On finite axi-symmetrical deformations of thin elastic shells of revolution

We derive a generalized version of the known system of two simultaneous second order differential equations for the problem of axi-symmetric torsionless deformations of elastic shells of revolution, for finite deformations and including transverse shear deformations and membrane drilling moments. Our generalization, which involves the introduction of a semicomplementary energy density, comes out in a particularly simple and compact form. We furthermore consider the effect of transverse normal stress deformations and discover the possibility of reducing this problem to a system of three simultaneous second order equations, with the supplementary third equation harmoniously adding itself to the two equations without consideration of transverse normal stress deformation effects.