Modeling the buckling of rectilinearly orthotropic truncated conical shells

A mathematical model is constructed to study the buckling of rectilinearly orthotropic, truncated conical shells. The model consists of three coupled variable coefficient partial differential equations for the shell displacements; the formulation presented takes into account the action of locally supported applied forces normal to the lateral surface of the shell and contains two fundamental novelties: the introduction of special combinations of constitutive parameters to gauge the deviation from isotropy and a transformation of both coordinates and displacements on the developed cone surface to render the problem tractable.