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 μ1 a function of AB and the mode number, where A and B are the pre-deformation inner and outer radii of the cylindrical shell, and μ1 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 μ1 to AB 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=μ1 A and b=μ2 B, and based on the bifurcation of μ1 and μ2 ratios with respect to radius. For this purpose, the compound matrix method is used to show the validity of the arguments.
Highlights
The study of nonlinear electro-elasticity is a major branch of physics and mathematics in solid mechanics and statics
Dorfmann and Ogden (2005) provided the theoretical grounds for characterizing the nonlinear features of electroelastic materials, applying the theory in some boundary value problems for initial models comprising simple electro-elastic materials, while showing the effects of the impact of the electric field on mechanical reactions of materials, Dorfmann and Ogden (2005). They investigated the effect of a radial electric field on the axial shear of a thick-walled circular cylindrical tube, describing nonlinear electromechanical reactions in shape-shifting materials and summarizing the required relations from nonlinear continuum mechanics, Melnikov (2016)
This section is divided to three parts. part 1 involves briefly compound matrix method, and we use this method for solving governing equations of our problems. part 2 show changes process thickness of cylinder respect to changes of modes
Summary
The study of nonlinear electro-elasticity is a major branch of physics and mathematics in solid mechanics and statics. Dorfmann and Ogden (2005) provided the theoretical grounds for characterizing the nonlinear features of electroelastic materials, applying the theory in some boundary value problems for initial models comprising simple electro-elastic materials, while showing the effects of the impact of the electric field on mechanical reactions of materials, Dorfmann and Ogden (2005). They investigated the effect of a radial electric field on the axial shear of a thick-walled circular cylindrical tube, describing nonlinear electromechanical reactions in shape-shifting materials and summarizing the required relations from nonlinear continuum mechanics, Melnikov (2016). He explained the dependence of pressure and reduced axial load in the deformation, showing the voltage between electrodes or the uniform surface charge distribution, Haughton and Ogden (1978)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
