A general displacement analysis of an orthotropic shell revolution

Abstract

A system of three dimensional partial differential equations in terms of displacements in curvilinear directions is developed to describe the behavior of an orthotropic shell with arbitrary loadings and boundary conditions. They system of equations is a generalization of the isotropic Navier elasticity equations and is exact within the limitations of assumed small displacements and linear stress-strain relations. The three-dimensional system is then reduced to the axisymmetric case which describes the behavior of a symmetrically loaded, plane isotropic shell of revoution with symmetrical boundary conditions. The resulting two-dimensional system of equations is numerically approximated by the method of divided differences, case into matrix form, and solved by matrix inversion.