FINITE AXISYMMETRIC DEFORMATION OF A THIN SHELL OF REVOLUTION.

Abstract

The finite axisymmetric deformation of a thin shell of revolution is treated in this analysis. The governing differential equations are given for hyperelastic shell materials with Mooney-Rivlin and exponential strain energy density functions. These equations are solved numerically using a 4th order Runge-Kutta integration procedure. A generalized Newton-Raphson iteration process is used to systematically improve trial solutions of the differential equations. The governing differential equations are differentiated with respect to time to derive associated rate equations. The rate equations are solved numerically to generate the tangent stiffness matrix which is used to determine the load deformation history of the shell with incremental loading. Numerical examples are presented to illustrate the major characteristics of the nonlinear shell behavior and recommendations are made for future research.