The Sanders-Koiter shell equations can be reduced to two coupled equations for all minimal midsurfaces
Gordon E. Latta, JAMES G. SIMMONDS · Quarterly of Applied Mathematics · 1975
For an elastically isotropic shell of constant thickness with an analytic midsurface of zero mean curvature, it is shown that the linear Sanders—Koiter equations can be reduced exactly to two coupled fourth-order partial differential equations, involving as unknowns a stress function and the rotation of the midsurface about the normal.