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

Abstract

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 𝜇𝜇 1 a function of 𝐴𝐴 𝐵𝐵� and the mode number, where 𝐴𝐴 and 𝐵𝐵 are the pre-deformation inner and outer radii of the cylindrical shell, and 𝜇𝜇 1 is the ratio of the deformed inner radius to 𝐴𝐴 . 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 𝜇𝜇 1 to 𝐴𝐴 𝐵𝐵� 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 𝐴𝐴 and 𝐵𝐵 , assuming 𝑎𝑎 = 𝜇𝜇 1 𝐴𝐴 and 𝑏𝑏 = 𝜇𝜇 2 𝐵𝐵 , and based on the bifurcation of 𝜇𝜇 1 and 𝜇𝜇 2 ratios with respect to radius. For this purpose, the compound matrix method is used to show the validity of the arguments.