non-uniform viscoelastic
thin shells, allowing for depth-dependent rheology and large lateral variations
of shell thickness and rheology. Coupling to tides yields two 2D linear partial
differential equations of the 4th order on the sphere which take into account
self-gravity, density stratification below the shell, and core viscoelasticity.
If the shell is laterally uniform, the solution agrees with analytical formulas
for tidal Love numbers; errors on displacements and stresses are less than 5%
and 15%, respectively, if the thickness is less than 10% of the radius. If the
shell is non-uniform, the tidal thin shell equations are solved as a system of
coupled linear equations in a spherical harmonic basis. Compared to finite
element models, thin shell predictions are similar for the deformations due to
Enceladus's pressurized ocean, but differ for the tides of Ganymede. If
Enceladus's shell is conductive with isostatic thickness variations, surface
stresses are approximately inversely proportional to the local shell thickness.
The radial tide is only moderately enhanced at the south pole. The combination
of crustal thinning and convection below the poles can amplify south polar
stresses by a factor of 10, but it cannot explain the apparent time lag between
the maximum plume brightness and the opening of tiger stripes. In a second
paper, I will study tidal dissipation in a non-uniform crust.
