Qualitative analysis for solutions of a class of nonlinear ordinary differential equations
The boundary value problem (BVP) for a class of nonlinear ordinary differential equations is examined. It can be used to describe the eversion problem for a spherical shell composed of a class of transversely isotropic incompressible Mooney-Rivlin materials. The solutions of the nonlinear equation describing the relation among deformed thickness, initial thickness and material parameters of the spherical shell are obtained. The effects of structure parameter and material parameters on the thickness of the everted spherical shell are discussed by numerical examples.
On the everted state of spherical and cylindrical shells
The existence, uniqueness, and qualitative nature of the everted state of spherical and cylindrical shells is examined for elastic materials with stress functions satisfying relatively simple restrictions. Qualitative analysis of the governing nonlinear ordinary differential equation is facilitated by recasting it in stress-stretch coordinates. One finds a continuum of solutions which meet the boundary conditions. Each corresponds uniquely to a shell of a particular thickness. We present numerical solutions which demonstrate the claims of the analysis.
Stability of thick spherical shells
The pressure-radius relation of spherical rubber balloons has been derived and its stability behavior investigated before. In this work, we show that similar results remain valid for thick spherical shells of Mooney-Rivlin materials. In addition, we show that eversion of a spherical shell is possible for any incompressible isotropic materials if the shell is not too thick.