Analytical General Solutions for Hygroelastic Deformation of Cylindrical Wood Cell Walls

This technical note provides analytical general solutions and independent numerical benchmarks for small-strain hygroscopic deformation of single- and multilayer cylindrical wood cell walls. The analysis unifies three closely related approaches: (1) the direct plane-stress solution of the radial Cauchy–Euler equilibrium equation; (2) the two-stage auxiliary-stress superposition described by Schulgasser and Witztum (2015); and (3) a generalized-plane-strain (GPS) formulation with coupled axial strain and optional torque-free twist. A detailed derivation shows why the direct plane-stress particular solution equals the first superposition stage, and establishes the limitations of the latter at a resonant anisotropy ratio. The GPS model is derived from a rotated four-component stiffness law, with radial displacement expressed using anisotropic power-law terms and separate moisture/axial and torsional coupling terms. Stable logarithmic particular solutions are provided for resonant exponents. Perfectly bonded multilayer problems are reduced to linear systems by enforcing interface continuity, radial surface tractions, global axial-force balance, and, when appropriate, zero resultant torque. Reproducible Python/Jupyter implementations compare the analytical fields against independently assembled one-dimensional Galerkin finite elements. The deposited tests cover one-, two-, and five-layer cylinders; plane strain, plane stress, restrained-twist and free-twist GPS; PS and GPS resonances; Schulgasser superposition; and compatible versus uniform helical eigen-shear fields. The illustrative layer properties are not experimentally calibrated, and validation against FEM should not be interpreted as experimental validation of wood cell-wall properties. The English edition omits off-topic derivations for anisotropic beam Airy functions and redundant development notes while retaining the full cylindrical derivations, computational benchmarks, figures, and numerical outputs.