Numerical Modeling of Initial Stress Stiffening Effect on the Dynamic Behavior of Axisymmetric Shells

Abstract

This paper presents a numerical model to simulate the initial stress stiffening effect, induced by radial pressure and/or axial load on the dynamic behavior of axisymmetric shells. This effect is particularly important for thin shells since their bending stiffness is very small compared to membrane stiffness. The theoretical formulation is based on a combination of the finite element method and classical shell theory. For a perfect geometrical consistency, two semi-analytical finite elements, conical and cylindrical, are used to model axisymmetric shells. The displacement functions are derived from exact solutions of Sanders' shell equilibrium equations. The results obtained using this approach are remarkably accurate. The potential energy is calculated to estimate the initial stiffening effect using direct membrane forces per unit width and rotations about the orthogonal axes. The final stiffness matrix of each finite element is composed of the regular stiffness matrix and the added stiffness matrix generated by membrane loads. The frequencies of vibration are compared with those obtained in other experimental and theoretical research works and very good agreement is observed.