Closed-form solutions of thin anisotropic cylinders under torsion, axial compression and combined load

Abstract

The major aim of this paper is to derive simple closed-form solutions which can be easily calculated using spreadsheet software, for thin anisotropic cylinders under torsion, axial compression and combined loads that include the effect of layup anisotropy. Previously derived partial differential equations of equilibrium that are solved by including layup anisotropy but neglecting transverse shear deformation and closed-form solutions are obtained. One of the three solutions satisfies a simply supported condition, another a fully fixed condition, and both of these can be applied to cylinders that are shorter and longer than the length of the bending boundary layer. The third solution is called the bending boundary layer solution, and it can only be applied when the cylinder is longer than the length of the bending boundary layer. In addition, guidelines for dividing mesh in finite element analyses of anisotropic cylinders are discussed in terms of the precision of the bending stress on the edge. A comparison of the closed-form solution and the precise solution including both layup anisotropy and transverse shear deformation shows that differences appear only on the bending-boundary layer, the differences increase with the radius to thickness ratio decreases, and the closed-form solution gives a safe-side estimate for design purposes.