A Donnell Type Theory for Asymmetrical Bending and Buckling of Thin Conical Shells

Equations, somewhat more accurate than those recently presented by N. J. Hoff, are derived for bending and buckling of thin circular conical shells under arbitrary loading. These equations reduce to Donnell’s equations for thin cylindrical shells when the cone semivertex angle becomes very small and the minimum radius of curvature of the median surface approaches a constant value. At the other end of the scale the equations reduce to the well-known equations for flat circular plates when the cone semivertex angle approaches a right angle. In addition, for the entire range of cone semivertex angles the equations reduce to the known equations for axisymmetrical bending when variations of the displacements around the circumference vanish. The problem of bending is reduced to the solution of a single fourth-order partial differential equation with variable coefficients.