Rotational symmetry vs. axisymmetry in shell theory

• Published in: International journal of engineering science 2010-11, Vol.48 (11), p.991-1005
• Main Authors: Antman, Stuart S., Bourne, David
• Format: Article
• Language: English
• Subjects: Axisymmetric; Differential equations; Effects of shearability; Exact sciences and technology; Flexing; Fundamental areas of phenomenology (including applications); Mathematical analysis; Mathematical models; Nonlinearly elastic shells; Physics; Rotational; Rotationally symmetric motions; Shear; Shearing; Shells; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics
• ISSN: 0020-7225; 1879-2197
• DOI: 10.1016/j.ijengsci.2010.09.009

This paper treats rotationally symmetric motions of nonlinearly axisymmetric shells that can suffer transverse shear as well as the usual flexure and base-surface extension and shear. It derives the governing equations in a convenient form and determines their mathematical structure. The complicated governing equations have the same virtue of the far simpler equations for axisymmetric motions that there is but one independent spatial variable. Consequently the constitutive equations enjoy convenient monotonicity properties. Besides deriving these equations, the main purposes of the paper are (i) to give a numerical illustration of the richness of rotationally symmetric motions caused by the coupling of the additional shearing modes with classical modes of deformation, and (ii) to discuss the subtle question of nonexistence of general axisymmetric motions of axisymmetric shells. The paper briefly treats spatially autonomous motions, which are governed by ordinary differential equations in time.