Abstract
Simple, closed-form solutions, which can be easily calculated using spreadsheet software, for thin and moderately thick anisotropic cylinders under torsion, axial compression and these combined loads that includes the effect of transverse shear deformation are derived. Previously derived partial differential equations of equilibrium, which are including both layup anisotropy and transverse shear deformation, are separated two equation groups by neglecting coupling stiffnesses (tension-shear, bending-torsion and tension-torsion couplings). One is tension-bending equation group and the other is torsional equation group, and these equation groups are solved independently and the closed-form solutions are obtained. One of the two tension-bending 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. In addition, it is shown that previously derived bending-boundary solution can be applied as the same form when the length of the cylinder is longer than the length of its bending boundary layer. Moreover, Donnell-type shallow-shell approximation is inappropriate for solving torsional deformation of moderately thick cylinder is also shown. Comparison between closed-form solution and precise solution including both layup anisotropy and transverse shear deformation shows that the difference can be negligible when cylinder is honeycomb-sandwich with symmetric facesheet but cannot be negligible when the symmetric cylinder has non-negligible tension-torsion coupling stiffnesses. Therefore, the estimation formula for the effect of tension-torsion coupling stiffnesses is also derived.
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