Cylindrical shell bending theory for orthotropic shells under general axisymmetric pressure distributions

The axisymmetric linear bending theory of shells is treated for thin-walled orthotropic cylindrical shells under any smooth axial distribution of normal and shear pressures. The equations are developed, solved and explored in this paper. The derivation is presented in terms of a generalised Hooke’s Law with coupling between the axial membrane stress resultant and axial bending moment. This formulation permits the shell to be alternatively treated as a composite isotropic cylinder with axial stiffeners, rendering it useful for many practical problems. A linear kinematic relationship is assumed between the generalised strains and displacements. Expressions for the linear axial bending half-wavelength are presented for special cases of the stiffness matrix.The equations developed here are simple enough to be applied to the analysis of anisotropic thin-walled cylindrical shells using basic spreadsheet tools, removing the need to perform an onerous finite element analysis. Engineering applications potentially include corrugated metal, axially-stiffened or reinforced concrete silos under granular solid pressures, tanks under hydrostatic pressures, tubular piles under earth pressures, gas-filled cisterns and chimneys.

► Linear analysis of isotropic cylindrical shells previously limited to basic pressure patterns.
► Theory extended to cover orthotropic and axially-stiffened cylinders.
► Equations given for very general axial pressure patterns, such as those occurring in practice.
► Solution is simple enough to be implemented with standard spreadsheet tools.
► Effect of axial stiffeners on linear axial bending half-wavelength illustrated.