Theoretical and numerical analysis of shells of revoluation undergoing finite strains and/or finite rotations

ABSTRACT In this study, a theoretical and numerical analysis of rubber-like shells of revolution undergoing axisymmetrical finite strains and finite rotations is rnade. The material is assumed to be rubber-like (isotropic in the unstrained state and hyperelastic). Transverse normal strains (therefore, thickness changes) and tranverse shear strains are taken into consideration. The problem is strongly nonlinear both physically and geometrically. The closed form solution of the corresponding algebraical and differential equations is not possible. Therefore, consulting some numerical approaches has become unavoidable. Corresponding nonlinear differential equations are converted into nonlinear algebraical equations by integrating matrices. The algebraical equations are, then, numerically solved by using Newton-Raphson Method. Two shell theories which have been recommended for the shells undergoing finite strains and finite rotations are compared numerically on some problems related with the subject.