Another approach of WKB method for the stability analysis of the bending of an elastic rubber block

Our concern in this paper is to study the bifurcation of the pure bending of a rubber block made of elastic Varga material which has a ratio of thickness A to length L. The governing equations are reduced to an eigenvalue system.We then apply the WKB method with repeated roots for describing the angle of bending and also the azimuthal shear. In this process, very interesting solvability conditions are derived and solved. We obtained sufficient conditions for different kinds of L/AL/A. Our findings shows that by increasing the value of L/AL/A the bending angle also increases.