On reductions of the differential equations for circular cylindrical shells

Abstract

The paper begins with a statement of the differential equations of equilibrium and compatibility for circular cylindrical shells in the form first given in a pioneering work by Schaefer, and with constitutive equations incorporating transverse shear deformations and moment components normal to the shell surface as stated earlier by the present author. It is then shown that this system of equations may be reduced, for a rather general class of orthotropic shells, to four simultaneous third-order equations for two stress functions and two displacement variables. Subsequent to this it is shown that for the case that transverse shear deformations and shell surface normal moment components are absent the four simultaneous equations degenerate in such a manner that a further reduction to two simultaneous fourth order equations, for one stress function and one displacement variable, becomes possible. For the case of the isotropic shell these are equivalent to results by Morley, Simmonds, and Wan which were obtained by somewhat different reduction procedures.