Numerical and asymptotic solutions are developed to the equations governing large torsional, axisymmetric deformation of rubberlike shells of revolution. The shell equations include large-strain geometric and material nonlinearities, transverse shear deformation, transverse normal stress and strain, and torsion. Both analyses allow ready incorporation of different strain-energy density functions. In the asymptotic analysis, the interior solution corresponds to that of nonlinear membrane theory and contains a primary boundary layer. The edge-zone solution gives a secondary boundary layer that, for large strain, divides into a bending-twisting moment component and a torsional-membrane component. The boundary layer behavior is illustrated for a clamped neo-Hookean cylinder subjected to internal pressure and axial torque.
List of symbols
Latin symbols
a a(mn) b Ca C F, C X, C~, Ce~ C ei Computational Mechanics 10 (1992) Greek symbols F~,ro y 0 23 Z 0 Radius-to-thickness ratio, fl = R/t Transverse shear strains Average transverse shear angles Decay function Circumferential coordinate Curvature change measures Reference-surface stretch components Three-dimensional stretch components Transverse normal stretch ratio, 23 = 1/(211222 --212221 ) Position vector to point on deformed reference surface Meridional angle prior to, after deformation Rotation of meridional shell face, X = ~b -Torsional rotation angle of point on reference surface Rotation angle of circumferential shell face M isc ellaneous symbols (~)
Undeformed quantity of (.) (.)., Differentiation with respect to ~~ (-)'
Differentiation with respect to g (.)* Nondimensional quantity of (.)