Large Elastic Deformation of Shear Deformable Shells of Revolution: Theory and Analysis

Abstract

Large axisymmetric deformation of pressurized shells of revolution is studied. The governing equations include the effects of transverse normal strain and transverse shear deformation for shells composed of an incompressible, hyperelastic material. Asymptotic solutions to the equations are developed which are valid for moderately large strains. Application to Mooney-Rivlin clamped spherical caps reveals that, for large enough bending and stretching, the consequences of shear deformation include: (1) bending moments can decrease at the edge after the load passes a critical point; (2) even thick shells can behave as membranes; (3) transition points can occur in the shell which divide regions of shell-like behavior from regions of membrane-like behavior.