Analysis of the bending of a neo-Hookean electro-elastic shell of arbitrary thickness under an externally-applied hydrostatic pressure

The present study analyzes the bending of a simple electro-elastic cylindrical shell by the compound matrix method. The cross-section of the circular cylindrical shell is a non-circular curved shape, with mu(1) a function of A/B W and the mode number, where A and B are the pre-deformation inner and outer radii of the cylindrical shell, and mu(1) is the ratio of the deformed inner radius to A. In the first step, a numerical model of the problem is developed to obtain specific differential equations. The modeling yields a system of two Ordinary Differential Equations with three boundary conditions of the same type. Next, it is shown that the dependence of mu(1) to A/B has a boundary layer structure. Simple numerical observations were made for bifurcation conditions. The analysis is, in fact, based on the variations of the inner and outer radii A and B, assuming a = mu(1) A and b = mu(2) B, and based on the bifurcation of mu(1) and mu(2) ratios with respect to radius. For this purpose, the compound matrix method is used to show the validity of the arguments.

Automated summary

The present study analyzes the bending of a simple electro-elastic cylindrical shell using the compound matrix method. It discusses the boundary layer structure of mu(1) dependence on A/B and carries out numerical observations for bifurcation conditions.