Jg. Simmonds, A SIMPLIFIED DISPLACEMENT-ROTATION FORM FOR THE EQUATIONS OF MOTION OF NONLINEARLY ELASTIC SHELLS OF REVOLUTION UNDERGOING COMBINED BENDINGAND TORSION, Journal of applied mechanics, 63(2), 1996, pp. 539-542
By appropriately defining two displacements and a rotation, it is show
n that the equations of motion of a shell of revolution undergoing com
bined axisymmetric bending and torsion, in which the extensional strai
ns and the rotations may be arbitrarily large, can be given a form in
which there are three effective extensional strains and two effective
bending strains, each of which is only linear or quadratic in the disp
lacements and rotation.